**Problem of the Week**

**Math Club**

**BUGCAT 2018**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:topsem:topsem_fall2018

**August 30**

Speaker:**Matt Zaremsky**(University at Albany)

Title:**The Bieri-Neumann-Strebel-Renz invariants of the Houghton groups***Abstract:*The Houghton groups $H_n$ are a family of groups that are straightforward to define but have a variety of bizarre and interesting properties. In this talk I will discuss my recent computation of the Bieri-Neumann-Strebel-Renz invariants $\Sigma^m(H_n)$ of the $H_n$. The computation reveals some geometry reminiscent of that expected for metabelian groups by Bieri's $\Sigma^m$-Conjecture, and has implications for the finiteness properties of certain subgroups of $H_n$. This talk will be self-contained, and I will not assume any particular familiarity with the Houghton groups or the BNSR-invariants.

**September 6**

Speaker:**Jonathan Williams**(Binghamton)

Title:**DGAs and Legendrian knots***Abstract:*In order to discuss recent work, I will introduce Legendrian contact homology as formulated by Chekanov.

**September 13**

Speaker:**Julie Bergner**(University of Virginia)

Title:**An introduction to 2-Segal sets via combinatorial examples***Abstract:*The notion of a 2-Segal object was recently defined by Dyckerhoff and Kapranov, and independently by Gálvez-Carrillo, Kock, and Tonks under the name of decomposition space. Whereas 1-Segal sets model the structure of a category, in which composition is defined and is associative, 2-Segal sets instead encode a more general structure in which composition need not exist or be unique, but is still associative when it is defined. The 2-Segal set associated to a graph gives a nice example where maps can be composed in different ways. In particular, following a definition of Dyckerhoff and Kapranov, this 2-Segal set has an associated Hall algebra which is much smaller than most natural examples of such algebras and has a curious description as a cohomology ring.

seminars/topsem/topsem_fall2018.txt · Last modified: 2018/09/17 12:27 by jwilliams

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