Date  Speaker  Title (click for abstract) 
Sep. 5th  No Seminar 

Sep. 12th  Hongbin Sun (Rutgers)  Geometric finite amalgamations of hyperbolic 3manifold groups are not LERF

Sep. 19th  Chenxi Wu (Rutgers)  An upper bound on the translation length in the curve complex

Sep. 26th  Semeon Artamonov (Rutgers)  Genus two analogue of A_1 spherical DAHA

Oct. 3rd  Xuwen Zhu (Stanford)  Deformation theory of constant curvature conical metrics

Oct. 6th (Friday)  Priyam Patel (UC Santa Barbara)  Algebraic and topological properties of big mapping class groups

Oct. 10th 


Oct. 17th  Jiayin Pan (Rutgers)  A proof of Milnor conjecture in dimension 3

Oct. 24th  Lizhi Chen (Lanzhou University, China) 

Oct. 31st 


Nov. 7th  Nadav Dym (Weizmann Institute of Science, Israel) 

Nov. 14th 


Nov. 21st  No Seminar  Happy Thanksgiving!

Nov. 28th  Kyle Hayden (Boston College) 

Dec. 5th 


Dec. 12th  Sam Taylor (Temple University) 

Geometric finite amalgamations of hyperbolic 3manifold groups are not LERFWe will show that, for any two finite volume hyperbolic 3manifolds, the amalgamations of their fundamental groups along nontrivial geometrically finite subgroups are always not LERF. A consequence of this result is: all arithmetic hyperbolic manifolds with dimension at least 4, with possible exceptions in 7dimensional manifolds defined by the octonion, their fundamental groups are not LERF. 
An upper bound on the translation length in the curve complexThis is a collaboration with Hyungyul Bsik and Hyunshik Shin. We found an asymptotic upper bound for the translation length in the curve complex for primitive integer points in a fibered cone. 
Genus two analogue of A_1 spherical DAHADouble Affine Hecke Algebra can be viewed as a noncommutative (q,t)deformation of the SL(N,C) character variety of the fundamental group of a torus. This deformation inherits major topological property from its commutative counterpart, namely Mapping Class Group of a torus SL(2,Z) acts by automorphisms of DAHA. In my talk I will define a similar algebra for a closed genus two surface and show that the corresponding Mapping Class Group acts by automorphisms of such algebra. (This talk is based on arXiv:1704.02947 joint with Sh. Shakirov) 
Deformation theory of constant curvature conical metricsIn this joint work with Rafe Mazzeo, we would like to understand the deformation theory of constant curvature metrics with prescribed conical singularities on a compact Riemann surface. We construct a resolution of the configuration space, and prove a new regularity result that the family of constant curvature conical metrics has a nice compactification as the cone points coalesce. This is one key ingredient to understand the full moduli space of such metrics with positive curvature and cone angles bigger than 2π. 
Algebraic and topological properties of big mapping class groupsThe mapping class group of a surface is the group of homeomorphisms of the surface up to isotopy (a natural equivalence). Mapping class groups of finite type surfaces have been extensively studied and are, for the most part, wellunderstood. There has been a recent surge in studying surfaces of infinite type and in this talk, we shift our focus to their mapping class groups, often called big mapping class groups. The groups arise naturally when studying group actions on surfaces (dynamics) and foliations of 3manifolds. In contrast to the finite type case, there are many open questions regarding the basic algebraic and topological properties of big mapping class groups. Until now, for instance, it was unknown whether or not these groups are residually finite. We will discuss the answer to this and several other open questions after providing the necessary background on surfaces of infinite type. This work is joint with Nicholas G. Vlamis. 
A proof of Milnor conjecture in dimension 3We present a proof of Milnor conjecture in dimension 3, which says that any open manifold of nonnegative Ricci curvature has a finitely generated fundamental group. The proof is based on the structure of Ricci limit spaces. 