Curriculum Vitae

cv photo

Alexander Iosevich
Department of Mathematics
University of Rochester
Last updated: September 19, 2017

Contents:

Personal Information
Education
External Funding
Positions Held
Research Interests
Graduate students
Undergraduate students
Conferences Organized
Editorial Board Membership
Selected Community Educational and Professional Activities
Teaching Awards
Selected invited talks
Invited talks and research stays
Lecture series
Published Papers and Papers Accepted for Publication

Personal Information:

Email: iosevich@math.rochester.edu
Date of Birth: December 14, 1967
Citizenship: United States of America

Education:

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

External Funding:


June 1997, United States National Science Foundation Grant in Classical

Analysis, Grant Number DMS97-06825 Amount: $53,000
March 2000, United States National Science Foundation Grant in Classical
Analysis, Grant Number DMS00-87339 Amount: $77,000
March 2003,  United States National Science Foundation Grant in Classical
Analysis, Grant Number DMS02-45369 Amount: $114,000
June 2005, United States National Science Foundation Collaborative Research Grant
Analysis, Grant Number DMS04-56306 Amount: $474,245
August 2009, United States National Science Foundation Grant in Number Theory
and Algebra, Grant Number DMS10-45404 Amount: $303,000
April 2015,
United States National Science Foundation Conference Grant
for the ICHAA conference at the CUNY Graduate Center Amount: $50,000
May 2015 United States National Security Agency Grant H98230-15-1-0319
in Combinatorics. Amount: $120,000


Positions Held:

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, joint 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

Research Interests:

Classical Analysis and Fourier Integral Operators
Geometric Combinatorics and Geometric Measure Theory
Additive and Analytic Number Theory

Convex Geometry and Probability Theory

Graduate students:

Ryan Mullen (M.S. 2002) Prognos Inc.
Daniel Weidinger (M.S. 2003) SETA Test Scientist at Shafer Corporation
Nicholas Wegman (M.S. 2006) Prognos Inc.
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
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

 
Undergraduate students:

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)
Yujia Zhai (2014) Cornell University (graduate student)

Brian McDonald (2016) University of Chicago (graduate student)
Lisa Rosenfeld (2016) FDIC Pittsburgh
Adam Scrivener (2016) Epic Systems, Madison, W
I
Ben Dees (2017) Johns Hopkins University, Baltimore, MD
Daniel Rubery (2017) Google
Adam Lott (2017) University of California Los Angeles

Conferences organized:

Excelsior Lectures in Analysis, with L. Lanzani, September 2016 (upcoming).
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. (Member of the organizing committee along 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 60th 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.


Editorial Board Membership:

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-Present

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

Carus Manuscripts (MAA) Editorial Board January 2017-

Integers Journal Editorial Board October 2016-Present

 

Selected educational and administrative activities:

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 2015
Summer research pro
gram for undergraduate students at the University of Rochester, June-August 2014.
Summer research program for undergraduate students at the University of Rochester, June-August 2013.
Summer research program for undergraduate students at the University of Rochester, June-August 2012.
Harmonic Analysis Editor of the Proceedings of the American Mathematical Society, 2010-Present.
Summer research program for undergraduate students at the University of Rochester, June-August 2011.
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.

Teaching Awards:

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

April 2018 A lecture series on the Falconer Conjecture at the Louisiana State University (upcoming)
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"

Invited Talks and Research Stays: (268 lectures and another 26 lectures from 8 lecture series)

2017 (268)

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)

November 2016 (upcoming) A colloquium talk at the University of Indiana  
 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 (upcoming) An invited lecture at the Prairie Analysis Seminar 2016
  Title: Distribution of simplexes in fractal subsets of Euclidean space
September 2016 (upcoming) A keynote address at the combinatorial geometry conference in Hanoi, Vietnam
 
Title: The analysis, combinatorics and number theory of the distance graph
September 2016 (upcoming) 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)

December 2014 An invited lecture at National Central University in Taiwan
 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)

December 2012, Invited lecture at the Applied Mathematic Seminar at the University College London
  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 (upcoming)
  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 (upcoming), 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, (upcoming), 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)

December 2005, Annual Meeting of the Canadian Mathematical Society
    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 Erdös distance problem" 
July 1999, Joint meeting of the American and Australian Mathematical Societies.
   Title: "Fourier basis, fractals, and the Erdös 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 Erdös 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: "Lp 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: Lp improving properties of measures supported on convex hypersurfaces"
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: "Maximal operators over smooth hypersurfaces"
June 1998, Department of Mathematics, University of New South Wales, Sydney, Australia
   Title: "Averages over convex hypersurfaces" 
April 1998, Dixieland Analysis Conference, Emory University, Atlanta, Georgia
   Title: "Lp improving properties of measures supported on convex hypersurfaces"
April 1998, Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
   Title: "Averages over convex surfaces"
February 1998, Department of Mathematics, Johns Hopkins University, Baltimore, Maryland
   Title: "Maximal averages over surfaces"
February 1998, Department of Mathematics, Georgetown University, Washington,
District of Columbia
   Title: "Averages over convex hypersurfaces"

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: "(Lp,Lq) mapping properties of averaging operators associated to homogeneous hypersurfaces"
May 1994, Harmonic Analysis Seminar, McMaster University
   Title: "Maximal operators associated to homogeneous and mixed homogeneous hypersurfaces in R3 "
June 1994, Functional Analysis Seminar, Technion, Haifa, Israel

   Title: "Maximal operators associated to homogeneous hypersurfaces in Rn"
June 1994, Mathematics Colloquium, University of Naples, Naples, Italy
   Title: "Maximal operators in Harmonic Analysis"
May 1994, Analysis Seminar, UCLA, Los Angeles, California
   Title: "Weighted oscillatory integrals and the associated maximal operators"

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"

Lecture Series (20 lectures) 

February 2017, (upcoming) 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.


2017 (101)


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


2016
(96)

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

Falconer distance problem, additive energy and Cartesian products, (with B. Liu), Annales Academiæ 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. Birkhäuser/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 Academiæ Scientiarum Fennicæ, 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).

Averages over hyperplanes, sum-product theory in finite fields, and the Erdos-Falconer distance conjecture, (with D. Hart, D. Koh and M. Rudnev), Transactions of the AMS, 363 (2011) 3255-3275.

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.

Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields, (with D. Covert, D. Hart, D. Koh and M. Rudnev), European J. of Combinatorics 31, 2010, 306-319.

2009 (59)

Geometric incidence theorems via Fourier analysis, (with H. Jorati and I. Laba), Transactions of the American Mathematical Society, volume 361 no. 12 6595-6611(2009).

Extension theorems for the Fourier transform associated with non-degenerate quadratic surfaces in vector spaces over finite fields, (with D. Koh), Illinois Mathematics Journal, 52, Number 2 (2009), 611-628.

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

Freiman's theorem, Fourier transform, and additive structure of measures, (with M. Rudnev), Journal of the Australian Mathematical Society, 86, 2009, 97-109.

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).

Orthogonal exponentials, difference sets, and arithmetic combinatorics, (with P. Jaming), Acta Math. Hungar. volume 121 (2008).

Cubic varieties, Erdos-Falconer distance problem and incidence problems in vector spaces over finite fields, (with Doowon Koh), SIAM Journal of Discrete Mathematics, volume 23, no. 1 (2008).

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

Covering the plane by rotations, (with M. Kolountzakis and M. Matolci), Conference proceedings of Complex and Harmonic Analysis, an international conference dedicated to the memory of N. Danikas http://web.auth.gr/comhar/.

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.

Sum-product estimates in finite fields via Kloosterman sums, (with D. Hart and J. Solymosi), International Mathematics Research Notices (2007).

Erdos distance problem in vector spaces over finite fields, (with M. Rudnev), Transactions of the American Mathematical Society, (2007).

Mean square discrepancy bounds for the number of lattice points inside large convex domains II: rough domains in the plane, (With E. Sawyer and A. Seeger), Journal D'Analyse, vol.101, (2007).

Average decay estimate for Fourier transforms of measures supported on curves, (with L. Brandolini, G. Gigante, A. Greenleaf, A. Seeger, and G. Travaglini), Journal of Geometric Analysis, (2007).

Mattila integrals associated with sign indefinite measures, (with M. Rudnev), Journal of Fourier Analysis and Applications, vol. 13, (2007).

On distance measures for well-distributed sets, (with M. Rudnev), Journal of Discrete and Computational Geometry, vol. 38, (2007),

2006 (40)

A Weyl type formula for Fourier spectra and frames, (With M. Kolountzakis), PAMS, vol. 6, (2006), pages  1-8.

Combinatorial complexity of convex sequences, (With S. Konyagin, M. Rudnev and V. Ten), Journal of Discrete and Computational Geometry, vol. 35, no. 1, (2006), pages 143-158.

2005 (38)

K-distance, Falconer conjecture, and discrete analogs, (With I. Laba), Integers, Electronic Journal of Combinatorial Numebr Theory, Proceedings of the Integers Conference in honor of Tom Brown, pages 95-106.

Non-isotropic distance measures for lattice generated sets, (with M. Rudnev), Publicaciones, vol. 49, (2005), pages 225-247.

Circular averages and Falconer/Erdos distance conjecture in the plane for random metrics, (With S. Hofmann), Proc. Amer. Mat. Soc. 133 (2005), pages 133-143.

2004 (35)

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

Falconer conjecture, spherical averages, and discrete analogs, (With G. Arutuynyants), (Towards a theory of geometric graphs, Contemporary Mathematics 342, Janos Pach, Editor).

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.

2003 (31)

The geometry of the Gauss map and the distribution of lattice points in convex planar domains, (With L. Brandolini, L. Colzani, A. Podkorytov, and G. Travaglini), Mathematika vol. 48 (2001), no. 1-2, pages 107-117  (appeared in 2003).

Sharp rate of average decay of the Fourier transform of a bounded set, (With L. Brandolini and S. Hofmann), GAFA, vol. 13, (2003).

A combinatorial approach to orthogonal exponentials, (with M. Rudnev), International Mathematics Research Notices, vol. 49, (2003), pp.1-12.

Spherical L1- averages of the Fourier transform of the characteristic function of a convex set and the geometry of the Gauss map, (with L. Brandolini and G. Travaglini), Trans. Amer. Math. Soc. vol. 355 (2003), pp. 3513-3535.

Fuglede conjecture holds for convex planar domains, (With N. Katz and T. Tao),  Math Research Letters, vol. 10, 2003, pp.1-11.

Three problems motivated by the average decay of the Fourier transform, (with E. Sawyer), (Mt. Holyoke conference proceedings; Contemporary Mathematics, volume 320, American Mathematical Society, 2003).

2002 (25)

Mean square discrepancy bounds for the number of lattice points inside large convex domains, (With E. Sawyer and A. Seeger), Journal D'Analyse, vol. 87 (2002), pages 209-230.

Dispersive effects in a modified Kuromoto-Sivashinsky equation, (with J. Miller), Comm. in PDE vol. 27 (2002), pages 2423-2448.

Two problems associated with convex finite type domains, (With E. Sawyer and A. Seeger), Publ. Mat., vol. 46, (2002), pages 153-177.

The rate of convergence of Fourier expansions in the plane, a geometric viewpoint, (with L. Brandolini, L. Colzani, and G. Travaglini), Mathematische Zeitschrift, vol. 242, Issue 4, (2002), pages 709-724.

2001 (21)

Lattice points and generalized diophantine conditions, Journal of Number Theory, vol. 90, no.1, (2001), pp.19-30.

Spherical means and the restriction phenomenon, (With L. Brandolini and G. Travaglini), Journal of Fourier Analysis and Applications, vol. 7, (2001), pp. 359-372.

Curvature, combinatorics, and the Fourier transform, Notices of the American Mathematical Society, vol. 48, no. 6, (2001), pp. 577-583.

Convex bodies with a point of curvature do not have Fourier bases, (With N. Katz and T. Tao), American Journal of Mathematics, Volume 123 (2001), pp. 115-120.
 

2000 (17)

Sharpness results and Knapp's homogeneity argument, (With G. Lu), Bulletin of the Canad. Math. Bull., Volume 43, (2000), pp. 63-68.

How large are the spectral gaps?, (With S. Pedersen), Pacific J. Math., Volume 192, (2000), pp. 307-314.

1999 (15)

On averaging operators associated with convex hypersurfaces of finite type, (With E. Sawyer and A. Seeger), J. Anal. Math., Volume 79 (1999), pp. 159-187.

Scaling properties of convex curves and surfaces, Analysis of  Divergence (Orono, ME, 1997), Appl. Numer. Harmon. Anal., Birkhauser Boston, Boston, MA, 1999, pp. 201-212.

Maximal averages over flat radial hypersurfaces, Rev. Mat. Ibero-Americana, Volume 15, (1999)., pp. 475-485.

Fourier bases and a distance problem of Erdos, (With N. Katz and S. Pedersen), Math Research Letters, Volume 6 (1999), Number 2, pp.105-128.

Fourier transform, L2 restriction theorem, and scaling, Bolletino U.M.I., Volume 8 (1999), pp. 383-387.

Six parameter patient registration directly from projection data, (With E. E. Fitchard, J. S. Aldridge, T. R. Mackie, P. J. Reckwerdt, G. H. Olivera), Nuclear Instruments and Methods in Physics Research Section A, Volume 421, Issue: 1-2, January 21, (1999), pp. 342-351.

Random fluctuations of convex domains and lattice points, (With K. Kinateder), Proceedings of the American Mathematical Society, vol. 127 (1999), no. 10, pp. 2981-2985.

1998 (8)

Spectral and tiling properties of the unit cube, (With S. Pedersen), International Math Research Notices, (1998), Number 16, pp. 819-828.

Some sharp restriction theorems for homogeneous manifolds, (With L. DeCarli), Journal of Fourier Analysis and Applications, Volume 4 (1998), Number 1, pp. 105-128.

1997 (6)

Maximal averages over surfaces, (With E. Sawyer), Advances in Mathematics, Volume 132 (1997), Number 1, pp. 46-119.

1996 (5)

Sharp (Lp,Lq) estimates for a class of averaging operators, (With E. Sawyer), Annals of the Fourier Institute in Grenoble, Volume 46 (1996), Number 5, pp. 1359-1384.

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

Oscillatory integrals and maximal averages over homegeneous surfaces, (With E. Sawyer), Duke Mathematical Journal, Volume 82 (1996), Number 1, pp. 103-141.

1995 (2)

A restriction theorem for flat manifolds of codimension two, (With L. DeCarli), Illinois Journal of Mathematics, Volume 39 (1995), Number 4, pp. 576-585.

1994 (1)

Maximal Operators associated to families of flat curves in the plane, Duke Mathematical Journal, Volume 76 (1994), Number 2, pp. 633-644.



The following papers have been accepted for publication but have not yet appeared:

Equilateral triangles in subsets of Euclidean space of large Hausdorff dimension, (with B. Liu), accepted for publication by Israel Math Journal. 

On necklaces inside thin subsets of ${\Bbb R}^d$, (with Allan Greenleaf and Malabika Pramanik), accepted for publication by the Mathematics Research Letters.

On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators, (with Mihalis Mourgoglou and Eyvindur Palsson), accepted for publication by the Mathematics Research Letters.