Geometry and Topology Seminar 20192020
The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm  2:10pm.
For more information, contact Shaosai Huang.
Spring 2020
date  speaker  title  host(s)  

Feb. 7  Xiangdong Xie (Bowling Green University)  Minicourse 1  (Dymarz)  
Feb. 14  Xiangdong Xie (Bowling Green University)  Minicourse 2  (Dymarz)  
Feb. 21  Xiangdong Xie (Bowling Green University)  Minicourse 3  (Dymarz)
} Fall 2019
Fall AbstractsRuobing ZhangThis talk centers on the degenerations of CalabiYau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing CalabiYau metrics may exhibit various wild geometric properties with highly nonalgebraic features. First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating CalabiYau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner. Emily StarkThe relationship between the largescale geometry of a group and its algebraic structure can be studied via three notions: a group's quasiisometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic nmanifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasiisometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse. Max ForesterI will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of rightangled Artin groups and certain rightangled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao. Yu LiWe develop a structure theory for noncollapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere. Archive of past Geometry seminars20182019 Geometry_and_Topology_Seminar_20182019
