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Jackie Lang, Temple University
We will discuss the computation of the endomorphism algebra that was introduced last time.
Zongyuan Li, Binghamton University
Abstract: In this talk, we discuss sharp conditions for Liouville-type theorems in conformally invariant elliptic PDEs. These equations, known as "nonlinear Yamabe equations", find their applications in studying conformal metrics on Riemannian manifolds. Based on recent joint work with Baozhi Chu and Yanyan Li (Rutgers).
Yier Lin, University of Chicago
TBA
Rakvi, University of Pennsylvania
tba
Hiro Lee Tanaka, Texas State University
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Temple)
Abstract: A $G$--bundle over $X$ is a family of copies of $G$, with one copy for every element of $X$. Families like this arise when studying nice functions on manifolds (i.e., in Morse theory) -- where instead of families of groups, families of broken lines live on moduli of gradient trajectories. And just like $G$--bundles are classified by an object called $BG$, it turns out you can write down the object that classifies families of broken lines -- this object is the stack of broken lines. The amazing fact is that this (geometric) object has an incredibly deep connection to the (algebraic) idea of associativity, and I'll try to explain why this is true. If time allows (which it might not) I'll try to explain why this object is expected to play a central role in enriching Morse theory and various Floer theories over stable homotopy theory. This is joint work with Jacob Lurie.
In the morning background talk (10am in room 278), I will discuss some needed background for the afternoon.
Michael Landry, Saint Louis University
PATCH Seminar (joint with Bryn Mawr, Haverford, Penn, and Swarthmore)
Background talk (11:30am in room 278): Objects associated with 3-manifolds fibering over the circle
Abstract: A fundamental example in low-dimensional topology is a closed oriented 3-manifold fibering over the circle. Thurston's study of this example led to the celebrated Nielsen-Thurston classification of surface homeomorphisms and the Thurston norm on homology. I will introduce these concepts before further developing some of the rich structure present in the example, touching on flows, foliations, and homeomorphisms of surfaces with infinitely generated fundamental group. I will mention joint work with Minsky and Taylor that fits into the story.
Research talk (4:00pm in room 336): Toward a dynamical theory of Thurston's norm
Abstract: One might hope to generalize the picture described in the previous talk to the setting of 3-manifolds that do not necessarily fiber over the circle. I will give some of the history of this endeavor, mentioning three conjectures of Mosher from the 1990s. Then I will describe joint work with Tsang that aims to make progress on these conjectures using modern objects called veering branched surfaces.
There are no conferences next week.