UT Junior Topology Seminar

The UT Junior Topology Seminar is run by and for graduate students interested in topology and geometric structures. Weekly talks are given by grads at all stages of the PhD program, on topics including introductions to foundational tools, exciting results from recent (or not-so-recent) papers, and students' original research. Speakers have the opportunity to gather constructive feedback after each talk.

The current semester's schedule is listed below. 

8/28 – "The Organizers"

Title: Organizing meeting and announcements

Abstract: Come sign up to give a talk! Is there anything you want to change about jtop this year? Any conference application deadlines coming up? Also, we will briefly talk about more organizing/volunteering opportunities.

9/2 – Jemma Schroder

Title: Corks & Exotica in Dimension 4

Abstract: This talk will be an introduction to exotic phenomena in dimension 4. We'll start with an overview of exotic phenomena in general and the h-cobordism theorem. We'll then discuss how its failure in dimension four can be used to build interesting h-cobordisms through surgery and handle attachments. Time permitting, we'll define corks and the cork theorem. This talk is aimed at 1st and 2nd years.

9/9 – Mark Saving

Title: What’s the deal with homotopy (co)limits?

Abstract: It is well-known that the fiber of an arbitrary continuous map is not homotopically well-defined. Instead, one must take the “homotopy fiber”, which involves a bizarre “fibrant replacement” construction and is only well-defined up to homotopy equivalence. What’s really going on here? On our journey to answer this question, we’ll learn why CW pairs are so important, what the universal property of homotopy (co)limits is, and why we fuse category theory and homotopy theory into infinity-category theory.

9/16 – Justin Chen

Title: Satellite operators and self-similarity

Abstract: In this talk, we'll investigate the action of satellite operators on the set of concordance classes of knots in S^3. In particular, we'll consider a conjecture by Cochran that the knot concordance set has a fractal structure, with satellite operators as self-similarity operators. Following Cochran's work, we'll look at different metric structures on the concordance set with respect to which this idea may be compatible.

9/23 – Hillary Kim

Title: Knot Floer Time

Abstract: I will be going over some theory behind Knot Floer but mainly some nice examples. There will be pictures!

9/30 – Ansel

10/7 – !! Bob Gompf (not jtop, but same time same place)

Title: On classifying smoothings of R^4 -- from the beginning to the present

Abstract: The field of 4-manifold topology was born around 1981 with two independent revolutionary breakthroughs: Freedman showed that topological 4-manifolds obeyed the well-developed theory of higher-dimensional manifolds, while Donaldson used gauge theory to show that smooth 4-manifolds are quite different from their high-dimensional counterparts. The clash between the two theories makes 4-manifold topology uniquely intricate within manifold theory. One of the most startling consequences is that unlike in other dimensions, Euclidean 4-space R^4 admits exotic smoothings. Equivalently, there are smooth 4-manifolds that are homeomorphic, but not diffeomorphic, to R^4. We will trace the classification theory of these manifolds from their discovery to the most recent development (joint with Aristotelis Panagiotopoulos) that they cannot be classified by any countable family of numerical invariants. 

10/14 – Adrian

Title: Seiberg-Witten and Parametrized Spectra

Abstract: 25 years ago Manolescu constructed a stable homotopy type from the Seiberg-Witten equations for 3-manifolds with b1=0. A few years ago Sasahira and Stoffregen show'd how to get a homotopy type from a 3-manifold with b1>0 provided that the triple-cup product vanishes. I hope to explain the ideas that went into these constructions as well as provide an argument that the stable homotopy type attained in the b1>0 case may actually be well-defined in the (bi)category of parametrized S1-equivariant spectra over CGWH spaces.

10/21 – Aru

10/28 – Sabian

11/4 – Jaewon*

*postdoc

11/11 – Amy

11/18 – Hongyi

11/25 – Thanksgiving, no jtop this week

12/2 – Abhishek