**Problem of the Week**

**Math Club**

**DST and GT Day**

**Number Theory Conf.**

**Zassenhaus Conference**

**Hilton Memorial Lecture**

seminars:topsem:topsem_spring2018

**March 22**

Speaker:**Yair Hartman**(Northwestern University)

Title:**Stationary C*-Dynamical Systems***Abstract:*We introduce the notion of stationary actions in the context of C*-algebras, and prove a new characterization of C*-simplicity in terms of unique stationarity. This ergodic-theoretic characterization provides an intrinsic understanding for the relation between C*-simplicity and the unique trace property, and provides a framework in which C*-simplicity and random walks interact. Joint work with Mehrdad Kalantar.

**March 15 (Special time 2:30 pm)**

Speaker:**Gili Golan**(Vanderbilt University)

Title:**Invariable generation of Thompson groups***Abstract:*A subset $S$ of a group $G$ invariably generates $G$ if for every choice of $g(s)\in G$, $s\in S$ the set $\{s^{g(s)}:s\in S\}$ is a generating set of $G$. We say that a group $G$ is invariably generated if such $S$ exists, or equivalently if $S=G$ invariably generates $G$. In this talk, we study invariable generation of Thompson groups. We show that Thompson group $F$ is invariable generated by a finite set, whereas Thompson groups $T$ and $V$ are not invariable generated. This is joint work with Tsachik Gelander and Kate Juschenko.

**March 8**

Speaker:**Lisa Piccirillo**(UT-Austin)

Title:**Stein Knot Traces***Abstract:*Four-manifolds which admit a Stein structure have many nice properties, for example the Stein structure gives bounds on the genus function of the manifold and Stein cobordisms induce nontrivial maps on the Heegaard Floer homology of the boundary. However, handed an arbitrary four-manifold it can be difficult to determine whether it admits a Stein structure. A question in the field asked whether it is ever straightforward to detect Stein structures on particularly simple manifolds; more technically it asked whether the four manifold $X_n(K)$ obtained by attaching an $n$-framed 2-handle to $B^4$ along $K$ is Stein if and only if $n<\overline{tb}(K)$. We answer this in the negative, and in fact show that a Stein $X_n(K)$ can have $n$ arbitrarily much larger than $\overline{tb}(K)$. This talk will focus on the constructive part of our proof, a technique due largely to Osoinach for building knots $K$ and $K’$ with $X_n(K)$ diffeomorphic to $X_n(K’)$. This is joint work with Tom Mark and Faramarz Vafaee.

**March 1**

Speaker:**Jun Li**(University of Michigan)

Title:**The symplectomorphism groups of rational surfaces***Abstract:*This talk is on the topology of $Symp(M,\omega)$, where $Symp(M,\omega)$ is the symplectomorphism group of a symplectic rational surface $(M,\omega)$. We will illustrate our approach with the 5 point blowup of the projective plane. For an arbitrary symplectic form on this rational surface, we are able to determine the symplectic mapping class group (SMC) and describe the answer in terms of the Dynkin diagram of Lagrangian sphere classes. In particular, when deforming the symplectic form, the SMC of a rational surface behaves in the way of forgetting strand map of braid groups. We are also able to compute the fundamental group of $Symp(M, \omega)$ for an open region of the symplectic cone. This is a joint work with Tian-Jun Li and Weiwei Wu.

**February 22 (special two-part talk: see next entry)**

Speaker:**Olakunle Abawonse**(Binghamton University)

Title:**Topology of the Grunbaum-Hadwiger-Ramos Hyperplane Mass Partition Problem***Abstract:*In this talk, we will discuss a problem raised by Ramos that asks for the smallest dimension $d=\Delta(j,k)$ such that for any $j$ measures in $\mathbb{R}^d$, there are $k$ affine hyperplanes that simultaneously cut each measure into $2k$ equal parts. We will give a general configuration space/test map scheme for this problem and show how the theory of relative equivariant obstruction theory applies to this problem.

This is part of a candidacy talk, with committee Laura Anderson (chair), Ross Geoghegan and Michael Dobbins. It is open to all.

**February 22 (Special time: 4:15pm)**

Speaker:**Olakunle Abawonse**(Binghamton University)

Title:**Hyperplane Mass Partitions Via Relative Equivariant Obstruction Theory***Abstract:*We will give solutions to some of the few cases in which the minimum value $d=\Delta(j,k)$ is known. We will achieve this by showing the non-existence of a certain $G$-equivariant map. By the theory of relative equivariant obstruction theory, this problem reduces to evaluating some obstruction classes.

This is part of a candidacy talk, with committee Laura Anderson (chair), Ross Geoghegan and Michael Dobbins. It is open to all.

**February 15**

Speaker:**Carlos Vega**(Binghamton University)

Title:**Null Distance on a Spacetime***Abstract:*In contrast to the Riemannian setting, a Lorentzian manifold (M,g) is not known to possess any naturally induced distance function. I will first try to explain why that is, starting with some of the basics of spacetime (Lorentzian) geometry. We will then discuss a `null distance function' introduced in joint work with Christina Sormani, some of its properties, examples, and some open questions.

**February 8**

Speaker:**Russell Ricks**(Binghamton University)

Title:**A Rank Rigidity Result for Certain Nonpositively Curved Spaces via Spherical Geometry***Abstract:*To understand the geometry of nonpositively curved (NPC) spaces, it is natural to classify the various types of spaces that can occur. The Rank Rigidity Theorem for compact NPC manifolds separates the class of compact NPC manifolds into three very distinct types, and proves that nothing else can exist.A version of Rank Rigidity has been conjectured for more general NPC spaces (CAT(0) spaces). In this talk, we discuss some progress toward this general conjecture, by reducing the problem to looking at patterns on spheres. In particular, we prove the conjecture for certain NPC spaces with one-dimensional boundary. Unlike previous results in this area, there are no additional constraints on the CAT(0) space (such as a manifold or polyhedral structure).

**February 1**

Speaker:**Jonathan Williams**(Binghamton University)

Title:**Sewing a homotopy into pieces***Abstract:*In this talk, I will try to explain the title. There will be 4-manifolds, many pictures, and very little background needed.

**January 16**(algebra crosspost - meets in WH-100E at 2:50)

Speaker:**Jonas Deré**(KU Leuven Kulak)

Title:**Which manifolds admit expanding maps***Abstract:*In 1981, M. Gromov completed the proof that every manifold admitting an expanding map is, up to finite cover, homeomorphic to a nilmanifold. Since then it was an open question to give an algebraic characterization of the nilmanifolds admitting an expanding map. During my talk, I will start by introducing the basic notions of expanding maps and nilmanifolds. Then I explain how the existence of such an expanding map only depends on the covering Lie group and on the existence of certain gradings on the corresponding Lie algebra. One of the applications is the construction of a nilmanifold admitting an Anosov diffeomorphism but no expanding map, which is the first example of this type.

seminars/topsem/topsem_spring2018.txt · Last modified: 2018/03/22 16:25 by jwilliams

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