Zurich colloquium in mathematics

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Date / Time

Speaker

Title

Location

28 February 2023
16:30-18:15

Martin Hairer
EPF Lausanne

Details

Title	Stochastic quantisation of Yang-Mills
Speaker, Affiliation	Martin Hairer, EPF Lausanne
Date, Time	28 February 2023, 16:30-18:15
Location	KO2 F 150
Abstract	I will report on recent progress on the problem of building a stochastic process that admits the hypothetical Yang-Mills measure as its invariant measure. One interesting feature of our construction is that it preserves gauge-covariance in the limit even though it is broken by the regularisation procedure. This is based on joint work with Ajay Chandra, Ilya Chevyrev, and Hao Shen.

Stochastic quantisation of Yang-Millsread_more

KO2 F 150

28 March 2023
16:30-18:15

Hannah Markwig
University of Tübingen

Details

Title	Counting bitangents of quartic curves - arithmetic, real, tropical
Speaker, Affiliation	Hannah Markwig, University of Tübingen
Date, Time	28 March 2023, 16:30-18:15
Location	KO2 F 150
Abstract	We showcase tropical geometry as a tool for geometric counting problems. A nice feature of tropical geometry is that many techniques can be applied simultaneously over various ground fields, e.g. for complex or real counting problems. Our prime example will be the count of bitangent liens to a smooth plane quartic. Already Plücker knew that a smooth complex plane quartic curve has exactly 28 bitangents. Bitangents of quartic curves are related to a variety of mathematical problems. They appear in one of Arnold's trinities, together with lines in a cubic surface and 120 tritangent planes of a sextic space curve. In this talk, we review known results about counts of bitangents under variation of the ground field. Special focus will be on counting in the tropical world, and its relations to real and arithmetic counts. We end with new results concerning the arithmetic multiplicity of tropical bitangent classes, based on joint work with Sam Payne and Kris Shaw.

Counting bitangents of quartic curves - arithmetic, real, tropicalread_more

KO2 F 150

16 May 2023
16:30-18:15

Sylvia Serfaty
Courant Institute of Mathematical Sciences

Details

Title	Systems of points with Coulomb interactions
Speaker, Affiliation	Sylvia Serfaty, Courant Institute of Mathematical Sciences
Date, Time	16 May 2023, 16:30-18:15
Location	KO2 F 150
Abstract	Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability. We will first review these motivations, then present the ''mean-field'' derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions,and finish with the description of the effect of temperature.

Systems of points with Coulomb interactionsread_more

KO2 F 150

23 May 2023
16:30-18:15

Details

Title	Systems of points with Coulomb interactions
Speaker, Affiliation
Date, Time	23 May 2023, 16:30-18:15
Location	KO2 F 150

Systems of points with Coulomb interactions

KO2 F 150

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