• Speaker: Eylem Zeliha Yildiz, MSU
• Title: From knot concordances to exotic 4-manifolds
• Date: 12/04/2017
• Time: 4:10 PM - 5:30 PM
• Place: C517 Wells Hall

I will discuss PL and smooth knot concordances in 3-manifolds and an application to constructing exotic 4-manifolds.

• Speaker: Daniel Le, University of Toronto
• Title: Finite linear groups and duality
• Date: 12/04/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Finite groups of Lie type provide an extremely rich source of examples for group theory and representation theory because they form a bridge between the discrete and continuous worlds. Deligne and Lusztig classified their representation theory following Drinfeld's crucial inspiration from the Langlands program. We describe how Deligne-Lusztig theory can be augmented using recent advances in the Taylor-Wiles method to obtain classifications of modular and integral representations of the finite linear group GL(3,q). This is joint work with B. Le Hung, B. Levin, and S. Morra.

• Speaker: Jianping Jiang, NYU Shanghai
• Title: SLE, Percolation and Ising Models
• Date: 12/05/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

We review the connection between SLE (Schramm-Loewner Evolution) and two-dimensional percolation. Then we focus on a certain scaling limit of the Ising model and how SLE methods yield exponential decay of correlations related to an old conjecture about particle masses.

• Speaker: Linhui Shen, Michigan State University
• Title: Cluster algebras and representation theory Part III
• Date: 12/07/2017
• Time: 10:00 AM - 10:50 AM
• Place: C304 Wells Hall

This is a continuation of the previous 2 talks.

• Speaker: Reza Bidar, MSU
• Title: Connection blocking in SL(n,R) quotients.
• Date: 12/07/2017
• Time: 2:00 PM - 3:00 PM
• Place: C304 Wells Hall

Let G be a connected Lie group and Γ⊂G a lattice. Connection curves of the homogeneous space M=G/Γ are the orbits of one parameter subgroups of G. To \textit{block} a pair of points m1,m2∈M is to find a \textit{finite} set B⊂M∖{m1,m2} such that every connecting curve joining m1 and m2 intersects B. The homogeneous space M is \textit{blockable} if every pair of points in M can be blocked. \par In this paper we investigate blocking properties of Mn=SL(n,R)/Γ, where Γ=SL(n,Z) is the integer lattice. We focus on M2 and show that the set of bloackable pairs is a dense subset of M2×M2, and we conclude manifolds Mn are not blockable. Finally, we review a quaternionic structure of SL(2,R) and a way for making co-compact lattices in this context. We show that the obtained quotient homogeneous spaces are not finitely blockable.

• Speaker: Xiaoqin Guo, University of Wisconsin-Madison
• Title: Harnack inequality, homogenization and random walks in a degenerate random environment
• Date: 12/07/2017
• Time: 4:10 PM - 5:00 PM
• Place: C304 Wells Hall

Stochastic homogenization studies the effective equations or laws that characterize the large scale phenomena for systems with complicated random dynamics at microscopic levels. In this talk, we explore the relation between stochastic homogenization and a probabilistic model called random motion in a random medium. In particular we focus on dynamics on the integer lattice which is non-reversible in time and defined by a non-divergence form linear operator which is non-elliptic. A difficulty in studying this problem is that coefficients of the operator are allowed to be zero. Using random walks in random media, we present a Harnack inequality and a quantitative result for homogenization for this random operator. Joint work with N.Berger (TU-Munich), M.Cohen (Jerusalem) and J.-D. Deuschel (TU-Berlin).