Alexander Iosevich

Department of Mathematics

University of
Rochester

Last updated: December 2, 2021

__Contents:__

__Personal Information__

__Education__

__External Funding__

__Positions Held__

__Research Interests
Graduate students
Undergraduate students
__

Editorial Board Membership

Selected invited talks

Elementary/High school student mentoring

__Email: __iosevich@math.rochester.edu

__Date of Birth:__ December 14,
1967

__Citizenship:__ United States of America

June 1993, Ph.D. in Pure
Mathematics, University of California at Los Angeles (UCLA)

Thesis: *"Maximal
operators associated to families of flat curves and
hypersurfaces"*

* *Advisor:
Christopher Sogge

June 1989, BS in Pure Mathematics, University of Chicago

**Awards and Honors: **

AMS
Fellow, Class of 2014

Professor
of the Year Award in the Natural Sciences, University of
Rochester, 2015

Analysis, Grant Number DMS97-06825 Amount: $53,000

March 2000, United States National Science Foundation Grant in Classical (PI)

Analysis, Grant Number DMS00-87339 Amount: $77,000

March 2003, United States National Science Foundation Grant in Classical (PI)

Analysis, Grant Number DMS02-45369 Amount: $114,000

June 2005, United States National Science Foundation Collaborative Research Grant (PI)

Analysis, Grant Number DMS04-56306 Amount: $474,245

August 2009, United States National Science Foundation Grant in Number Theory (PI)

and Algebra, Grant Number DMS10-45404 Amount: $303,000

April 2015, United States National Science Foundation Conference Grant (PI)

for the ICHAA conference at the CUNY Graduate Center Amount: $50,000

May 2015 United States National Security Agency Grant H98230-15-1-0319 (PI)

in Combinatorics. Amount: $120,000

November 2019 HDR TRIPODS (NSF): Collaborative Research: Foundations of Greater Data Science (co-I)

Amount: $814,165

July 1, 2010-Present, Professor of
Mathematics, University
of Rochester, Rochester, NY

September 1, 2005-May 31, 2010, Professor of Mathematics, University of
Missouri-Columbia, Columbia, Missouri

January 1, 2008-July 31, 2008, Visiting Faculty and Program
Organizer, Fields Institute of Mathematics, Toronto, Canada

September 1, 2002 to August 31, 2005, Associate Professor in
Department of Mathematics, University of
Missouri-Columbia,

Columbia, Missouri

July 2000 to September 2002,
Assistant Professor in Department of Mathematics, University of
Missouri-Columbia, Columbia, Missouri

May 2000 to April 2001, tenured
Associate Professor in Department of Mathematics,

Georgetown University,
Washington, District of Columbia

July 1998 to May 2000, Assistant
Professor in Department of Mathematics,

Georgetown University,
Washington, District of Columbia

Summer 1999, University of Illinois
at Chicago, j*oint research with N. Katz facilitated by a CRB
Grant.*

September 1995 to December 1998,
Assistant Professor in Department of

Mathematics, Wright State University,
Dayton, Ohio

June/July 1998, Visiting Research
Fellowship, University of New South Wales, Sydney, Australia.

Fall 1997, General Membership at the
Mathematical Sciences Research Institute, Berkeley, California

September 1993 to September 1995,
Postdoctoral Fellow, McMaster
University,

Hamilton, Ontario, Canada

September 1989 to September 1993,
Graduate Student, Teaching Assistant and

Research Fellow, UCLA, Los Angeles,
California

Classical Analysis and Fourier Integral Operators

Discrete Geometry and Geometric
Measure Theory

Additive and Analytic Number Theory

Data Science and Neural Networks

Ryan Mullen (Masters 2002) Prognos
Inc.

Daniel Weidinger (Masters 2003) SETA Test Scientist at Shafer
Corporation

George Arutunyants (Ph.D. 2006) The head of analytics at Prognos
Inc.

Derrick Hart (Ph.D. 2008) Assistant Professor of Mathematics

Doowon Koh (Ph.D. 2008) Associate Professor of Mathematics at
Chungbuk University, Korea

Janet Sipes (M.S. 2009) Arizona State University (graduate
student)

Hannah Morgan (M.S. 2009) University of Chicago (graduate
student)

Jeremy Chapman (Ph.D. 2010) Associate Professor of Mathematics
at Lyons College, Arkansas

Steven Senger (Ph.D. 2010) Assistant Professor of Mathematics at
the Missouri State University

Le Anh Vinh (Ph.D. 2011) Professor at the University of Hanoi

David Covert (Ph.D. 2011) Assistant Professor of Mathematics at
the University of Missouri-St. Louis

Krystal Taylor (Ph.D. 2012) Assistant Professor of Mathematics
at the Ohio State University

Esen Aksoy (Ph.D. 2014) Texas A&M University in Qatar

Mike Bennett (Ph.D. 2015) Visiting Assistant Professor at
the Rochester Institute of Technology

Dillon Ethier (Ph.D. 2016) Seeking employment in statistical
consulting industry

Brendan Murphy (Ph.D. 2016) Heilbron Postodoctoral Researcher at
the University of Bristol

Bochen Liu (Ph.D. 2017) Postdoctoral Resercher at Bar-Ilan
University, Israel

Philipp Birklbauer (Ph.D. 2019) Computer programmer in Chicago,
Illinois

Dionel Jamie (Masters 2019) Ph.D. student at the University of
Wisconsin-Madison

Nik Chatzikonstanti (Ph.D. 2020) Posdoctoral Researcher at the
Okinawa Institute of Technology

Jonathan Passant (Ph.D. 2021) Heilbron Postdoctoral Researcher
at the University of Bristol

Alex
McDonald (Ph.D. 2021) Postdoctoral researcher at Ohio State
University

Belmiro Galo (Ph.D. 2021) Visiting Assistant Professor of
Mathematics at Colgate

Brianna Vick (Ph.D. 2021) Assistant
Professor of Mathematics at Clayton University

Gail Jardine (Ph.D. 2022-expected)

Tingsong Jiang (Ph.D. 2022-expected)

Tritium Shen (Ph.D. 2022-expected)

Anirudh Gurjale (Ph.D. 2022-expected)

Firdavs Rakhmonov (Ph.D. 2023-expected)

Brian McDonald (Ph.D. 2023-expected)

Donggeun Ryou (Ph.D. 2023-expected)

The following is the list of
students who completed an undergraduate honors thesis under my
direction.

Xiaoqing Tang (2012) Microsoft

Emmett Wyman (2014) Johns Hopkins University (graduate
student) and now a postdoc
at Northwestern

Yujia Zhai (2014) Cornell
University (graduate student) and now a postdoc at Bordeaux

Luke Vaicunas (2015) Parker Avery

Brian McDonald (2016) University of Chicago (graduate student)
and now a graduate student at Rochester

Lisa Rosenfeld (2016) FDIC Pittsburgh

Adam Scrivener (2016) Epic Systems, Madison, WI

Ben Dees (2017) Johns Hopkins University, Baltimore, MD
(graduate students)

Daniel Rubery (2017) Google

Adam Lott (2017) University of California Los Angeles (graduate
student)

David Soukup (2018) University of California Los Angeles
(graduate student)

Dionel Jaime (2018) University of Rochester (graduate student)

Zhonghui Sun (2018) Michigan State University (graduate student)

Manuel Stoeckl (2019) Dartmouth University (graduate student)

Zachary Polansky (2019) Google

Byron Osterweil (2020) University of California-Irvine (graduate
student)

Dustin Kasser (2020) University of Georgia (graduate student)

Linus Ge (2021) Ohio State University (graduate student)

Xiaobo Luo (2021) Harvard University (graduate student)

Yiyang Su (2021) Michigan State University (graduate student)

Cole Miller (2021-Expected)

Mandar Juvekar (2022-Expected)

Arian
Nadjimzadah (2022-Expected)

Conor Taliancic (2022-Expected)

CIMPA workshop on analysis
and probability in Armenia, July 2021

CIRM
(Luminy) workshop on geometric measure theory, ergodic
theory and combinatorics, January 2021

ICERM
workshop on Frame Theory and Exponential Bases, June
4-8, 2018

Excelsior Lectures in Analysis, with L. Lanzani, September
2017 at Syracuse University.

Excelsior Lectures in Analysis, with L. Lanzani,
September 2016 at the University of Rochester.

International Conference
on Harmonic analysis and Applications, with A. Mayeli and
G. Olafsson, June 2015.

AMS Special Session, Rochester, NY, special session in memory of
Daryl Geller, with A. Mayeli.

Fields Institute Program, entitled "Trends in Harmonic
Analysis", January 1- June 30, 2008, (with I. Laba, M. Lacey,
and E. Sawyer).

AMS Special Session, Davidson, North Carolina, March 2007 (with
M. Lacey and K. Oskolkov).

AMS Special Session, Salt Lake City, Utah, October 3-5, 2006
(with M. Lacey).

Combinatorial and
additive number theory (CANT 2005). A conference in
celebration of Mel Nathanson�s 60^{th} birthday. (Member
of the organizing committee).

CMS conference at
Simon Fraser University in Vancouver (with I. Laba), December
6-8, 2003.

ESI
(Schrodinger Insitute in Vienna) Workshop on mathematics
related to the Kakeya Needle Problem, (with I. Laba and D.
Muller), Vienna, Austria, Fall 2003.

A conference
on Harmonic Analysis and Partial Differential Equations at
the University of Missouri, May 8-11, 2002, (with L. Grafakos,
S. Hofmann, and I. Verbitsky).

Workshop on convexity and
Fourier analysis, (with L. Brandolini, L. Colzani, and G.
Travaglini), Milan, Italy, June 2001.

In 2008, Izabella
Laba, Sinai Robins and I launched a new journal- Online Journal
of Analytic Combinatorics, or OJAC for short. The current
managing editors of the journal are Alex Iosevich, Sinai Robins
and Steven Senger. Please check out the OJAC web page at http://www.analytic-combinatorics.org/index.php/ojac

Journal
of Pseudo-Differential Operators and Applications 2008-Present

Harmonic
analysis editor of the Proceedings of the American
Mathematical Society 2011-January 2020

Member
of the editorial board of the Journal of Fourier Analysis and
Applications 2016-Present

Carus Manuscripts (MAA) Editorial Board January 2017-Present

Integers Journal Editorial Board October 2016-Present

__Selected educational and
administrative activities:__

Member
of the University of Rochester AAUP Chapter, July
2020-Present.

Meliora Committee (advisory committee to the Chair of the
Department of Mathematics) August 2019-April 2020.

Committee on salary gender equity, University of Rochester,
member, September 2018-May 2019.

GradStemForAll summer program with emphasis on women and
underrepresented groups, 2018-Present.

American Engagement Network, member, April 2018-Present.

AQUAD Review University of Massachusetts-Boston, March 2018.

Mentored Allen Liu, an Intel High School Science Competition
Finalist, 2016.

The Classical Analysis moderator for arxiv.org, September
2014-Present.

Member of the Math Arxiv advisory committee, April
2014-Present.

Summer research program for
undergraduate students at the University of Rochester,
June-August 2011-Present.

Director of Graduate Studies at the University of Rochester
Department of Mathematics, January 2010-August 2014.

Member of the AMS Committee on Meetings and Conferences, January
2009-April 2012.

Summer program for high school students on Fourier analysis in
finite fields at the University of Missouri, July 24-28, 2006.

Campus Writing Program's Fall 2005 Faculty Workshop.

Summer
program
for high school students on the Erdos distance problem at the
University of Missouri, August 1-5, 2005.

Putnam coach, University of Missouri-Columbia, 2000-2009.

MU McNair scholars program- departmental liason, 2004-2010.

Summer
program for high school students on geometric combinatorics at
the University of Missouri, August 9-13 2004.

Volunteer for the 2004 MAA High School Lectureship Program.

Faculty mentor for the University of
Missouri summer minority outreach program, Summer 2003, mentor
for Ivy Hunter.

Participant
in the Teaching Renewal Conference at the University of
Missouri 2002.

Member of the Judge Panel of the 2000
USA College Academic Team. Sponsored by USA TODAY, 2000.

High School Outreach Program,
sponsored by Wright State University, 1996.

Volunteer tutor, Bret Harte
Elementary School, Chicago, Illinois, 1986.

**Elementary/High
****s****chool student mentoring:**

Tyler Jones-Salisbury (2005-2009)

Allen Liu (2014-2017)

Davey Fitzpatrick (2015-2018)

Ty Lewis (2020-2021)

Noah Lee (2019-2020)

Maxwell Sun (2019-Present)

Kevin Xue (2021-Present)

Professor
of the Year Award in the Natural Sciences, University of
Rochester, 2015

Nominated for the University of Missouri Kemper Award for
Excellence in Teaching, 2008 and 2009.

Nominated for Provost's Outstanding Junior Faculty Teaching
Award, University of Missouri, 2003

Wolper's house teaching award,
University of Missouri, 2001.

Wright State University Athletics
Department Award, 1997.

Wright State University Athletics
Department Award, 1995.

Nominated for Undergraduate Student
Government Teaching Award at McMaster University, 1994.

**Selected
Invited Talks**

February 2019 A
plenary lecture at the Weitzmann Institute
Conference in honor of Alexander Olevskii

Title: Geometric measure theory and
applications to frame theory

September 2018 A plenary lecture at the 7th
International Conference "Harmonic Analysis and
Approximation", Armenia

Title: Finite point configurations and frame
theory

February 2018 A lecture series on the Falconer Conjecture at
the Louisiana State University

Title: Falconer distance conjecture and applications to
functional analysis

September 2017 A plenary lecture at the conference at the
University of Wroclaw in honor of Eli Stein

Title: Finite point configurations, Hausdorff dimension
and rigidity

October 2016 A plenary lecture at the Integers Conference in
Georgia

Title: Geometric configurations in vector spaces over
finite fields

September 2016 A keynote address at the combinatorial
geometry conference in Hanoi, Vietnam

Title: Analytic, combinatorial and number theoretic
methods in the study of finite point configurations

May 2015 A plenary lecture at the Complex Analysis and
Dynamical Systems VII conference in Nehariya, Israel

Title: The Fuglede
Conjecture holds in two dimensional vector spaces over prime
fields.

August 2012 A lecture series at Chungbuk University, South Korea

Title: Multi-linear bounds and applications to geometric
measure theory and combinatorics

March 2012 An invited lecture
at the analysis seminar at Princeton University

Title: Distribution of simplexes in discrete and
continuous settings and multi-linear operators

June 2011 An invited lecture at the Edinburgh Workshop on
Harmonic Analysis

Title: Geometric consequences of analytic inequalities

September 2008, An invited lecture at the Oberwolfach (Germany)
meeting on Discrete Geometry

Title: Geometric
configurations in Euclidean, integer and finite field
geometries: combinatorial and algebraic aspects

July 2008, An invited lecture
at the Oberwolfach (Germany) meeting on Harmonic Analysis

Title: Geometric configurations in Euclidean, integer and
finite field geometries

April 2008, An invited lecture
at the Fields Institute (Toronto, Canada) Conference on Additive
Number Theory

Title: Distribution of dot products in vector spaces in
finite fields and applications to problems in additive number
theory and geometric combinatorics

October 2007, A plenary
address to the American Mathematical Society at DePaul
University, Chicago

Title: Incidence
theory: discrete, continous and arithmetic aspects

March 2007, A plenary address
to the American Mathematical Society at Davidson College, North
Carolina

Title: Incidence theory: discrete, continous and
arithmetic aspects

November 2006, A lecture
series on harmonic analysis at the University of Bristol (four
lectures)

Title: Harmonic analysis in vector spaces over finite
fields

May 2006, CUNY, New York, CANT 2006 (three lectures)

Title: "Three lectures on analytic, combinatorial and
number theoretic aspects of incidence theory"

May 2003, Princeton University
Analysis Seminar

Title: Combinatorics of
distance sets and applications

April 2003, Riviere-Fabes Symposium
in Analysis

Title: Analysis and
combinatorics of distance set

March 2003, The Erwin Schrodinger
International Institute (Vienna, Austria) for Mathematical
Physics

Title: Analysis and
combinatorics of distances sets

June 2002, University of Padova
(Padova, Italy), Minicorsi di Analisi Matematica (three lectures)

Title: "Geometric
combinatorics and applications to analysis"

**I nvited
Talks and Research Stays:** (318 lectures and 29 lectures from 10
lecture series)

__C____ount____ries:__
Argentina, Armenia, Australia, Austria, Canada, Catalonia, Czech
Republic, China, England, Finland, France, Germany, Greece,
Israel, Italy, Poland, Russia, Scotland, Spain, Ukraine,
Vietnam, Wales.

**2021 **(318)

October
2021 A presentation to the Ohio State
mathematics undergraduates about how
to apply and prepare for graduate
programs in mathematics

Title: Graduate school and
beyond

October 2021 An invited lecture at
Seminari a Distanze di Analisis
Armonica

Title: The
Vapnik-Chervonenkis
dimension and
point
configurations

September 2021 An invited number
theory seminar lecture at Williams
College

Title: The Vapnik-Chervonenkis
dimension and point configurations

August 2021 An
invited lecture at the International
Seminar Series on Harmonic Analysis
and Applications

Title: Point configurations,
operator bounds and complexity

June
2021 An invited Lecture at the Harmonic and Spectral
Analysis Conference

Title: On graphs,
group actions and point sets

May 2021 An invited lecture at the Combinatorics and
Number Theory Confierence

Title: On graphs, group actions and point sets

May 2021 An invited lecture at the online AMS
conference

Title: On point
configurations and frame theory

February 2021 An invited lecture at the Point
Distributions Webinar

Title: On point configurations and frame theory

2020

November 2020 An invited lecture at CUNY Number Theory seminar

Title: Discrete energy and applications to combinatorial geometry

October 2020 An invited lecture at the FFT seminar (Norbert Wiener Center)

Title: Exponential frames and curvature

June 2020 An invited lecture at the CodEx2020 seminar

Title: Finite point configurations and frame theory

June 2020 An invited lecture at Mel Nathanson 75th birthday conference at CUNY (zoom)

Title: An approximate version of Erdos' single distance conjecture

June 2020 An invited lecture at the annual meeting of Italian harmonic analysts (zoom)

Title: A survey of recent results on distance sets and point configurations

February 2020 An invited colloquium lecture at the Florida International University

Title: Configuration problems and frame theory

February 2020 An invited seminar talk at the Florida International University

Title: Sums and products in integers modulo a prime

January 2020 JMM Special Session on Geometric Combinatorics

Title: Triangles, quadrilaterals and group actions

**2019 **(302)

December 2019 An invited lecture in
Hanoi, Vietnam

Title: Discrete and analytic aspects of incidence
theory

September 2019 An invited lecture at the University of
Missouri analysis conference

Title: Curvature and frame theory

June 2019 An invited lecture at the Harmonic Analysis and
PDE conference in Helsinki, Finland

Title: On configuration problems and applications in
classical analysis and beyond

June 2019 An invited lecture at the harmonic analysis in
Tianjin, China

Title:
On configuration problems and applications in classical
analysis and beyond

May 2019 A keynote lecture at the conference in Holon,
Israel in honor of Vladimir Mazya's 80th birthday

Title: On orthogonal Gabor bases in the presence of
curvature

May 2019 A special analysis seminar at Cornell

Title: Analytic and combinatorial methods in frame
theory

April 2019 Colloquium at the University of Miami

Title: Analytic, geometric and combinatorial aspects
of finite point configurations

March 2019 A lecture at the LeMoyne University Math Club

Title: The Erdos distance problem

March 2019 An analysis seminar lecture at the University of
Pennsylvania

Title: On the continual symbiosis between frame theory
and geometric combinatorics

March 2019 An analysis seminar lecture at the University of
Illinois

Title: Some recent developments on the Erdos and
Falconer distance problems and applicationsiet

February 2019 A plenary lecture at the Weitzmann Institute
Conference in honor of Alexander Olevskii

Title: Geometric measure theory and applications to
frame theory

January 2019 A plenary lecture at the Second Vietnam
Workshop on Graph Theory and Discrete Geometry, Hanoi,
Vietnam

Title: Erdos distance problem for smooth metrics

**2018 **(290)

November 2018 A plenary
lecture at the Mid Atlantic Analysis Meeting, Virgina Tech
University

Title: Finite point configurations: from Furstenberg
to Falconer

October 2018 A plenary lecture at the NEAM2018 analysis
conference

Title: Gabor bases and geometric measure theory

September 2018 An invited lecture at the Fourier Bases
conference in Iraklion, Greece

Title: Gabor bases and the Erdos distance problem

September 2018 A plenary lecture at the 7th International
Conference "Harmonic Analysis and Approximation", Armenia

Title: Finite point configurations and frame theory

August 2018 Faculty colloquium at Penn State University

Title: Finite point configurations

August 2018 MASS colloquium at Penn State University

Title: Tiling and exponential bases: analytic,
combinatorial and number theoretic ideas

August 2018 Number theory seminar at Penn State University

Title: Some number theoretic aspects of the theory of
exponential bases

June 2018 An invited lecture at the ICERM workhop Frame
Theory and Exponential Bases

Title: On interaction between geometric measure theory
and the existence problems for exponential bases

May 2018 An invited lecture at the Workshop on Real Analysis
and its applications to partial differential equations and
geometric measure theory, in honor of Steve Hofmann's 60th
birthday, ICMAT, Madrid

Title: Analytic and combinatorial aspects of frame
theory

May 2018 American Engagement Network conference in
Washington D.C.

May 2018 An invited lecture at the CalTech Analysis Seminar

Title: Gabor bases and geometric combinatorics

March 2018 An invited lecture at the University of
Massachusetts-Lowell

Title: Finite point configurations: congruence and
rigidity

March 2018 An invited lecture at the University of Tel-Aviv
analysis seminar

Title: Exponential bases and Gabor bases: discrete and
continuous aspects

February 2018 A research visit to ICERM

February 2018 An invited lecture series at the Louisiana
State University

Title: The Falconer conjecture and connections with
frame theory

February 2018 An invited colloquium talk at the Arizona
State University

Title: Combinatorial, number theoretic and analytic
aspects of frame theory

February 2018 An invited number theory seminar lecture at
the Arizona State University

Title: The Fuglede Conjecture in vector spaces over
prime fileds

January 2018 An invited lecture series (two lectures) at the
Vietnam University of Science

Title: Geometric combinatorics in vector spaces over
finite fields

January 2018 An invited lecture at the Vietnam Institute of
Mathematics

Title: The Fuglede conjecture in vector spaces over
finite fields

**2017 **(272)

December
2017 A colloquium lecture at the University of
Massachusetts-Lowell

Title: On discrete and continuous aspects of frame
theory

October 2017 An invited seminar lecture at the Georgia
Institute of Technology analysis seminar

Title: Indicator functions of smooth convex sets cannot
serve as window functions for orthogonal Gabor bases

October 2017 An invited lecture at the Oberwolfach meeting on
Geometric Measure Theory

Title: Lp-dimension and application to the Furstenberg
intersection conjecture

September 2017 An invited 40 minute lecture at the AMS Session
on Global Analysis at the University of Central Florida

Title: Finite point configurations

September 2017 An invited lecture at the conference in honor
of Eli Stein in Wroclaw, Poland

Title: Finite point configurations:
analysis, combinatorics and number theory

August 2017 A plenary lecture at the CIMPA 2017 Buenos Aires,
Argentina

Title: Finite point configurations: analysis,
combinatorics and number theory

May 2017 An invited lecture at the conference in honor of
Peter Jones in Seoul, Korea

Title: Rigidity, simplexes and multi-linear operators

May 2017 An invited lecture at the MSRI workshop on harmonic
analysis

Title: Rigidity, simplexes and multi-linear
operators

April 2017 An AMS Special Session on Frame Theory at Hunter
College, NYC

Title: Finite point configuration and the underlying
operators

March 2017 A colloquium talk at Virginia Tech University

Title: Analytic, number theoretic and combinatorial
perspectives on orthogonal bases and tiling

March 2017 A plenary lecture at the Ohio River Analysis
Meeting

Title: On bi-linear analogs of generalized Radon
transform

January 2017 An invited lecture at the JMM2017 Special Session
for women in mathematics dedicated to Cora Sadosky

Title: A group action approach to the non-trivial
exponent for every point configuration in vector spaces over
finite fields

** 2016 **(260)

Title: Fourier bases and tiling

November 2016 An invited lecture at the University of Delaware Analysis Seminar

Title: The Fuglede conjecture in vector spaces over finite fields

October 2016 A colloquium talk at SUNY Albany

Title: Finite point configurations in discrete, continuous and arithmetic settings

October 2016 A plenary lecture at the Northeast Analysis Meeting

Title: The Fuglede conjecture holds in vector spaces over finite fields

October 2016 A plenary lecture at the Integers conference in Georgia.

Title: The analysis, combinatorics and number theory of the distance graph

September 2016 An invited lecture at the Prairie Analysis Seminar 2016

Title: Distribution of simplexes in fractal subsets of Euclidean space

September 2016 A keynote address at the combinatorial geometry conference in Hanoi, Vietnam

Title: The analysis, combinatorics and number theory of the distance graph

September 2016 A colloquium talk at Ohio State University

Title: The analysis, combinatorics and number theory of finite point configurations

June 2016 An invited lecture at the CRM analysis conference, Barcelona, Catalonia.

Title: The analysis, combinatorics and number theory of the distance graph

June 2016 An invited lecture at the conference on discrepancy theory in Varenna, Italy.

Title: The analysis, combinatorics and number theory of the distance graph

May 2016 An invited lecture at the CANT 2016 conference at CUNY

Title: The analysis, combinatorics and number theory of the distance graph

April 2016 An invited lecture at the Syracuse analysis seminar

Title: Fuglede conjecture holds in two dimensional vector spaces over finite fields

February 2016 An invited lecture at ICERM workshop on Geometric Measure Theory

Title: Finite point configurations in Euclidean space

Feburary 2016 A colloquium lecture at George Washington University

Title: The Fuglede Conjecture: analysis, combinatorics and number theory

February 2016 An invited lecture at FFT 2016, University of Maryland

Title: Geometric configurations and Fourier analysis

**2015 **(245)

December 2015 An invited lecture at
the joint CUNY/NYU Analysis seminar

Title: The Fuglede
conjecture in vector spaces over finite fields

December 2015 An invited lecture at the Ohio State Analysis/PDE
seminar

Title: The Fuglede conjecture in vector spaces over finite
fields

Setember 2015 An invited lecture at the CIRM Number Theory
conference in Marseilles, France

Title: The Fuglede conjectre holds in two-dimensional
vector spaces over finite fields

May 2015 An invited lecture at CANT 2015 conference at the CUNY
Graduate Center

Title: The Fuglede Conjecture holds in two dimensional
vector spaces over prime fields.

May 2015 A plenary lecture at the Complex Analysis and Dynamical
Systems VII conference in Nehariya, Israel

Title: The Fuglede
Conjecture holds in two dimensional vector spaces over prime
fields.

April 2015 An invited colloquium lecture at Worcester
Polytechnic Institute

Title: Some simple ideas in the study of simplexes in
Euclidean space

March 2015 An invited at the sectional AMS meeting in Washington
D.C.

Title: Density of exponential frames and spectra in
fractal domains

February 2015 An invited colloquium lecture at the University of
Massachusetts-Lowell

Title: Distribution of simplexes, geometric combinatorics
and fractals

**2014 **(237)

Title: Distribution of simplexes in fractal subsets of the Euclidean space and Riemannian manifolds

December 2014 An invited lecture at the CMMSC One Day Workshop at NCTU, Taiwan

Title: Convolution operators on fractal domains and applications to geometric measure theory

July 2014 An invited lecture at the Oberwalfach Harmonic Analysis meeting

Title: Fractal analogs of classical Fourier inequalities

April 2014 An invted lecture at the IPAM workshop II

Title: Geometric configurations in vector spaces over finite fields

April 2014 An invited lecture at sectional meeting of the AMS in Baltimore

Title: Trace inequalities and application to multi-linear bounds

March 2014 An invited lecture at the IPAM workshop I

Title: The square root law and the structure of rings

March 2014 An invited lecture at IPAM graduate student tutorials

Title: Erdos type problems in discrete, continuous and arithmetic settings

January 2014 An invited lecture at joint meetings of the AMS

Title: Distribution of simplexes in arithmetic settings

January 2014 An invited lecture at the geometry seminar at Tel-Aviv University

Title: Distribution of simplexes in arithmetic settings

January 2014 An invited lecture at the analysis seminar at Bar-Ilan University

Title: An elementary viewpoint on multi-linear operators

**2013** (227)

December 2013 An invited
seminar lecture at the University College London

Title: An
elementary viewpoint on multi-linear operators

December 2013 An invited seminar lecture at the Reading
University

Title: Distribution
of simplexes in arithmetic settings

December 2013 An invited lecture at the Heilbron Seminar,
University of Bristol

TItle: Distribution
of simplexes in arithmetic settings

September 2013 A colloquium lecture at Kent State
University

Title: Restricted convolution inequalities,
multilinear operators and applications

September 2013 An invited lecture at the Kent State
Analysis Seminar

Title: Some elementary observations about
multi-linear operators

August 2013 An invited lecture at the Kent State Analysis
Seminar

Title: Group actions and distribution of simplexes
in the Euclidean space

May 2013 An invited lecture at the Integral Transforms and
Spectral Theory in Analysis and Geometry workshop in
Nahariya, Israel

Title: Intersections of sets, group actions and
Erdos-Falconer problems

April 2013 An
invited lecture at the University of Minnesota
PDE-Analysis seminar

Title: Trace inequalities, multi-linear
operators and geometric applications

March 2013 University of Rochester Number Theory
Seminar

Title: From fractals to diophantine equations

March 2013 An invited lecture at the Analysis Symposium at
the University of Georgia

Title: Intersections of sets and Fourier Analysis

February 2013 A colloquium lecture at the University of
Georgia

Title: Simplexes and Fourier Analsysis

**2012**
(216)

Title: Multi-linear operators, geometric measure theory and combinatorics

October 2012, University of Rochester Number Theory Seminar

Title: Beck's theorem and areas of triangles in planes over finite fields

October 2012 AMS Sectional Meeting in Akron, OH, special session on harmonic analysis and convex geometry

Title: Trace inequalities, multi-linear operators and applications

October 2012 An invited colloquium lecture at the University of Southern Georgia

Title: Analytic methods in geometric combinatorics

September 2012 AMS Sectional Meeting in Rochester, NY, Special Session on Number Theory

Title: Distribution of lattice points in annuli and geometric measure theory

September 2012 AMS Sectional Meeting in Rochester, NY, Special Session on Partial Differential Equations

Title: Bilinear estimates and applications

August 2012 Lecture series at Chungbuk University, South Korea

Title: Convolution inequalities, multi-linear operators and geometric measure theory

May 2012 A series of lectures at the CANT2012 conference in CUNY, New York City

Title: Harmonic analysis in geometric combinatorics

April 2012 An invited expository lecture for graduate students at the Probabilistic Methods in Harmonic Analysis conference in Bedlewo, Poland

Title: From analysis to combinatorics

April 2012 An invited lectre at the Probabilistic Methods in Harmonic Analysis conference in Bedlewo, Poland

Title: Multi-linear generalized Radon transforms and applications to geometry and combinatorics

April 2012 A colloquium talk at SUNY-Albany

Title: Bilinear operators and geometric combinatorics

April 2012 An invited lecture at the special session on harmonic analysis at the AMS sectional meeting in Lawrence, KS

Title: Lattice points, multi-linear operators and distribution of simplexes

March 2012 An invited lecture at the analysis seminar at the Univeristy of Pennsylvania

Title: Multi-linear operators, geometric measure theory and discrete geometry

March 2012 An invited lecture at the applied mathematics seminar at the University of Delaware

Title: Applications of multi-linear operator bounds to problems in geometry

March 2012 An invited lecture at the discrete mathematics seminar at the University of Delaware

Title: Distribution of simplexes in vector spaces over finite fields

March 2012 An invited lecture at the analysis seminar at Princeton University

Title: Distribution of simplexes in discrete and continuous settings and multi-linear operators

March 2012 A presentation to the graduate students at Paris-Orsay

Title: The method of stationary phase, elementary incidence theory and connections beween the two

March 2012 An invited lecture at the analysis seminar at the University of Paris-Orsay

Title: Multi-linear operators and geometric measure theory

January 2012 An invited lecture at AMS special session in Boston

Title: Finite point configurations in Euclidean space

January 2012 An invited lecture at the Tufts workshop on Geometric and Fourier analysis

Title: Multi-linear generalized Radon transforms and applications to geometric measure theory

**2011**
(196)

October 2011 An invited
lecture at the MIT analysis seminar

Title: Generalized Radon transforms, lattice points
near families of surfaces and non-isotropic dilations

September
2011 AMS conference at Ithaca, NY

Title: Regular value theorem in a fractal setting

July 2011 An invited lecture at the Fields Institute
conference in honor of Eric Sawyer (was unable to cross
the border due to a paperwork mixup)

Title: Lattice points, fractal sets and generalized
Radon transforms

June 2011 An invited lecture at the Edinburgh Workshop on
Harmonic Analysis

Title: Geometric consequences of analytic
inequalities

June 2011 An invited lecture at the analysis/combinatorics
seminar at the University of Bristol

Title: The paraboloid: a ubiquitous counter-example

June 2011 An invited lecture at the University of Cardiff

Title: Application of generalized Radon transforms
to problems in geometric measure theory

May 2011 An invited lecture at CANT conference at CUNY

Title: On directions determined by subsets of
vector spaces over finite fields

May 2011 An invited lecture at the Banff meeting on convex
geometry

Title: Distribution of lattice points near families
of surfaces

April 2011 An invited lecture at the University of South
Carolina workshop on harmonic analysis

Title: Lattice points, fractal sets and
generalized Radon transforms

April 2011 A faculty colloquium talk at the University of
Rochester

Title: Discrete and continuous aspects of incidence
theory

April 2011 An invited lecture at the Informal Analysis
Seminar at Kent State University

Title: Harmonic analytic estimates in geometric
measure theory

March 2011 Analysis seminar at the Kennesaw State
University

Title: Fourier analytic methods in sum-product
theory

March 2011 Colloquium at the Clayton State University

Title: On sums and products in finite fields

March 2011 AMS conference at Statesboro, GA

Title: Distribution of lattice points near variable
families of surfaces in Euclidean space

March 2011 AMS conference at Statesboro, GA

Title: Regular value theorem in a fractal setting

February 2011 Analysis seminar at the University of Miami

Title: Regular value theorem in a fractal
setting and connections with discrete geometry and number
theory.

February 2011 Anaysis seminar at the Florida International
University

Title: Regular value theorem in a fractal
setting and connections with discrete geometry and number
theory.

January 2011 Joint meeting of the analysis and
combinatorics seminars at the University of Pennsylvania

Title: Regular value theorem in a fractal setting
and connections with discrete geometry and number theory.

January 2011 Colloquium, Pennsylvania State University

Title: Regular value theorem in a fractal setting.

January 2011 AMS Special Session on Integral Geometry at
the Annual Meeting of the AMS in New Orleans

Title: Finite point configurations in the
continuous setting.

January 2011 LSU workshop on geometry and analysis

Title: Regular value theorem in a fractal setting.

**2010**
(175)

December 2010 Special
session on spectral theory at the CBMS conference in
Vancouver, Canada

Title:
On a fractal variant of the regular value theorem

December 2010 Special session on harmonic
analysis and additive number theory at the CBMS conference
in Vancouver, Canada

Title: On simplexes determined by subsets of the
Euclidean space.

November 2010 Graduate student seminar at CUNY

Title: On a fractal variant of the regular value
theorem

October 2010 Number theory seminar at the University of
Rochester

Title: Sums and products in discrete and continuous
settings

October 2010 An analysis seminar at the University of
British Columbia

Title: On sums-product theorem and simplexes in
vector spaces over finite fields

September 2010 An analysis seminar lecture at Cornell
University

Title: On simplexes determined by fractal subsets
of the Euclidean space

March 2010 An invited lecture at Centro di Ricerca
Matematica Enrico di Giorgi, Pisa

Title: Finite point configurations in discrete and
continuous settings

January 2010 An analysis seminar talk at the Michigan
State University

Title: Uniform distribution, finite point
configurations and number theoretic consequences

**
2009** (168)

December 2009 An invited
40 minute lecture at the AMS/Korean Mathematical Society
Special Session on Harmonic Analysis in Seoul, Korea

Title: Finite point configuration in the Euclidean
setting via Fourier analysis and geometric combinatorics

November 2009 An invited lecture at the AMS Special
Session on Addition Number Theorey at the University of
California-Riverside

Title: Uniform distribution, pseudo-random graphs
and finite point configurations in Euclidean space

July 2009 An invited lecture at the University of Crete

Title: Finite point configurations in
discrete and continous settings

June 2009 An invited lecture at the University of Milano

Title: Finite point configurations in
discrete and continous settings

June 2009 An invited lecture at the Conference on Harmonic
Analysis, Geometric Measure Theory and Quasiconformal
Mappings at CRM, Barcelona

Title: Finite point configurations in discrete and
continous settings

May 2009 An analysis seminar lecture at the University of
Arizona

Title: Finite point configurations in discrete and
continous settings

April 2009 An invited lecture at the Spring Lecture Series
2009, University of Arkansas

Title: Geometric configurations in Euclidean space
the associated models in vector spaces over finite fields

February 2009, A colloquium talk at the University of
Illinois-Chicago

Title: Sums and products in discrete, continuous
and arithmetic settings

February 2009, A seminar talk at the University of
Illinois at Urbana-Champaign

Title: Geometric configurations in the discrete and
continuous settings

January 2009, A colloquium talk at Rochester University

Title: Geometric configurations in discrete,
continuous and number theoretic settings

**2008**
(158)

November 2008, An invited
seminar lecture at the University of Wisconsin-Madison

Title: Geometric configurations in fractals

October 2008, An analysis seminar talk at the Arizona
State University

Title: Geometric configurations in fractals

October 2008, A colloquium talk at the Arizona State
University

Title: Geometric configurations in
Euclidean, integer and finite field geometries:
combinatorial and algebraic aspects

October 2008, A series of lectures at Baylor University

Title: Geometric combinatorics, arithmetic and
Fourier analysis

September 2008, An invited lecture at Oberwolfach
(Discrete Geometry)

Title: Geometric configurations in
Euclidean, integer and finite field geometries:
combinatorial and algebraic aspects

July
2008, An invited lecture at the University of Crete

Title: Mixed norm restriction theorems and
connections with fractal geometry

July 2008, An invited lecture at the University of Padova

Title: Geometric configurations in
Euclidean, integer and finite field geometries

July 2008, An invited lecture at the University of Torino

Title: Geometric configurations in
Euclidean, integer and finite field geometries

July 2008, An invited lecture at Oberwolfach (Harmonic
Analysis)

Title: Geometric configurations in Euclidean,
integer and finite field geometries

June 2008, An invited lecture at the Arizona State
University MTBI program

Title: Geometric configurations: an
elementary viewpoint

April 2008, A seminar lecture at Wayne State University

Title: Fourier analysis in vector spaces over
finite fields

April 2008, An invited lecture at the Fields Institute
Conference on Additive Number Theory

Title: Distribution of dot products in vector
spaces in finite fields and applications to problems in
additive number theory and geometric combinatorics

March 2008, A colloquium talk at the McMaster University

Title: Harmonic analysis in vector spaces over
finite fields and applications to additive combinatorics

**2007 **(145)

October
2007, A seminar talk at the Louisiana State University

Title: Radon transforms and applications
to problems in additive number theory

October
2007, A colloquium at the Louisiana State University

Title: Incidence theory: discrete,
continous and arithmetic aspects

October
2007, An invited 50 minute address to the American
Mathematical Society at DePaul University, Chicago

Title: Incidence theory: discrete,
continous and arithmetic aspects

October 2007, A colloquium talk at the University of
Indiana, Bloomington

Title: Sums and products in finite fields- an
analytic perspective

September 2007, An invited lecture at the agebra seminar
at Emory

Title: Sums and products in finite fields

September 2007, An invited lecture at the analysis seminar
at Georgia Tech

Title: Radon transforms and applications to
problems in additive number theory

September 2007, An invited lecture at a mini-conference on
discrepancy theory at the University of South Carolina

Title: Radon transforms and applications to
problems in additive number theory

September 2007, A colloquium lecture at the University of
Cincinnati

Title: Radon transforms and applications
to problems in additive number theory

September 2007, A seminar talk at the Georgia Institute of
Technology

Title: Sums and products in finite fields-
an analytic perspective

August 2007, A seminar talk at UMKC (Kansas City)

Title: Sums and products

June 2007, An invited lecture at the University of Padova

Title: Integral geometric viewpoint on
sums and products in finite fields

June 2007, An invited lecture at the University of Bologna

Title: Incidence theory via Fourier analysis in
vector spaces over finite fields

June 2007, An invited lecture at the University of Milan

Title: Integral geometric viewpoint on
sums and products in finite fields

May 2007, An invited lecture at the annual meeting of
Italian harmonic analysts at Caramanico

Title: Incidence theory via Fourier analysis and
applications to geometry and arithmetic

May 2007, A seminar lecture at the University of Bergamo

Title: Integral geometric viewpoint on sums and
products in finite fields

April 2007, DePaul University analysis seminar

Title: Fourier analysis and incidence theory

March 2007, A colloquium lecture at the Bogazici
University

Title: Analytic, combinatorial and number theoretic
aspects of incidence theory

March 2007, A lecture at the Istanbul Institute of
Mathematics

Title: Sums/Products via Fourier analysis

March 2007, King's College, London, an analysis seminar
lecture

Title: Ramsey Theory and Fourier analysis

March
2007, An invited 50 minute address to the American
Mathematical Society at Davidson College, North Carolina

Title: Incidence theory: discrete, continous and
arithmetic aspects

January 2007, An invited lecture at Bar-Ilan University

Title: Geometric combinatorics via Fourier analysis

**2006 **(124)

November 2006, A seminar
talk at the University of Crete

Title: Sums and products in finite fields
via Kloosterman sum estimates.

October
2006, AMS lecture in Salt Lake City, Utah

Title: Sums and products in finite fields via
Kloosterman sum estimates.

September 2006, A seminar lecture at Michigan State
University

Title: Erdos/Falconer distance problem in
vector spaces over finite fields.

August 2006, An invited lecture at the Rudelson CBMS
lecture series conference at Kent State University

Title: Analysis, combinatorics and number
theory of the Mattila integral.

July 2006, An invited lecture at the Koldobsky CBMS
lecture series conference at the Kansas State University

Title: Analysis, combinatorics and number
theory of the Mattila integral.

July 2006, A lecture at the Universidad Autonoma Barcelona
(CRM)

Title: Analysis, combinatorics and number
theory of the Mattila integral.

July 2006, A lecture at the University of Milano

Title: Analysis, combinatorics and number
theory of the Mattila integral-lattice points on surfaces.

July 2006, A lecture at the University of Bergamo

Title: Analysis, combinatorics and number
theory of the Mattila integral-Fourier analysis in finite
fields.

June 2006, a plenary lecture at Harmonic Analysis
conference in Zharos, Crete

Title: Analysis, combinatorics and
number theory of the Mattila integral.

April 2006, AMS Special Session in Miami

Title: Erdos/Falconer distance problem
in vector spaces over finite fields

March 2006, Combinatoria Number Theory program in Montreal

Title: Fourier analytic approach to
incidence theorems in vector spaces over finite fields

January 2006, Colloquium at Northeastern University

Title: Analytic, combinatorial and
number theoretic aspects of distance set theory

January 2006, Colloquium at the University of Georgia

Title: Analytic, combinatorial and number
theoretic aspects of distance set theory

January 2006, Analysis Seminar, University of Crete

Title: Erdos/Falconer distance problems
in vector spaces over finite fields

January 2006, Pure Mathematics Seminar, University of
Bristol

Title: Erdos/Falconer distance problem
in vector spaces over finite fields

**2005 **(109)

Title: Erdos distance problem in vector spaces over finite fields

November 2005 Colloquium lecture at Kent State University

Title: Analytic, combinatorial and number theoretic aspects of distance set theory

October 2005, lecture at the Integers conference at the University of Western Georgia

Title: Erdos distance problem in vector spaces over finite fields

October 2005, seminar talk at the University of South Carolina

July 2005 University of Crete, Greece

Title: Mean square averages of the Fourier transform and geometric combinatorics

July 2005, Oberwalfach, Germany

Title: Some observations on the interaction of harmonic analysis and geometric combinatorics

June 2005, University of Orleans, France

Title: Mean square averages of the Fourier transform and geometric combinatorics

June 2005, University of Bristol, England

May 2005, CUNY conference in honor of Mel Nathanson's 60th birthday

Title: Analysis and combinatorics of distance sets

January 2005, Texas A&M University

Title: Gaussian curvature, geometric combinatorics, and the Fourier transform

**2004 **(101)

September
2004 AIM workshop on additive number theory/ geometric
combinatorics

July 2004 Trimester in Harmonic Analysis, Pisa,
Italy

Title: Average decay of the Fourier
transform and applications

June 2004 University of Madrid, Spain,
Analysis Seminar

Title: Combinatorial complexity of
convex sequences and related problems in combinatorial
geometry

June 2004 Trimester in Harmonic Analysis, Pisa, Italy

Title: Combinatorial complexity of
convex sequences and connections with Fourier analysis

May
2004 Georgia Institute of Technology; an invited lecture
associated with

a
series of CBMS lectures to be delivered by C. Thiele.

Title: Combinatorial complexity of convex sequences

May
2004 CUNY Conference on Additive and Combinatorial Number
Theory

Title: Combinatorial complexity of convex sequences

May
2004
University of Edinburgh

Title: Some remarks on the Mattila integral
and related problems

May
2004, University of Bristol, England

Title: Mean square discrepancy bounds for the distribution
of lattice points in convex domains

April 2004, University of Athens

Title: Convex sequences and the
Erdos/Falconer distance problems

April
2004, University of Crete

Title: Some remarks on the Mattila integral

March
2004 Annual meeting of the Italian harmonic analysts
(plenary lecture)

Title: Some remarks on the Mattila integral

March
2004 University of Bergamo, Italy, seminar

Title: Average decay of Fourier transforms of measures and
applications

March
2004 University of Milano, Italy, seminar

Title: Combinatorial complexity of convex sequences and
related problems

March
2004 Florida State University, AMS Special Session on
Harmonic Analysis

Title: Combinatorial complexity of convex sequences

February
2004 University of Michigan (differential equations
seminar)

Title: Average decay of the Fourier transform, Salem sets,
and related problems

January
2004, Temple University, Philadelphia (colloquium)

Title: Combinatorial complexity of convex sequences:
combinatorial and analytic methods

**2003
**(86)

December 2003,
University of British Columbia (research collaboration
with I. Laba)

November
2003, University of California-Los Angeles

Title: Distribution of lattice points in convex domains:
mean square estimates

October
2003, Conference on additive number theory, University of
West Georgia

Title: Distribution of lattice points in convex domains:
mean square estimates

October
2003, University of Wisconsin-Madison

Title: A Weyl type formula for exponential spectra and
frames

June
2003, Harmonic Analysis and Partial DIfferential
Equations; Annual Summer Session

Title: Combinatorial approach to orthogonal exponentials

June
2003, Joint meeting of the Real Sociedad Mathematika
Espanola and the AMS in Seville, Spain

Title: Variants of the Falconer and Erdos distance
problems

June
2003, University of Milan

Title: Variants of the Falconer and Erdos distance
problems

May
2003, Conference on additive number theory and
applications to harmonic analysis

Title: Applications of geometric measure and geometric
combinatorics in harmonic analysis

May
2003, Princeton University Analysis Seminar

Title: Combinatorics of distance sets and applications

April
2003, Riviere-Fabes Symposium in Analysis

Title: Analysis and combinatorics of distance set

March
2003, The Erwin Schrodinger International Institute for
Mathematical Physics

Title: Analysis and combinatorics of distances sets

February
2003, Georgia Institute of Techology (research
collaboration)

**2002
**(76)

October 2002, AMS Special
Session in Madison, Wisconsin

Title: "Distribution of lattice points inside random
ellipsoids"

July
2002, Convex geometry workshop in Vancouver, Canada

Title: "Lattice points inside random ellipses"

June 2002, University of Milano, Bicocca

Title: "Distribution of lattice points inside random
ellipses"

June
2002, University of Pisa, AMS Special Session

Title: "Convex bodies, orthogonal exponentials and
geometric combinatorics"

June
2002, Universidad Autonoma de Madrid

Title: "Some elementary combinatorial geometry and
applications to harmonic analysis"

June
2002, University of Iraklion, Crete

Title: "Lattice points inside random ellipses"

March
2002, McGill University, Montreal, Canada

Title: "Average decay of the Fourier transform and
distribution of lattice points in convex domains"

March
2002, AMS Special Session in Harmonic Analysis

Title: "Average decay of the Fourier transform and
applications"

January
2002, Universita di Milano-Bicocca

Title: "Applications of the average decay of the Fourier
transform of measures"

**2001 **(67)

December 2001, Georgia
Institute of Technology

November
2001, Colloquium, Case Western Reserve University

Title: "Combinatorics of convex sets and applications"

November
2001, Seminar, University of Wisconsin, Madison

Title: "Combinatorics of convex sets and applications"

November
2001, Research visit at McMaster University, Hamilton,
Ontario

October
2001, Seminar, University of Bristol, England

Title: "Combinatorial approach to orthogonal exponentials"

September
2001, Colloquium , University of British
Columbia,Vancouver, British Columbia, Canada

Title: "Combinatorial aspects of convexity"

August
2001, Convex geometry conference in Anogia, Crete

Title: "Various notions of dimension of convex sets and
applications"

May
2001, Partial Differential Equations Seminar, University
of Missouri-Columbia

Title: "Regularity of generalized Schrodinger equations"

May
2001, Algebra Seminar, University of Missouri-Columbia

Title: "Quadratic forms and the Steinhaus tiling problem"

March
2001, Oscillatory Integrals and Dispersive Equations, IPAM
conference in Los Angeles, California

July
2001, Mt. Holyoke Harmonic Analysis/ PDE AMS conference

Title: "Distribution of lattice points in convex domains"

April
2001, University of Milan-Bicocca

Title: "Extracting geometric information from square
functions"

March
2001, AMS Special Session in Harmonic Analysis, Lawrence,
Kansas

Title: "Distribution of lattice points inside convex
domains"

**2000 **(57)

December 2000, Meeting of
the Canadian Mathematical Society, Vancouver, British
Columbia, Canada

Title: "Distribution of lattice points in convex domains
and the geometry of the Gauss map"

November
2000, University of Wisconsin-Madison

Title: "Distribution of lattice points in convex domains
and the geometry of the Gauss map"

November
2000, McMaster University, Hamilton, Ontario

Research collaboration with Eric Sawyer

November
2000, Banach space seminar, University of
Missouri-Columbia

Title: "Exponential bases and tiling- combinatorics and
the Fourier transform"

October
2000, Northwestern University, Chicago, Illinois

Title: "Distribution of lattice points in convex domains
and related problems"

October
2000, Special Session in Harmonic Analysis, San Francisco,
California

Title: "Distribution of lattice points in convex domains"

September
2000, Analysis seminar, Washington University in St. Louis

Title: "Distribution of lattice points in convex domains"

September -November 2000, Probability seminiar, University
of Missouri-Columbia

Title: "A brief introduction to the Kakeya problem and
related issues"

July
2000, Meeting of harmonic analysts at El Escorial, Spain.

June
2000, Meeting of the Greek analysts in Iraklion, Crete

Title: "Fourier bases and the associated combinatorics"

June 2000, University of Iraklion, Crete

Title: *"Distribution of lattice points in convex
planar domains"*

June
2000, University of Milan-Bicocca

Title: *"Elementary applications of the pigeon-hole
principle in analysis"*

June
2000, Annual meeting of the Italian harmonic analysts

Title: *"Distribution of lattice points in convex
domains"*

February
2000, University of Missouri-Columbia

Title: *"The role of Gaussian curvature in harmonic
analysis"*

February
2000, Syracuse University

Title:* "Fourier bases, tiling, and the Erdos Distance
Problem"*

February
2000, McMaster University

*Joint research with E. Sawyer
*

**1999 **(44)

December 1999, University
of Wisconsin- Madison.

Title: *"Fourier bases, tiling, and the Erdos Distance
Problem"*

August
1999, University of Illinois at Chicago

*Joint research with N. Katz facilitated by a CRB Grant.*

August
1999, University of Illinois at Chicago

Title: *"Fourier basis, orthogonality, and a variant of
Erd�s distance problem"*

July
1999, Joint meeting of the American and Australian
Mathematical Societies.

Title: *"Fourier basis, fractals, and the Erd�s
distance problem"*

June
1999, University of Milan

Title: "*Maximal averages over
fractals"*

June
1999, Meeting of the Italian Mathematical Society, Aosta,
Italy

Title: *"Fourier basis and the Erd�s distance problem"*

May
1999, Wright State University

Title: *"The role of curvature in harmonic analysis"*

March
1999, McMaster University

Title: *"Averages over surfaces and related problems"*

March
1999, Wright State University

*
Joint research with S. Pedersen*.

March
1999, Indiana University Purdue University Indianapolis

*Joint research with E. Sawyer.*

February
1999, University of Maryland-College Park

Title: "*Lattice points, Fourier bases, and related
problems*"

January
1999, Conference on Singular and Oscillatory Integrals in
honor of Steve Wainger,

University
of Wisconsin, Madison, Wisconsin

Title: "*Lattice points, Fourier bases, and related
problems*"

**1998 **(35)

September 1998, AMS
Special Session on orthogonal polynomials and related
problems,

DePaul
University, Chicago, Illinois

Title: "*Smooth hypersurfaces of infinite type*"

August
1998, GAFA Conference, Kiel, Germany

Title:* "L ^{p} improving properties of measures
supported on convex finite type hypersurfaces"*

July 1998, Visiting Research Fellowship, University of Milan, Milan, Italy

July 1998, University of Turin, Turin, Italy

Title:

June/July 1998, Visiting Research Fellowship, University of New South Wales, Sydney, Australia.

July 1998, Department of Mathematics Analysis Seminar, Macquarie University, Sydney, Australia

Title:

June 1998, Department of Mathematics, University of New South Wales, Sydney, Australia

Title:

April 1998, Dixieland Analysis Conference, Emory University, Atlanta, Georgia

Title:

April 1998, Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia

Title:

February 1998, Department of Mathematics, Johns Hopkins University, Baltimore, Maryland

Title:

February 1998, Department of Mathematics, Georgetown University, Washington,

District of Columbia

Title:

**1997 **(26)

Fall 1997, General
Membership at the Mathematical Sciences Research
Institute, Berkeley, California

November
1997, Visiting Research Fellowship, University of Naples,
Naples, Italy

November
1997, Department of Mathematics, University of Naples,
Naples, Italy

Title: *"Scaling properties of infinitely flat curves
and surfaces"*

November
1997, Department of Mathematics, University of Milan,
Milan, Italy

Title: *"Scaling properties of
infinitely flat curves and surfaces"*

October
1997, Department of Mathematics, University of Rochester,
Rochester, New York

Title: *"Scaling properties of convex hypersurfaces"*

September
1997, Mathematical Sciences Research Institute, Berkeley,
California

Title:* "Scaling properties of convex finite type
hypersurfaces"*

September
1997, Department of Mathematics, Florida State University,
Tallahassee, Florida

Title: *"Scaling properties of convex hypersurfaces"*

September
1997, Integrable Systems & Nonlinear PDE Seminar,
Department of Mathematical Sciences,

Indiana
University Purdue University Indianapolis, Indianapolis,
Indiana

Title: *"Scaling properties of infinitely flat curves
and surfaces"*

May 1997, European Union HCM "Fourier Analysis Network"
Harmonic Analysis in Varenna Meeting, Varenna, Italy

Title: *"Averages over convex hypersurfaces"*

March
1997, Wright State University Analysis Seminar, Dayton,
Ohio

Title: *"Fourier transform, restriction theorems, and
scaling"*

March
1997, American Mathematical Society Annual Analysis
Conference in Auburn, Alabama

Title: *"Maximal averages over convex surfaces"*

**1996
**(15)

December 1996, Department
of Mathematics, University of Wisconsin, Madison,
Wisconsin

Title: *"Maximal averages, convex hypersurfaces, and
rotational curvature in time"*

October
1996, Department of Mathematics Colloquium, University of
Cincinnati, Cincinnati, Ohio

Title: *"The Fundamental Theorem of Calculus and
Beyond"*

July
1996, Department of Mathematics, University of Turin,
Turin, Italy

Title: *"Schulz's Theorem, mixed homogeneity, and
maximal operators"*

July
1996, Department of Mathematics, University of Naples,
Naples, Italy

Title: *"Maximal operators in Harmonic Analysis"*

June
1996, Department of Mathematics, McMaster University,
Hamilton, Ontario, Canada

Title: *"Maximal averages over mixed homogeneous
surfaces"*

**1995**
(10)

December 1995, Department
of Mathematics, University of Wisconsin, Madison,
Wisconsin

Title:* "Oscillatory integrals with homogeneous phases
and maximal averages over surfaces"*

November
1995, American Mathematical Society Conference in Kent,
Ohio, Special Session on

Harmonic
Analysis and Applications, Kent State University, Kent,
Ohio

Title: *"Averaging and maximal averaging operators
associated to homogeneous hypersurfaces"*

February 1995, Analysis Seminar, University of Toronto,
Toronto, Ontario, Canada

Title: *"Maximal operators and oscillatory integrals
associated to finite type hypersurfaces"*

**1994**
(7)

September 1994, Harmonic
Analysis Seminar, McMaster University, Hamilton, Ontario,
Canada

Title: *"(L ^{p},L^{q}) mapping
properties of averaging operators associated to
homogeneous hypersurfaces"*

May 1994, Harmonic Analysis Seminar, McMaster University

Title:

June 1994, Functional Analysis Seminar, Technion, Haifa, Israel

Title:

June 1994, Mathematics Colloquium, University of Naples, Naples, Italy

Title:

May 1994, Analysis Seminar, UCLA, Los Angeles, California

Title:

**1993 **(2)

November 1993, Harmonic
Analysis Seminar, McMaster University

Title: *"A restriction theorem for operators associated
to homogeneous manifolds in codimension two"
*

**1991 **(1)

March 1991, Classical
Analysis Seminar, UCLA, Los Angeles, California

Title:* "Maximal operators associated to families of
flat curves in the plane"*

February 2017, A lecture
series on the Falconer conjecture at the Louisiana State
University.

August 2012, A lecture
series on multilinear operators and geometric measure
theory at Chungbuk University, South Korea

May 2012, A lecture
series on application of harmonic analysis to geometric
combinatorics at CANT2012 conference in CUNY, New York

October 2008, A lecture
series on interaction of harmonic analysis, geometric
combinatorics and additive number theory at Baylor
University (three lectures)

November 2006, A lecture
series on harmonic analysis in vector spaces over finite
fields at the University of Bristol (four lectures)

May 2006, CUNY, New York,
CANT 2006 (three lectures)

Title: "Three lectures on analytic,
combinatorial and number theoretic aspects of incidence
theory"

June 2002, University of
Padova, Minicorsi di Analisi Matematica
(three lectures)

Title: "Geometric combinatorics and applications to
analysis"

July 1998, A series of
talks at the University of Milan on avergaing operators
over hypersurfaces (four lectures)

__PUBLICATIONS:__

__Published Papers and Papers
Accepted for Publication:__

**The published papers
are listed first, organized by year of publication.
Accepted papers are listed below, immediately following
the published papers.
**

**2021 **(130)

__Sums of Powers in Large Finite Fields: A Mix
of Methods , (__

__Weyl Law Improvement for Products of Spheres,
(with ____E. Wyman), __*Anal.
Math.* 47 (2021), no.
3, 593–612.

__An improved result for Falconer's distance set
problem in even dimensions , (__

Configuration sets with nonempty interior, (Greenleaf, Allan; Iosevich, Alex; Taylor, Krystal),
*J. Geom. Anal.* 31 (2021), no. 7, 6662–6680.

On restriction estimates for the zero radius sphere over
finite fields, (with Koh,
Doowon; Lee,
Sujin; Pham,
Thang; Shen,
Chun-Yen),
*Canad. J. Math.* 73 (2021), no. 3, 769–786.

Existence of
similar point configurations in thin subsets of Euclidean
space, (with A. Greenleaf and M. Mkrtchyan), *Math.
Z.* 297 (2021), no.
1-2,
855-865.

__
__

**
2020 **(123

__Falconer-type estimates for dot products,
(with S. Senger),
Bull.
Hellenic Math. Soc. 64 (2020), 98–110.__

**A new bound
for the Erdős distinct distances problem in
the plane over prime field***s,
(with D. Koh, T. Pham. C. Shen and L. Vinh). **Acta
Arith.* 193 (2020), no. 2, 165**-**174.

**New
bounds for distance-type problems over prime
fields, **

__ On
Falconer's distance set problem in the plane,
(with L. __Guth,

**2019
**(118)

__Finite
trees inside thin
subsets of Euclidean
space, (with K.
Taylor) accepted for
publication by the
Proceedings of the
Analysis and
Operator Theory
conference in
Rostov, Russia.
__

__Embedding
distance graphs in
finite field vector
spaces, (with H.
Parshall), __
*J.
Korean Math. Soc.* 56 (2019), no.
6, 1515�1528.

Equilateral triangles in subsets of Euclidean space of large Hausdorff dimension, (with B. Liu) Israel Math Journal, May, 2019, Volume 231, issue 1, pages 123-137.

On the quotient set of the distance set, (with D. Koh and H. Parshall), Moscow Journal of Combinatorics and Number Theory 8 (2019), no. 2, 103�115.

What is Falconer's conjecture? Notices of the AMS, March 2019.

Fourier analysis and Hausdorff dimension, by Pertti Mattila, Mathematical Intelligencer, March, 2019, Volume 41, Issue 1, 83-86.

Pinned distance problem, slicing measures and local smoothing estimates, (with B. Liu), Transactions of the AMS, volume 371, no. 6, 4459-4474.

Maximal
operators: scales, curvature and the fractal dimension,
(with B. Krause, E. Sawyer, K. Taylor and I.
Uriarte-Tuero),
*Anal.
Math.* 45 (2019), no.
1, 63�86.

__Tight
wavelet frame sets on
finite vector spaces,
(with C. Lai and A.
Mayeli), The Journal of
Applied and
Computational Harmonic
Analysis, volume 46,
issue 1.
__

2018

Tiling, circle packing and exponential sums over finite fields, (with C. D. Haessig, A. Iosevich, J. Pakianathan, S. Robins and L. Vaicunas), Analysis Mathematica, 44 (2018), no. 4, 433-449.

Distances from points to planes, (with P. Birklbauer and T. Pham), Acta Arithmetica 186 (2018) no. 3 219-224.

On discrete values of bilinear forms, (with O. Roche-Newton and M. Rudnev) Mat. Sb. 209 (2018), no. 10, 71-88.

Direction
sets, Lipschitz graphs and density, (with J.
Pakianathan), Bull. Hellenic Math. Soc. 62 (2018) 61-65.

** 2017 **(104)

Tiling sets
and spectral sets over finite fields, (with Aten, C.; Ayachi, B.; Bau, E.; FitzPatrick, D.; Liu, H.; Lott, A.; MacKinnon, I.; Maimon, S.; Nan, S.; Pakianathan, J.; Petridis, G.; Rojas Mena, C.; Sheikh, A.; Tribone, T.; Weill, J.; Yu, C.) *J. Funct. Anal.* 273 (2017), no. 8, 2547�2577.

On necklaces
inside thin subsets of ${\Bbb R}^d$, (with A.
Greenleaf and M. Pramanik), Math Research Letters, 24
(2017), 347-362.

A
two-parameter finite field Erdős-Falconer distance problem*,
**(with
P. Birklbauer) Bull. Hellenic Math. Soc. *61 (2017),
21-30

Elementary methods for
incidence problems in finite fields,
(with J. Cilleruelo,
B. Lund, Ben, O.
Roche-Newton and
M. Rudnev), Acta
Arith. 177 (2017), no. 2, 133-142.

The Fuglede conjecture
holds in ${\Bbb Z}_p \times {\Bbb
Z}_p$ (with A. Mayeli and J.
Pakianathan), Anal. PDE 10 (2017), no.
4.

The square root law and
structure of finite rings, (with
B. Murphy and J. Pakianathan), Moscow
Journal of Combinatorics and Number
Theory, Volume 7, Issue 1, (2017).

On
angles determined by fractal subsets
of Euclidean space, (with M.
Mourgoglou and E. Palsson), volume 23,
number 6, (2016).

Group actions and geometric combinatorics in 𝔽dq, (with M. Bennett, D. Hart, Derrick, J. Pakianathan and M. Rudnev), Forum Math. 29 (2017), no. 1, 91-1

(96)

2016

Sharpness of Falconer's $\frac{d+1}{2}$ estimate, (with Steven Senger), Annales Academic Scientiarum Fennicae, volume 41, (2016).

Falconer distance problem, additive energy and Cartesian products, (with B. Liu), Annales Academic Scientiarum Fennicae, volume 41, (2016).

Finite chains inside thin subsets of ${\Bbb R}^d$, (with M. Bennett and K. Taylor), Analysis and PDE, volume 9, no. 3, (2016).

Long
paths in the distance graph over large subsets of vector
spaces over finite fields, (with M. Bennett, J.
Chapman, D. Covert, D. Hart and J. Pakianathan), Journal
of Korean Mathematical Society, volume 53, pages 115-126
(2016).

Intersections
of sets, diophantine equations and Fourier analysis,
(with Suresh Eswarathasan, Alex Iosevich, Krystal Taylor),
Journal d'Analyse, volume 128, pages 159-178 (2016).

Sets
of finite perimeter and geometric variational problems.
An introduction to geometric measure theory [book
review of MR2976521]. Bull. Amer. Math. Soc. (N.S.) 53
(2016), no. 1, 167**-**171.

**2015
**(90)

A
group-theoretic viewpoint on Erdős-Falconer problems and
the Mattila integral, (with A. Greenleaf, B. Liu and
E. Palsson), Rev. Mat. Iberoam. 31 (2015), no. 3, 799-810.

Multi-linear
generalized Radon transforms and point configurations,
(with L. Grafakos, A. Greenleaf and E. Palsson), Forum
Math. 27 (2015), no. 4, 2323-2360.

Areas
of triangles and Beck's theorem in planes over finite
fields, (with M. Rudnev and Y. Zhai), Combinatorica
35 (2015), no. 3, 295-308

Decay
of the Fourier transform, (with Elijah Liflyand),
Analytic and geometric aspects. Birkhauser/Springer,
Basel, (2015).

On
volumes determined by subsets of the Euclidean space,
(with A. Greenleaf and M. Mourgoglou), Forum Mathematicum,
volume 27, issue 1, (2015).

Paley-Wiener spaces and applications, (with A. Mayeli) J. Funct. Anal. 268 (2015), no. 2, 363-375.

**2014
**(84)

Three-point
configurations determined by subsets of the
two-dimensional finite plane via the Elekes-Sharir
paradigm, (with
M. Bennett and J. Pakianathan)
Combinatorica 34 (2014), no. 6, 689-706

Theory
of dimension for large discrete sets and applications,
(with M. Rudnev and I. Uriarte-Tuero), Math. Model. Nat.
Phenom. 9 (2014), no. 5, 148-169.

Sharpness
of Falconer's estimate and the single distance problem
in Z_q^d, (with S. Senger), Combinatorial and
additive number theory-CANT 2011 and 2012, 63-77, Springer
Proc. Math. Stat., 101, Springer, New York, (2014).

**2013
**(81)

Restricted convolution inequalities, multi-linear operators and applications, (with D. Geba, A. Greenleaf, E. Sawyer and E. Palsson), Math Research Letters, volume 20, No. 4 (2013).

Geometric
configurations in the ring of integers modulo p^l,
(with D. Covert and J. Pakianathan), volume 61, issue 5,
(2013).

Size of
orthogonal sets of exponentials on the disk,
(with M. Kolountzakis), Revista Iberoamericana, volume 29,
739-747 (2013).

Periodicity
of the spectrum in dimension one,
(with M. Kolountzakis), Analysis and PDE, volume 6, no. 4
(2013).

**
2012 **(78)

Multi-parameter
projection theorems with applications to sums-products and
finite point configurations in the Euclidean setting, (with B. Erdogan and D. Hart),
(Springer volume in honor of Kostya Oskolkov's 65th
birthday).

Distance graphs
in vector spaces over finite fields, (with D. Hart, D.
Koh, S. Senger, and Ignacio Uriarte-Tuero), (Springer volume in honor of Kostya
Oskolkov's 65th birthday).

Three point
configuration, a bilinear operator and applications to
discrete geometry, (with A. Greenleaf),
Analysis & PDE 5-2 (2012), 397-409.

Pinned distance
sets, k-simplices, Wolff's exponent in finite fields and
sum-product estimates, (with Jeremy
Chapman, M. Burak Erdoğan, Derrick Hart, Alex Iosevich and
Doowon Koh), Mathematische Zeitschrift, *Math.
Z.* 271
(2012),
no.
1-2, 63-93.

On the Mattila-Sjolin theorem, (with M. Mourgoglou and K. Taylor), Annales Academic Scientiarum Fennicae, 37 no. 2, (2012).

On
sets of directions determined by fractal subsets of the
Euclidean space, (with
M. Mourgoglou and S. Senger), Journal D'Analyse, 116 no. 1,
(2012).

**
2011 **(72)

Lattice points
close to families of surfaces, non-isotropic dilations and
generalized Radon transforms, (with K.
Taylor), New York Journal of Mathematics, 17, 1-19, (2011).

Fourier integral operators, fractal sets and the regular value theorem, (with S. Eswarathasan and K. Taylor), Advances in Mathematics, 228, (2011).

An
analog of the Furstenberg-Katznelson-Weiss theorem on
triangles in sets of positive density in finite field
geometries, (with D. Covert, D. Hart, S. Senger and
I. Uriarte-Tuero), Discrete Math. 311, no. 6, 423-430,
(2011).

On application of Guth-Katz theorem,
(with M. Rudnev and O. Roche-Newton), Mathematics Research
Notices 18, no. 4, 1-7.

On directions determined by subsets of vector spaces over finite fields, (with H. Morgan and J. Pakianathan), Integers, 11, (2011).

Erdos
distance problem, (with J. Garibaldi and S. Senger),
AMS Student Library Series, 56, (2011).

**2010**
(65)

A universal Stein-Tomas restriction estimate for measures in three dimensions, (with S. Roudenko), Festschrift dedicated to Mel Nathanson's 60th birthday, Springer, (2010) 171-178.

Extension
theorems for paraboloids in the finite field setting,
(with D. Koh), Mathematische Zeitschrift, 266, (2010) no.2
471-487.

Extension
theorems for spheres in the finite field setting, (with
D. Koh), Forum Math. 22 (2010), no. 3, 457-483.

The discrepancy
of a needle on a checkerboard II, (with M. Kolountzakis)
Unif. Distrib. Theory 5 (2010), no. 2, 1-13.

Sets
with integral distances in finite fields, (with I.
Shparlinski and M. Xiong) Trans. Amer. Math. Soc. 362 2010,
no. 4, 2189--2204.

**2009**
(59)

On
rapid generation of ${\rm SL}\sb 2(\Bbb F\sb Q)$, (with J.
Chapman) Integers 9 (2009), A4, 47-52.

**2008**
(55)

Orthogonal systems in vector spaces over finite fields, (with S. Senger), Electronic J. of Combinatorics, volume 15, December (2008).

Powder diffraction from a combinatorial and analytic
viewpoint, (with M. Rudnev), Integers, volume 8, (2008).

Sums and
products in finite fields: an integral geometric viewpoint,
(with D. Hart), Contemporary Mathematics, volume 464,
(2008).

*Fourier analysis and geometric
combinatorics **Topics in
mathematical analysis, * 321--335, Ser.
Anal. Appl. Comput., 3, *World
Sci. Publ., Hackensack, NJ,* 2008.

Ubiquity of simplexes in vector spaces over finite fields, (with D. Hart), Analysis Mathematica, volume 34 (2008).

**2007**
(47)

A view from the top: analysis, combinatorics and number
theory, (book), AMS Student Library Series, volume 39.

**2006**
(40)

2005
(38)

** 2004** (35)

Fourier analysis and convexity. Edited by Luca
Brandolini, Leonardo Colzani, Alex Iosevich and Giancarlo
Travaglini. Applied
and Numerical Harmonic Analysis. *Birkh�user
Boston, Inc., Boston, MA*

Lattice
points inside random ellipsoids, (with S. Hofmann and D.
Weidinger), Michigan Math. J. 52 (2004), no. 1, pages 13-21.

Distance sets of well-distributed planar sets, (with I.
Laba), Journal of Discrete and Computational Geometry,
vol. 31 no. 2, pages 243-250.

** 2002** (25)

** 2001** (21)

** 2000** (17)

** 1999** (15)

** 1998 **(8)

** 1997 **(6)

** 1996 **(5)

*Averages
over homogeneous hypersurfaces, Forum Mathematicum, Volume
8 (1996), Number 2, pp. 219-235.*

** 1995 **(2)

** 1994 **(1)

A new bound on Erdos distinct distance problem in the plane over prime fields, (with Thang, Vinh, Koh and Shen), accepted for publication by Acta Arithmetica.