Rutgers Geometry/Topology seminar: Fall 2017 - Spring 2018

Tuesdays 3:30-4:30 in Hill 525


Fall 2017

Date Speaker Title (click for abstract)
Sep. 5th No Seminar
Sep. 12th Hongbin Sun (Rutgers) Geometric finite amalgamations of hyperbolic 3-manifold 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)
1pm-2pm Hill 005
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)

Abstracts

Geometric finite amalgamations of hyperbolic 3-manifold groups are not LERF

We will show that, for any two finite volume hyperbolic 3-manifolds, 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 7-dimensional manifolds defined by the octonion, their fundamental groups are not LERF.

An upper bound on the translation length in the curve complex

This 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 DAHA

Double 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 metrics

In 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 groups

The 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, well-understood. 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 3-manifolds. 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 3

We present a proof of Milnor conjecture in dimension 3, which says that any open manifold of non-negative Ricci curvature has a finitely generated fundamental group. The proof is based on the structure of Ricci limit spaces.

Organizers: Feng Luo, Xiaochun Rong, Hongbin Sun