The SGGTC seminar meets on Fridays in Math 407 at 1pm, unless noted otherwise (in red).

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 Date Speaker Title Jan. 20 Wai-kit Yeung (Cornell University) Perverse sheaves, knot contact homology and relative Calabi-Yau completions Jan. 27-29 FRG Workshop: Crossing the Walls in Enumerative Geometry Feb. 3 Daniel Tubbenhauer (University of Bonn) Representation theory of Coxeter groups:Some first steps Feb. 10 Pavel Mnev (University of Notre Dame) TBA Feb. 17 Feb. 24 Mar. 3 Bohan Fang (Peking University) TBA Mar. 10 Weiwei Wu (University of Georgia) TBA Mar. 17 Mar. 24 Mar. 31 Ran Tessler TBA Apr. 7 Apr. 14 Apr. 21 Apr. 28

# Abstracts

#### January 20, 2017: Wai-kit Yeung " Perverse sheaves, knot contact homology and relative Calabi-Yau completions"

Abstract: In this talk, I will present joint work [arXiv:1610.02438] with Yu. Berest and A. Eshmatov, where we give a universal construction, called homotopy braid closure, that produces invariants of links in R^3 starting with a braid group action on objects of a (model) category. Applying this construction to the natural action of the braid group B_n on the category of perverse sheaves on the two-dimensional disk with singularities at n marked points, we obtain a differential graded (DG) category that gives knot contact homology in the sense of L. Ng. As an application, we show that the category of finite-dimensional modules over the 0-th homology of this DG category is equivalent to the category of perverse sheaves on R^3 with singularities at most along the link. If time allows, I will also discuss my recent work [arXiv:1612.06352] that generalizes this picture using non-commutative algebraic geometry.

#### February 3, 2017: Daniel Tubbenhauer " Representation theory of Coxeter groups:Some first steps"

Abstract: This talk is an introduction as well as a survey about 2-representation theory of Coxeter groups. The motivation to study such 'higher' representations is as follows: In groundbreaking work Chuang-Rouquier and, independently, Khovanov-Lauda introduced 2-representation theory of Lie algebras and their quantum analogs. As a 'higher' version of classical representation theory of Lie groups, their ideas have already led to many successive works as well as applications throughout mathematics (and physics). Historically speaking, what should have come first' is 2-representation theory of finite groups. Sadly the story of higher' representations of finite groups is not understood at all at the moment. But, quite recently, Mazorchuk-Miemietz made very good progress towards a 'higher' analog of representations of finite-dimensional algebras (as e.g. groups rings of finite groups), and applied it quite successful to one of the most well-behaved family of finite groups: finite Coxeter groups. Already in this case a lot of interesting new phenomena show up, most of which are neither present in classical representation theory nor in the story of Chuang-Rouquier, Khovanov-Lauda, and which might lead to interesting connections and applications in the years to come. However, in this talk we will focus on one (completely explicit) example, i.e. the first non-trivial family of examples given by the dihedral groups, where already several new phenomena are visible. Based on joint work with Marco Mackaay, Volodymyr Mazorchuk and Vanessa Miemiet

## Our e-mail list.

Announcements for this seminar, as well as for related seminars and events, are sent to the "Floer Homology" e-mail list maintained via Google Groups.