Curriculum Vitae

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

Contents:

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"
June 1989, BS in Pure Mathematics, University of Chicago

Awards and Honors:

AMS Fellow, Class of 2014

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 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) 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). 2006 (40) 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 2002 (25) 2001 (21) 2000 (17) 1999 (15) 1998 (8) 1997 (6) 1996 (5) 1995 (2) 1994 (1) 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.