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Current contacts: Dave Futer, Matthew Stover, or Sam Taylor.
The Seminar usually takes place on Wednesdays at 2:30 PM in Room 617 of Wachman Hall.
Samuel Taylor (Temple University)
Our goal will be to describe some work-in-progress (joint with Landry and Minsky) that classifies transverse surfaces to pseudo-Anosov flows on 3—manifolds. This is an introductory talk and there’ll be lots of background and examples.
Thomas Ng, Brandeis University
Abstract: Quotients of free products are natural combinations of groups that have been exploited to study embedding problems. These groups have seen a resurgence of attention from a more geometric point of view following celebrated work of Haglund--Wise and Agol. I will discuss a geometric model for studying quotients of free products. We will use this model to adapt ideas from Gromov's density model to this new class of quotients, their actions on CAT(0) cube complexes, and combination theorems for residual finiteness. Results discussed will be based on ongoing work with Einstein, Krishna MS, Montee, and Steenbock.
Anubhav Mukherjee, Princeton University
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: The groundbreaking research by Freedman, Kreck, Perron, and Quinn provided valuable insights into the topological mapping class group of closed simply connected 4-manifolds. However, the development of gauge theory revealed the exotic nature of the smooth mapping class group of 4-manifolds in general. While gauge theory can at times obstruct smooth isotopy between two diffeomorphisms, it falls short of offering a comprehensive understanding of the existence of diffeomorphisms that are topologically isotopic but not smoothly so. In this talk, I will elucidate some fundamental principles and delve into the origins of such exotic diffeomorphisms. This is my upcoming work joint with Slava Krushkal, Mark Powell, and Terrin Warren.
In the morning background talk (at 10am), I will give an overview of mapping class groups of 4-manifolds.
Jean-Pierre Mutanguha, Princeton University and IAS
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Abstract: Free-by-cyclic groups can be defined as mapping tori of free group automorphisms. I will discuss various dynamical properties of automorphisms that turn out to be group invariants of the corresponding free-by-cyclic groups (e.g. growth type). In particular, certain dynamical hierarchical decompositions of an automorphism determine canonical hierarchical decompositions of its mapping torus. In the intro talk, I will discuss how Bass-Serre theory (actions on simplicial trees) gives us a grip on these groups.
In the morning background talk, at 11:30am, I will introduce free-by-cyclic groups from a tree's point of view.
Chi Cheuk Tsang (UQAM)
The minimum dilatation problem asks for the minimum value of the dilatation among all pseudo-Anosov maps defined on a fixed surface. This value can be thought of as the smallest amount of mixing one can perform on the surface while still doing something topologically interesting. In this talk, we will present some recent progress on the fully-punctured version of this problem. The strategy for proving these results involves something called standardly embedded train tracks. We will explain what these are and formulate some future directions that may be tackled using this technology. This is joint work with Eriko Hironaka, and with Erwan Lanneau and Livio Liechti.
Rylee Lyman Rutgers University, Newark
Title/abstract TBA
Allison Miller, Swarthmore College
Title/abstract TBA
Michael Magee, Durham University
Title/abstract tba
Hongbin Sun, Rutgers University
Title/abstract tba
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