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During the past decade or so there have been dramatic developments in the interaction between analysis, combinatorial number theory and theoretical computer science: specifically between harmonic analysis and combinatorial number theory and between geometric functional analysis and the theory of algorithms.
Not only have discoveries in one area been used in others but, even more strikingly, there has emerged a commonality of methods and ideas among these apparently diverse areas of mathematics. The use of harmonic analysis in number theory is at least a century old, but in the recent works of Gowers, Green and Tao and others on the existence of arithmetic progressions in subsets of the integers, and in particular the sequence of primes, it has developed into an entire area: additive combinatorics. Classical inequalities of harmonic analysis, such as the isoperimetric inequality, have discrete analogues that are often more subtle than the continuous versions and have wide-ranging applications: for example the discrete isoperimetric inequality of Talagrand, which inspired his work on spin-glass models.
Through the study of the influence of variables on Boolean functions, discrete harmonic analysis has started to play a crucial role in theoretical computer science. And at the same time it has become clear that many problems in theoretical computer science and combinatorial optimisation are actually geometric problems in "disguise". In other cases, the problems are so complex that the best available approximation algorithms were devised by embedding the underlying combinatorial structure into a familiar geometry (such as Euclidean space) so that it becomes "geometrically obvious" what to do.
The purpose of this programme is to bring together researchers in these diverse areas of mathematics, to encourage more interaction between these fields, and to provide an opportunity for UK mathematicians to engage with an important part of the mathematical computer science community.
Click here to download the programme's final scientific report
Title | Year | Programme |
---|---|---|
An incidence theorem in higher dimensionsAuthors: Terence Tao, Jozsef Solymosi |
2010 | DAN |
Sums of dilates in groups of prime orderAuthors: Alain Plagne |
2010 | DAN |
A curved Brunn-Minkowski inequality on the discrete hypercube or: What is the Ricci curvature of the discrete hypercube?Authors: Yann Ollivier, C Villani |
2010 | DAN |
Invariances in variance estimatesAuthors: Franck Barthe, Dario Cordero-Erausquin |
2010 | DAN |
Hypercontractive measures, Talagrand's inequality, and influencesAuthors: Dario Cordero-Erausquin, Michel Ledoux |
2010 | DAN |
Hypercontractive inequality for pseudo-Boolean functions of bounded Fourier widthAuthors: A Yeo, Gregory Gutin |
2010 | DAN |
Combinatorial optimization over two random point setsAuthors: Charles Bordenave, Franck Barthe |
2010 | DAN |
A remark on the slicing problemAuthors: Grigorios Paouris, Beatrice-Helen Vritsiou, A Giannopoulos |
2010 | DAN |
Approximate Gaussian isoperimetry for $\it k$ setsAuthors: Gideon Schechtman |
2010 | DAN |
Stabilizing isomorphisms from l_p (l_2) into L_p [0, 1]Authors: Gideon Schechtman, R Levy |
2010 | DAN |
Transversal multilinear Radon-like transforms: local and global estimatesAuthors: Neal Bez, S Gutierrez, Jonathan Bennett |
2010 | DAN |
Global nonlinear Brascamp-Lieb inequalitiesAuthors: Neal Bez, S Gutierrez, Jonathan Bennett |
2010 | DAN |
On the logarithimic calculus and Sidorenko's conjectureAuthors: Balazs Szegedy, JL Xiang Li |
2010 | DAN |
On reverse hypercontractivityAuthors: Krzysztof Oleszkiewicz, Arnab Sen, Elchanan Mossel |
2010 | DAN |
Lower bounds for the average and smoothed number of Pareto optimaAuthors: Luis Rademacher, N Goyal |
2010 | DAN |
The diminishing segment processAuthors: P Kevei, V Vigh, Gergely Ambrus |
2010 | DAN |
Maximal equilateral setsAuthors: Konrad Swanepoel, R Villa |
2010 | DAN |
Sets of unit vectors with small subset sumsAuthors: Konrad Swanepoel |
2010 | DAN |
Two steps transportation problemAuthors: Ezio Marchi |
2010 | DAN |
The effective LVMM method in Lotka-Volterra systemsAuthors: Ezio Marchi |
2010 | DAN |
An observation related to the method of Lemke-HobsonAuthors: Ezio Marchi, M Maton |
2010 | DAN |
A simple or deep mathematical problem?Authors: Ezio Marchi |
2010 | DAN |
Average equilibrium pointsAuthors: Ezio Marchi |
2010 | DAN |
Temperature effect on collagen-like structureAuthors: L Millan, Ezio Marchi |
2010 | DAN |
A difference equation involving Fibonacci numbersAuthors: Ezio Marchi |
2010 | DAN |
Further remarks for difference equationsAuthors: Ezio Marchi |
2010 | DAN |
Matricial PotentiationAuthors: Ezio Marchi, M Matens |
2010 | DAN |
On a relevant aspect in difference equationsAuthors: Ezio Marchi |
2010 | DAN |
Representation of rational numbers through a Lissajou's geometric figureAuthors: Ezio Marchi |
2010 | DAN |
10 January 2011 to 14 January 2011
28 March 2011 to 1 April 2011
27 June 2011 to 1 July 2011
4 July 2011 to 8 July 2011
Wednesday 19th January 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Guillaume Aubrun Université Claude Bernard Lyon 1 |
Room 1 | |
Friday 21st January 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Terence Tao University of California, Los Angeles |
Room 1 |
Wednesday 26th January 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Jordan's theorem on finite linear groups and its approximate Analogues |
Room 1 | |
15:15 to 16:15 |
Jozsef Solymosi University of British Columbia |
Room 1 | |
Friday 28th January 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Terence Tao University of California, Los Angeles |
Room 1 | |
Wednesday 2nd February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Per Austrin University of Toronto |
Room 1 | |
Friday 4th February 2011 | |||
---|---|---|---|
11:00 to 12:00 |
Kenneth Falconer University of St Andrews |
Room 1 | |
Wednesday 9th February 2011 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 | |
|
15:15 to 16:15 |
Sergei Konyagin Steklov Mathematical Institute, Russian Academy of Sciences |
Room 1 |
Friday 11th February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Johan Håstad KTH - Royal Institute of Technology |
Room 1 | |
Saturday 12th February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Michael Bateman University of California, Los Angeles |
Room 1 |
Wednesday 16th February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Artem Zvavitch Kent State University |
Room 1 | |
Friday 18th February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Krzysztof Oleszkiewicz Uniwersytet Warszawski |
Room 1 | |
Monday 21st February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Olivier Guedon Université de Marne-la-Vallée |
Room 1 | |
Wednesday 23rd February 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Mark Rudelson University of Missouri |
Room 1 | |
15:15 to 16:15 |
Alain Plagne Centre de Physique Théorique de l’Ecole Polytechnique (CPHT) |
Room 1 | |
Wednesday 2nd March 2011 | |||
---|---|---|---|
14:00 to 15:00 | Room 1 | |
|
15:15 to 16:15 |
Gergely Ambrus Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences |
Room 1 | |
Wednesday 9th March 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Harald Andres Helfgott University of Bristol/Ecole Normale Superieure |
Room 1 | |
15:15 to 16:15 |
Arnab Sen University of Cambridge |
Room 1 | |
Wednesday 16th March 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Charles Bordenave Université de Toulouse |
Room 1 | |
15:15 to 16:15 |
Gilles Lancien Université de Franche-Comté |
Room 1 |
Tuesday 5th April 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Avi Wigderson Institute for Advanced Study, Princeton |
Room 1 | |
15:15 to 16:15 |
David Ellis University of Cambridge |
Room 1 | |
Thursday 7th April 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Stefan Ingi Valdimarsson University of Iceland |
Room 1 | |
15:15 to 16:15 |
Avi Wigderson Institute for Advanced Study, Princeton |
Room 1 | |
Tuesday 12th April 2011 | |||
---|---|---|---|
13:45 to 14:45 |
Avi Wigderson Institute for Advanced Study, Princeton |
Room 1 | |
Wednesday 13th April 2011 | |||
---|---|---|---|
13:45 to 14:45 |
Alain Pajor Université de Marne-la-Vallée |
Room 1 | |
Thursday 14th April 2011 | |||
---|---|---|---|
13:45 to 14:45 |
Endre Szemeredi Rutgers, The State University of New Jersey |
Room 1 | |
Thursday 21st April 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Mark Jerrum Queen Mary University of London |
Room 2 |
Wednesday 27th April 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Misha Rudnev University of Bristol |
Room 1 | |
15:15 to 16:15 |
Luis Alexis Rademacher Ohio State University |
Room 1 |
Tuesday 3rd May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Michael Bateman University of California, Los Angeles |
Room 1 | |
Wednesday 4th May 2011 | |||
---|---|---|---|
13:45 to 14:45 |
Shachar Lovett Institute for Advanced Study, Princeton |
Room 1 | |
Friday 6th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Nets Hawk Katz Indiana University |
Meeting Room |
Monday 9th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Nets Hawk Katz Indiana University |
Room 1 | |
Tuesday 10th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Sergey Bobkov University of Minnesota |
Room 1 | |
Thursday 12th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Michael Bateman University of California, Los Angeles |
Room 1 | |
Wednesday 18th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Yann Ollivier Université Paris Saclay |
Room 1 | |
Thursday 19th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Yann Ollivier Université Paris Saclay |
Room 2 | |
Tuesday 24th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Konstantin Makarychev IBM Research |
Room 1 | |
Wednesday 25th May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Konrad Swanepoel London School of Economics |
Room 1 | |
15:15 to 16:15 |
Konstantin Makarychev IBM Research |
Room 1 | |
Tuesday 31st May 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Alexander Volberg Michigan State University |
Room 1 | |
Wednesday 1st June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Shin-ichi Ohta Kyoto University |
Room 1 | |
15:15 to 16:15 |
Mark Braverman University of Toronto |
Room 1 | |
Monday 6th June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Alexander Volberg Michigan State University |
Room 1 | |
Tuesday 7th June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Emanuel Milman Technion - Israel Institute of Technology |
Room 1 | |
Tuesday 14th June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Hamed Hatami McGill University |
Room 1 | |
Wednesday 15th June 2011 | |||
---|---|---|---|
15:30 to 16:30 |
Mokshay Madiman Stanford University |
Room 2 | |
17:00 to 17:50 |
Assaf Naor New York University |
Room 1 | |
Tuesday 21st June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Gregory Gutin Royal Holloway, University of London |
Room 2 | |
Wednesday 22nd June 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Jan Maas Rheinische Friedrich-Wilhelms-Universität Bonn |
Room 2 | |
15:30 to 16:30 |
Bo'az Klartag Tel Aviv University |
Room 2 | |
Tuesday 5th July 2011 | |||
---|---|---|---|
14:00 to 15:00 |
Imre Leader University of Cambridge |
Room 1 | |
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