Organizing Committee
- Huijun Fan (SMS PKU)
symplectic geometry and mathematical physics, geometric analysis - Sergey Gorchinskiy (MI RAS)
algebra and geometry: algebraic geometry, K-theory - Hailiang Li (SMS CNU)
fluid mechanics, partial differential equations, analysis - Jinsong Liu (AMSS)
algebraic geometry: singularity theory - Yi Liu (BICMR)
Topology of 3-manifolds, hyperbolic geometry - Denis Osipov (MI RAS)
algebraic geometry, number theory, integrable system - Ye Tian (UCAS, AMSS)
Number Theory, Arithmetic Geometry, Iwasawa Theory - Alexey Tuzhilin (MSU)
geometry: Riemannian and metric geometry - Yue Yang (CE PKU)
computation mathematics and mechanics - Ping Zhang (AMSS)
P. D. E.: fluid equation and semi-classical analysis - Alexander Zheglov (MSU)
geometry: algebraic geometry, integrable system
PROGRAM
11:00 (МСК)
| Yongquan Hu MCM, AMSS |
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Bio: Yongquan Hu received PhD degree from University Paris-Sud in 2010. After that, he has worked at University of Rennes 1 (France) as a Maître de Conférence. Starting from 2015, he is a Professor at Morningside Center of Mathematics, Academy of Mathematics and Systems Science. His research interest lies in p-adic and mod p Langlands program. |
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Serre’s modularity conjecture and mod p Langlands program
Serre made a remarkable conjecture in his 1987 paper relating \(mod\) \(p\) representations of \(Gal(\bar{Q}/Q)\) to \(mod\) \(p\) modular forms. In this talk, I will review Serre’s conjecture (by numerical examples) and explain its relation to \(mod\) \(p\) Langlands program. I will also discuss some recent progress on the subject.
12:00 (GMT+3)
| Viktor Petrov S-Petersburg branch of Steklov Mathematical Institute of RAS |
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Bio: Viktor Petrov is a professor at St. Petersburg State University. He got his PhD degree in 2005 and Dr.Sci. degree in 2022, both from St. Petersburg State University. He was a postdoc at the University of Alberta (Edmonton, AB) and Max Planck Institute (Bonn, Germany). Viktor Petrov was awarded by the St. Petersburg Mathematical Society the prize for young mathematicians and won the "Young Russia Mathematics" contest (twice). |
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Tits construction and the Rost invariant.
Simple Lie algebras over an algebraically closed field of characteristic 0 are described by Dynkin diagrams. Over a non-closed field, the same Dynkin diagram can correspond to many simple algebras, so it is interesting to study constructions of simple Lie algebras and invariants that make it possible to recognize their isomorphism or reflect some of their properties. One such construction of exceptional (i.e., types \(E_6\), \(E_7\), \(E_8\), \(F_4\) or \(G_2\)) Lie algebras was proposed by Jacques Tits; the Jordan algebra and an alternative algebra are given as input, and the output is a Lie algebra, and all real forms of Lie algebras can be constructed in this way. One of the most useful invariants (with meaning in the third Galois cohomology group) was constructed by Markus Rost. We show that a Lie algebra of (outer) type \(E_6\) is obtained by the Tits construction if and only if the Rost invariant is a pure symbol. As an application of this result we prove a Springer-type theorem for an \(E_6\)-homogeneous manifold.
The meeting will be held in the form of a webinar on the Voov platform.
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