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Discrete Analysis

Author: Cambridge University

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Description

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.

Read more at: http://www.newton.ac.uk/programmes/DAN/
92 Episodes
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Positive projections

Positive projections

2011-07-0759:13

Leader, I (University of Cambridge) Tuesday 05 July 2011, 14:00-15:00
The logarithmic Laplace transform in convex geometry

The logarithmic Laplace transform in convex geometry

2011-06-2456:59

Klartag, B (Tel-Aviv) Wednesday 22 June 2011, 15:30-16:30
Gradient flows of the entropy for finite Markov chains

Gradient flows of the entropy for finite Markov chains

2011-06-2459:26

Maas, J (Bonn) Wednesday 22 June 2011, 14:00-15:00
Applications of Discrete Harmonic Analysis, Probabilistic Method and Linear Algebra in Fixed-Parameter Tractability and Kernelization

Applications of Discrete Harmonic Analysis, Probabilistic Method and Linear Algebra in Fixed-Parameter Tractability and Kernelization

2011-06-2454:57

Gutin, G (Royal Holloway) Tuesday 21 June 2011, 14:00-15:00
Quantitative geometry and efficient classification procedures

Quantitative geometry and efficient classification procedures

2011-06-2251:42

Naor, A (New York) Wednesdayy 15 June 2011, 17:00-17:50
Towards an entropy-based sumset calculus for additive combinatorics and convex geometry

Towards an entropy-based sumset calculus for additive combinatorics and convex geometry

2011-06-2058:28

Madiman, M (Yale) Wednesday 15 June 2011, 15:30-16:30
Is asymptotic extremal graph theory of dense graphs trivial?

Is asymptotic extremal graph theory of dense graphs trivial?

2011-06-2001:02:20

Hatami, H (McGill) Tuesday 14 June 2011, 14:00-15:00
Stochastic completeness for random walks and jump processes

Stochastic completeness for random walks and jump processes

2011-06-2001:02:47

Grigoryan, A (Bielefeld) Friday 10 June 2011, 14:00-15:00
Isoperimetric and concentration inequalities

Isoperimetric and concentration inequalities

2011-06-1301:07:42

Milman, E (Technion) Tuesday 07 June 2011, 14:00-15:00
Singular integrals in bad neighborhoods II: Stochastic Optimal Control and sharp estimates of Singular Integrals

Singular integrals in bad neighborhoods II: Stochastic Optimal Control and sharp estimates of Singular Integrals

2011-06-1301:07:02

Volberg, A (Michigan) Monday 06 June 2011, 14:00-15:00
Computability and Complexity of Julia Sets

Computability and Complexity of Julia Sets

2011-06-0354:15

Braverman, M (Toronto) Wednesday 01 June 2011, 15:15-16:15
Ricci curvature of Finsler manifolds, towards applications in the geometry of Banach spaces

Ricci curvature of Finsler manifolds, towards applications in the geometry of Banach spaces

2011-06-0358:54

Ohta, S (Kyoto) Wednesday 01 June 2011, 14:00-15:00
Singular integrals in bad neighborhoods I: Singular integrals for Geometric Measure Theory

Singular integrals in bad neighborhoods I: Singular integrals for Geometric Measure Theory

2011-06-0359:17

Volberg, A (Michigan) Tuesday 31 May 2011, 14:00-15:00
Vertex Sparsifiers and Lipschitz Extendability

Vertex Sparsifiers and Lipschitz Extendability

2011-06-0354:09

Makarychev , Y (Toyota Technological Institute) Wednesday 25 May 2011, 15:15-16:15
Favourite distances in high dimensions

Favourite distances in high dimensions

2011-06-0352:11

Swanepoel, K (London School of Economics) Wednesday 25 May 2011, 14:00-15:00
How to Play Unique Games Against a Semi-Random Adversary

How to Play Unique Games Against a Semi-Random Adversary

2011-06-0354:32

Makarychev, K (IBM Research) Tuesday 24 May 2011, 14:00-15:00
Discrete Ricci curvature with applications

Discrete Ricci curvature with applications

2011-06-0301:12:23

Ollivier, Y (Universite Paris-Sud) Wednesday 18 May 2011, 14:00-15:00
3-terms arithmetic progressions in finite fields (IV)

3-terms arithmetic progressions in finite fields (IV)

2011-06-0301:03:45

Bateman, M (UCLA) Thursday 12 May 2011, 14:00-15:00
Rates of convergence in the entropic central limit theorem

Rates of convergence in the entropic central limit theorem

2011-06-0350:24

Bobkov, S (Minnesota) Tuesday 10 May 2011, 14:00-15:00
3-terms arithmetic progressions in finite fields (III)

3-terms arithmetic progressions in finite fields (III)

2011-06-0301:01:03

Katz, N (Indiana) Monday 09 May 2011, 14:00-15:00
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