Mon, September 28, 2020
Public Access

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September 2020
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11:00am [11:30am] Oorna Mitra, IMSc
Date and Time: Monday 28 September, 11.30 am - 12.30 pm Google Meet link: Speaker: Oorna Mitra, IMSc Title: Twisted Conjugacy in Linear Groups over Polynomial and Laurent Polynomial Algebras over Finite Fields Abstract: Given an automorphism \phi : G \to G, one has the \phi-twisted conjugacy action of G on itself, given by g.x = g x\phi(g^{-1}). The orbits of this action are called the \phi-twisted conjugacy classes. In this talk, we will talk about twisted conjugacy in general and special linear groups over F[t] and F[t, t^{-1}] where F is any subfield of the algebraic closure of \mathbb{F}_p. This is joint work with P. Sankaran. Some new results by Shripad Garge and myself regarding twisted conjugacy in other classical groups over \mathbb{F}_q[t] and \mathbb{F}_q[t,t^{-1}] will also be mentioned.

4:00pm [4:00pm] Frank Gounelas, TU Munich
Speaker: Frank Gounelas, TU Munich Time: Monday 28th September 4 to 5pm (joining time 3.50pm IST) Google Meet Link: Title: Curves on K3 surfaces Abstract: I will survey the recent completion (joint with Chen-Liedtke) of the remaining cases of the conjecture that a projective K3 surface contains infinitely many rational curves. As a consequence of this along with the Bogomolov-Miyaoka-Yau inequality and the deformation theory of stable maps, I will explain (joint with Chen) how in characteristic zero one can deduce the existence of infinitely many curves of any geometric genus moving in maximal moduli on a K3 surface. In particular this leads to an algebraic proof of a theorem of Kobayashi on vanishing of global symmetric differentials and applications to 0-cycles.