PROGRAM
12:30 (Moscow time)
| Yu Jun | Professor, Beijing International Center for Mathematical Research |
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Bio: Jun Yu obtained PhD from ETH Zurich in 2012, and then did postdoc in IAS Princeton and MIT. He is now an assistant professor in Beijing international center for mathematical research at Peking University. His research field is representation theory and Langlands program, including the branching rule problem, the orbit method philosophy, and the beyond endoscopy program. |
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Restriction of unitary representations of Spin(N,1) to parabolic subgroups
The orbit method predicts a relation between restrictions of irreducible unitary representations and projections of corresponding coadjoint orbits. In this talk we will discuss branching laws for unitary representations of Spin(N,1) restricted to parabolic subgroups and the corresponding orbit geometry. In particular, we confirm Duflo's conjecture in this setting. This is a joint work with Gang Liu (Lorraine) and Yoshiki Oshima (Osaka).
13:30 (Moscow time)
| Dmitry Timashev | Professor, Moscow State University |
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Bio: Dmitry Timashev recieved PhD degree from Moscow State University in 1997. From 1997, he is working at the Department of Higher Algebra in the Faculty of Mathematics and Mechanics, Moscow State University, currently at the position of associate professor. His research interests include Lie groups and Lie algebras, algebraic transformation groups and equivariant algebraic geometry, representation theory and invariant theory. |
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Characterizing homogeneous rational projective varieties with Picard number 1 by their varieties of minimal rational tangents
Abstract: It is well known that rational algebraic curves play a key role in the geometry of complex projective varieties, especially of Fano manifolds. In particular, on Fano manifolds of Picard number (= the 2nd Betti number) one, which are sometimes called "unipolar", one may consider rational curves of minimal degree passing through general points. Tangent directions of minimal rational curves through a general point x in a unipolar Fano manifold X form a projective subvariety ℂ{x,X} in the projectivized tangent space ℙ(TxX), called the variety of minimal rational tangents (VMRT).
In 90-s J.-M. Hwang and N. Mok developed a philosophy declaring that the geometry of a unipolar Fano manifold is governed by the geometry of its VMRT at a general point, as an embedded projective variety. In support of this thesis, they proposed a program of characterizing unipolar flag manifolds in the class of all unipolar Fano manifolds by their VMRT. In the following decades a number of partial results were obtained by Mok, Hwang, and their collaborators.
Recently the program was successfully completed (J.-M. Hwang, Q. Li, and the speaker). The main result states that a unipolar Fano manifold X whose VMRT at a general point is isomorphic to the one of a unipolar flag manifold Y is itself isomorphic to Y. Interestingly, the proof of the main result involves a bunch of ideas and techniques from "pure" algebraic geometry, differential geometry, structure and representation theory of simple Lie groups and algebras, and theory of spherical varieties (which extends the theory of toric varieties).
The meeting will be held in the form of a webinar on the Zoom platform.
Pre-registration for the event is not required.
To join Zoom meeting（You can join in the meeting without a phone number）:
https://zoom.com.cn/j/61567007575?pwd=b1lJQlRZWmxKWnpCMkJQNGY3SEpCdz09
Meeting ID: 615 6700 7575
Password：742316
Instructions for installing and using the Zoom platform are available here:
https://support.zoom.us/hc/ru/articles/201362033-Начало-работы-на-ПК-и-Mac