September 29-October 3, 2014 IMA Workshops ORGANIZERS David Conlon, University of Oxford Ernie Croot, Georgia Institute of Technology Van Vu, Yale University Tamar Ziegler , Hebrew University SPEAKERS Tim Austin, Courant Institute of Mathematical Sciences Vitaly Bergelson, The Ohio State University Emmanuel Breuillard, Université de Paris XI (Paris-Sud) Boris Bukh, Carnegie Mellon University Mei-Chu Chang, University of California, Riverside David Conlon, University of Oxford Ernie Croot, Georgia Institute of Technology Jacob Fox, Massachusetts Institute of Technology Bob Guralnick, University of Southern California Akos Magyar , University of British Columbia Hamed Hatami, McGill University Frederick Manners, University of Oxford Lilian Matthiesen, Institut de Mathematiques de Jussieu Jozsef Solymosi, University of British Columbia Terence Tao, University of California, Los Angeles Van Vu, Yale University Melanie Wood, University of Wisconsin, Madison Yufei Zhao, Massachusetts Institute of Technology Tamar Ziegler , Hebrew University Additive and Analytic Combinatorics Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as harmonic analysis, ergodic theory, and representation theory. As it turns out, many combinatorial ideas that have existed in the combinatorics community for quite some time can be used to attack notorious problems in other areas of mathematics. A typical example is the Green- Tao theorem on the existence of long arithmetic progressions in primes, which uses a famous theorem of Szemerédi on arithmetic progressions in dense sets as a key component. The ﬁeld is also of great interest to computer scientists; a number of the techniques and theorems have seen application in, for example, communication complexity, property testing, and the design of randomness extractors. www.ima.umn.edu/2014-2015/W9.29-10.3.14 The IMA is a NSF-funded institute

Additive and Analytic Combinatorics · 10/3/2014 · Additive and Analytic Combinatorics Additive combinatorics is the theory of counting additive structures in sets. This theory

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Page 1: Additive and Analytic Combinatorics · 10/3/2014 · Additive and Analytic Combinatorics Additive combinatorics is the theory of counting additive structures in sets. This theory

September 29-October 3, 2014

IMA Workshops

OrgAnIzers

David Conlon, University of Oxfordernie Croot, Georgia Institute of TechnologyVan Vu, Yale University Tamar ziegler, Hebrew University

speAkersTim Austin, Courant Institute of Mathematical Sciences

Vitaly Bergelson, The Ohio State University

emmanuel Breuillard, Université de Paris XI (Paris-Sud)

Boris Bukh, Carnegie Mellon University

Mei-Chu Chang, University of California, Riverside

David Conlon, University of Oxford

ernie Croot, Georgia Institute of Technology

Jacob Fox, Massachusetts Institute of Technology

Bob guralnick, University of Southern California

Akos Magyar, University of British Columbia

Hamed Hatami, McGill University

Frederick Manners, University of Oxford

Lilian Matthiesen, Institut de Mathematiques de Jussieu

Jozsef solymosi, University of British Columbia

Terence Tao, University of California, Los Angeles

Van Vu, Yale University

Melanie Wood, University of Wisconsin, Madison

Yufei zhao, Massachusetts Institute of Technology

Tamar ziegler, Hebrew University

Additive and Analytic Combinatorics

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as harmonic analysis, ergodic theory, and representation theory. As it turns out, many combinatorial ideas that have existed in the combinatorics community for quite some time can be used to attack notorious problems in other areas of mathematics. A typical example is the Green-Tao theorem on the existence of long arithmetic progressions in primes, which uses a famous theorem of Szemerédi on arithmetic progressions in dense sets as a key component. The field is also of great interest to computer scientists; a number of the techniques and theorems have seen application in, for example, communication complexity, property testing, and the design of randomness extractors.

www.ima.umn.edu/2014-2015/W9.29-10.3.14

The IMA is a NSF-funded institute