Vera Serganova
"Supersymmetry and tensor categories"
Abstract: TBA
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Ngo Bao Chau
"Geometry of the Hitchin fibration and application to local harmonic analysis”
Abstract :The Hitchin fibration, introduced first in differential geometry, conceal deep informations on orbital integrals in non-archimedean reductive groups. I will explain how these objects are related, and explain the proof of the fundamental lemma based on the Beilinson-Bernstein-Deligne decomposition theorem applied to the Hitchin fibration. I will try to explain a new proof based on p-adic integration on the same Hitchin fibration, due to Groechenig-Wyss-Ziegler.
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John Ball
"The mathematics of liquid crystals"
Abstract: TBA
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Yulij Ilyashenko
"Global bifurcations on the two sphere: first steps of a new theory"
Abstract :This talk gives a survey of the first four years of the development of a new branch of the bifurcation theory: global bifurcations on the two sphere outlined in [1]. Bifurcations in generic one-parameter families were classified; the answer appeared to be somewhat unexpected [2] [3] [4] An important and non-trivial question "who bifurcates?" was answered. Natalya Goncharuk and the speaker defined a set called large bifurcation support; bifurcations that occur in a small neighborhood of this set determine the global bifurcations on the two-sphere [5]. This result is a starting point for systematic classification of global bifurcations in two-parameter families. Structurally unstable three-parameter families were discovered [6]; new examples were found recently. New numeric invariants for three-parameter families are recently found [7]. There was a conjecture that in a small neighborhood of a hyperbolic polycycle the family that unfolds it is structurally stable. This conjecture is now disproved. Functional invariants of topological classification of generic families of vector fields are found. Open problems will be stated.
Referenses
- Yu. Ilyashenko, Towards the general theory of global planar bifurcations, in the book “Mathematical Sciences withMultidisciplinary Applications, In Honor of Professor Christiane Rousseau. And In Recognition of the Mathematics for Planet Earth Initiative”, Springer 2016, pp 269 – 299.
- N. Solodovnikov, Global bifurcations in generic one-parameter families with a separatrix loop on S2, Moscow Math. J., 2018, pp. 93 â•fi 115
- N. Goncharuk, Yu. Ilyashenko, N. Solodovnikov, Global bifurcations in generic one-parameter families with a parabolic cycle on S2, to appear in MMJ
- V. Starichkova, Global bifurcations in generic one-parameter families on S2, Regular and Chaotic Dynamics, 2018, Vol. 23, No. 6, pp. 1 - 18.
- N. Goncharuk, Yu. Ilyashenko, Large bifurdation supports, submitted
- Yu. Ilyashenko, Yu. Kudryashov and I. Schurov , Global bifurcations in the two-sphere: a new perspective, Invent. math., 2018, Volume 213, Issue 2, pp 461 â•fi 506
- N. Goncharuk, Yu. Kudryashov, Bifurcations of the polycycle ‘tears of the heart’: multiple numerical invariants, to appear in MMJ
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Constantine Dafermos
"Zero Relaxation Limit"
Abstract: TBA