Student Topology
Organizers: Ciprian Bonciocat & Hongjian Yang
Upcoming Events
Not every cork is strong, but many are strong. Meanwhile, many corks are given by involutions and hence have order two. Nonetheless, there exist infinite-order corks, constructed by Gompf. To celebrate the 10th anniversary of their introduction, we will discuss their strength.
Past Events
Classical Morse homology recovers the ordinary homology of a closed manifold using the data of critical points and gradient flows. In the 1990s, Cohen-Jones-Segal proposed a categorification of this data, called the "flow category", with an eye towards developing homotopical refinements of…
Harnack’s Curve Theorem is a classical result in plane curve geometry concerning the maximum number of connected components of a real algebraic curve. In this talk, we translate this classical problem into topology and present a proof using Smith theory and equivariant Bredon cohomology. If time…
Introductory talk
In this expository talk, I will explain Shing-Tung Yau's (丘成桐) proof that any two complex structures on CP^2 are biholomorphic to one another. In fact, Yau proved that any complex surface homotopic to CP^2 must be biholomorphic to the standard complex structure on CP^2. Fun Fact: In the same…
In this talk I will sketch some details of Lagrangian torus fibrations, including the Arnold-Liouville theorem, integral affine geometry, and the characteristic class of a fibration. Then I will talk a little about singularities of fibrations and give examples of Lagrangian torus fibrations for…
In this talk, we explore knot traces in smooth four-manifolds. We focus on the paper The Trace Embedding Lemma and Spinelessness by Kyle Hayden and Lisa Piccirillo. Time permitting, we may also step into the symplectic world, including some joint work in progress with Kai Nakamura…
The key ingredient in the combinatorial approach to Khovanov-Rozansky homology (which categorifies the sl_N Reshetikhin–Turaev invariant) is to make sense of the (2-)category of sl_N foams. I'll explain how this was done via categorified skew Howe duality by Queffelec and Rose.
In ordinary HF theory, the relevant moduli spaces can always be oriented, in order to produce a homology theory defined over Z. In this talk, I will discuss the question of orienting moduli spaces in the hat version of Real HF, at least when the branch locus is connected; the obstruction ends up…