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)

10/14 – Adrian

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