**Problem of the Week**

**Math Club**

**BUGCAT 2019**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:topsem

We meet **Thursdays** at **2:50–3:50 pm** in **WH-100E** followed by refreshments served from 4:00–4:25 pm in WH-102. This semester's organizer is Jenya Sapir.

Some seminar speakers will also give a colloquium talk at **4:30 pm** on the same day as the seminar talk. This seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

The seminar has an announcement mailing list open to all. There is also a Google calendar with the seminar schedule (also in iCal).

**August 22**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**August 29**

Speaker:**Catherine Pfaff**(Queen's University)

Title:**Typical Trees: An $Out(F_r)$ Excursion***Abstract:*Random walks are not new to geometric group theory (see, for example, work of Furstenberg, Kaimonovich, Masur). However, following independent proofs by Maher and Rivin that pseudo-Anosovs are generic within mapping class groups, and then new techniques developed by Maher-Tiozzo, Sisto, and others, the field has seen in the past decade a veritable explosion of results. In a 2 paper series, we answer with fine detail a question posed by Handel-Mosher asking about invariants of generic outer automorphisms of free groups and then a question posed by Bestvina as to properties of $\mathbb R$-trees of full measure in the boundary of Culler-Vogtmann outer space. This is joint work with Ilya Kapovich, Joseph Maher, and Samuel J. Taylor.

**September 5**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**September 12**

Speaker:**Caglar Uyanik**(Yale University)

Title:**Dynamics on geodesic currents and atoroidal subgroups of $Out(F_N)$***Abstract:*Geodesic currents on surfaces are measure theoretic generalizations of closed curves on surfaces and they play an important role in the study of the Teichmuller spaces. I will talk about their analogs in the setting of free groups, and try to illustrate how the dynamics and geometry of the $Out(F_N)$ action reflects on the algebraic structure of $Out(F_N)$.

**September 19**

Speaker:**Cary Malkiewich**(Binghamton University)

Title:**What algebraic K-theory has to do with fixed-point theory***Abstract:*The goal of this talk is to give a gentle introduction to algebraic $K$-theory and the Dennis trace. We'll see how the concept naturally arises when we try to enumerate all the ways to algebraically count the fixed points of a map $f: X \rightarrow X$ for a finite CW complex $X$.

**September 26**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**October 3**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**October 10**

Speaker:**Inbar Klang**(Columbia University)

Title: Hochschild homology for $C_n$-equivariant things*Abstract:*After introducing Hochschild homology and topological Hochschild homology, I will talk about about the twisted versions of these that can be defined in the presence of an action of a finite cyclic group. I will discuss joint work with Adamyk, Gerhardt, Hess, and Kong in which we develop a theoretical framework and computational tools for these twisted Hochschild homology theories.

**SPECIAL DATE AND TIME: October 15, 1:15 - 2:15, WH 100E**(Joint with the Combinatorics Seminar)

Speaker:**Emanuele Delucchi**(Fribourg/Freiburg)

Title:**Fundamental Polytopes of Metric Spaces via Parallel Connection of Matroids***Abstract:*Motivated by applications in phylogenetics, Linard Hoessly and I tackle the problem of a combinatorial classification of finite metric spaces via their fundamental polytopes, as suggested by Vershik in 2010. We consider a hyperplane arrangement associated to every split pseudometric and, for tree-like metrics, we study the combinatorics of its underlying matroid. We give explicit formulas for the face numbers of fundamental polytopes and Lipschitz polytopes of all tree-like metrics, and we characterize the metric trees for which the fundamental polytope is simplicial.

**October 17**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

**October 24**

Speaker:**Nicholas Vlamis**(CUNY, Queen's College and Graduate Center)

Title:**Topology of (big) mapping class groups***Abstract:*Mapping class groups inherit a natural topology from the compact-open topology on homeomorphism groups. When the underlying surface is of infinite type, this topology is no longer discrete, which allows us to study these mapping class groups from the perspective of topological group theory. We will explain how to see that mapping class groups are Polish groups and how we can use topological aspects to prove algebraic statements.

**SPECIAL DATE AND TIME: October 28, 4:15 - 5:15, WH 100E**

Speaker:**Yash Lodha**(EPFL)

Title:**Property FW and smoothability***Abstract:*I shall describe joint work with Matte Bon and Triestino. We demonstrate that aperiodic actions of Kazhdan groups by countably singular diffeomorphisms on closed manifolds are smoothable. In the case of the circle, we obtain a proof that groups of piecewise linear or piecewise projective homeomorphisms are not Kazhdan unless they are finite. The key new idea is the application of Property FW, which is a weakening of Kazhdan's property (T).

**October 31**

Speaker:**Eduard Schesler**(Universität Bielefeld)

Title:**The Sigma conjecture for solvable $S$-arithmetic groups via discrete Morse theory on Euclidean buildings.***Abstract:*Given a finitely generated group $G$, the $\Sigma$ invariants of $G$ consist of geometrically defined subsets $\Sigma^k(G)$ of the set $S(G)$ of all characters $\chi: G\to \mathbf{R}$ of $G$. These invariants were introduced independently by Bieri-Strebel and Neumann for $k=1$ and generalized by Bieri-Renz to the general case in the late 80's in order to determine the finiteness properties of all subgroups $H$ of $G$ that contain the commutator subgroup $[G,G]$. In this talk we determine the Sigma invariants of certain $S$-arithmetic subgroups of Borel groups in Chevalley groups. In particular we will determine the finiteness properties of every subgroup of the group of upper triangular matrices $B_n(\mathbf{Z}[1/p]) < SL_n(\mathbf{Z}[1/p])$ that contains the group $U_n(\mathbf{Z}[1/p])$ of unipotent matrices where $p$ is any sufficiently large prime number.

**November 7**

Speaker:**Edgar Bering**(Temple University)

Title:**TBA***Abstract:*TBA

**November 14**

Speaker:**Ian Frankel**(Queens University)

Title:**TBA***Abstract:*TBA

**November 21**

Speaker:**Yu Zhang**(Ohio State University)

Title:**TBA***Abstract:*TBA

**November 28**

**December 5**

Speaker:**TBA**(Institution)

Title:**TBA***Abstract:*TBA

seminars/topsem.txt · Last modified: 2019/10/22 09:23 by sapir

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