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 Events
Stanford University
Wed 3 Jan 2018, 12:00pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Stability in the homology of Torelli groups
ESB 4133 (PIMS Lounge)
Wed 3 Jan 2018, 12:00pm-1:00pm

Abstract

The Torelli subgroups of mapping class groups are fundamental objects in low-dimensional topology, through some basic questions about their structure remain open. In this talk I will describe these groups, and how to use tools from representation theory to establish patterns their homology. This project is joint with Jeremy Miller and Peter Patzt. These "representation stability" results are an application of advances in a general algebraic framework for studying sequences of group representations.
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University of Adelaide
Wed 3 Jan 2018, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Equivariant formality of homogeneous spaces
ESB 4133 (PIMS Lounge)
Wed 3 Jan 2018, 3:15pm-4:15pm

Abstract

Equivariant formality, a notion in equivariant topology introduced by Goresky-Kottwitz-Macpherson, is a desirable property of spaces with group actions. Examples of equivariantly formal spaces include compact symplectic manifolds equipped with Hamiltonian compact Lie group actions and projective varieties equipped with linear algebraic torus actions. Less is known about compact homogeneous spaces G/K equipped with the isotropy action of K, which is not necessarily of maximal rank. In this talk we will review previous attempts of characterizing equivariant formality of G/K, and present our recent results on this problem using an analogue of equivariant formality in K-theory. Part of the work presented in this talk is joint with Jeffrey Carlson.
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Stanford University
Tue 9 Jan 2018, 3:00pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Totally geodesic submanifolds of Teichmuller space and the Kontsevich-Zorich cocycle
ESB 4133 (PIMS Lounge)
Tue 9 Jan 2018, 3:00pm-4:00pm

Abstract

One of the ways we understand Teichmuller space, endowed with the Teichmuller metric, is by studying Teichmuller discs. They exist in great abundance: There is a Teichmuller disc through any point and in any direction. Typically, their projection to moduli space is dense, and yet infinitely often their projection is a closed subvariety of moduli space called a Teichmuller curve. Recently, in joint work with Eskin, McMullen, and Mukamel, we discovered the first non-trivial examples of higher dimensional analogues of Teichmuller discs, namely totally geodesic submanifolds.

In this talk, we will explain that such higher dimensional totally geodesic submanifolds are much more rigid and rare than Teichmuller discs: Each must cover a closed subvariety of moduli space, and only finitely many such subvarieties exist in each moduli space. This result is an application of joint work with Eskin and Filip on the Kontsevich-Zorich cocycle. One of the goals of the talk will be to explain what this cocycle is and why it lies at the heart of Teichmuller dynamics.
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MIT
Mon 15 Jan 2018, 2:00pm SPECIAL
Topology and related seminars
ESB 4127
Floer transport and Lagrangian non-Abelianization
ESB 4127
Mon 15 Jan 2018, 2:00pm-3:00pm

Abstract

In this talk I will explain how to endow the moduli space of objects in certain wrapped Fukaya categories with a cluster structure. This will be achieved by counts of holomorphic disks between Lagrangians which are described by trivalent graphs. In particular, we will be recovering the Fock-Goncharov coordinates on the moduli space of flat connections on a surface and provide a symplectic interpretation for the non-Abelianization procedure via spectral networks.
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University of British Columbia
Wed 31 Jan 2018, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
TBA
ESB 4133 (PIMS Lounge)
Wed 31 Jan 2018, 3:15pm-4:15pm

Abstract

 
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