Zurich colloquium in mathematics

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Date / Time

Speaker

Title

Location

29 October 2013
17:15-18:15

Prof. Dr. Philippe Michel
EPF Lausanne

Details

Title	Bounded gaps between primes (after Y. Zhang)
Speaker, Affiliation	Prof. Dr. Philippe Michel, EPF Lausanne
Date, Time	29 October 2013, 17:15-18:15
Location	KO2 F 150
Abstract	A few months ago, Yitang Zhang, a little known chinese mathematician working at University of New Hampshire, stunned the mathematical community by establishing the existence of infinitely many pairs of prime numbers whose distance from each other is bounded by an absolute constant (Zhang obtained 70 millions). In this lecture, we will discuss the circle of ideas that have made this extraordinary achievement possible. If time permits, we will also describe a collaborative mathematical effort initiated by Terry Tao -the Polymath 8 project- whose objective is to reduce the value of the gap constant (currently its value is less than 5000).

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KO2 F 150

12 November 2013
17:15-18:15

Prof. Dr. Ezra Getzler
Northwestern University, USA

Details

Title	Higher groupoids
Speaker, Affiliation	Prof. Dr. Ezra Getzler, Northwestern University, USA
Date, Time	12 November 2013, 17:15-18:15
Location	KO2 F 150
Abstract	Lie groupoids are a fundamental part of the language of differential geometry: they bring both differentiable actions of Lie groups and foliations under a single roof. In complex geometry, they underly the work of Kuranishi and others on moduli of holomorphic vector bundles. In this talk, we will report on recent work (joint with Kai Behrend) generalizing the theory of Lie groupoids to higher groupoids - where the symmetries have symmetries of their own, and so on. We will show how this yields a language for extending Kuranishi's ideas to the setting of complexes of holomorphic bundles (or better, of twisted complexes).

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KO2 F 150

26 November 2013
17:15-18:15

Prof. Dr. Ragnar Winther
University of Oslo, Norway

Details

Title	Finite element exterior calculus - a link between topology and numerical analysis
Speaker, Affiliation	Prof. Dr. Ragnar Winther, University of Oslo, Norway
Date, Time	26 November 2013, 17:15-18:15
Location	KO2 F 150
Abstract	The purpose of this talk is to illustrate how computational methods for certain partial differential equations can be constructed and analyzed in the setting of discrete differential complexes. In fact, we will show how various stability and convergence properties can be derived in an abstract setting of Hilbert complexes, and discuss how the proper assumptions can be verified in the more concrete setting of the de Rham complex and its discretizations. A key tool in our analysis is the concept of bounded cochain projections, which represents the connection between the differential complex and its discretization. We will discuss several possibilities of such constructions.

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KO2 F 150

10 December 2013
17:15-18:15

Prof. Dr. Martin Hairer
The University of Warwick, United Kingdom

Details

Title	Dynamics near criticality
Speaker, Affiliation	Prof. Dr. Martin Hairer, The University of Warwick, United Kingdom
Date, Time	10 December 2013, 17:15-18:15
Location	KO2 F 150
Abstract	Heuristically, one can give arguments why the fluctuations of classical models of statistical mechanics near criticality are typically expected to be described by nonlinear stochastic PDEs. Unfortunately, in most examples of interest, these equations seem to make no sense whatsoever due to the appearance of infinities or of terms that are simply ill-posed. I will give an overview of a new theory of "regularity structures" that allows to treat such equations in a unified way, which in turn leads to a number of natural conjectures. One interesting byproduct of the theory is a new (and rigorous) interpretation of "renormalisation group techniques" in this context. At the technical level, the main novel idea involves a complete rethinking of the notion of "Taylor expansion" at a point for a function or even a distribution. The resulting structure is useful for encoding "recipes" allowing to multiply distributions that could not normally be multiplied. This provides a robust analytical framework to encode renormalisation procedures.

Dynamics near criticalityread_more

KO2 F 150

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