Research

I am a graduate student at the University of Georgia and my advisor is David Gay. My interests lie in low dimensional topology. Lately, I have been thinking about diffeomorphisms of 4-manifolds, knotted surfaces, and exotic phenomena. 

Talks

Here are some talks I've given recently about my work,  with notes included when I can. Any mistakes are my own! You can also find notes from some expository talks in a separate list at the bottom. 

Invited talks:

A Cork Theorem for Diffeomorphisms

University of Virginia Geometry Seminar, December 2023.
Special Session in Topology of 3- and 4-Manifolds at the AMS Central Sectional meeting, October 2023.

Diffeomorphisms of the 4-sphere (notes)

Cornell Topology Festival, May 2023.

Diffeomorphisms and the Goeritz Group of a Trisection 

Topology in Dimension 4.5 at BIRS, November 2022. 

Twisted trisections (notes)

Special Session on 4-dimensional Topology at the AMS Western Sectional Meeting, October 2022.
Special Session on Interactions Between 3- and 4-Manifolds at the AMS Southeast Sectional Meeting, October 2022.
Virtual Trisectors meeting, May 2022.


Contributed talks:

Corks for Diffeomorphisms

GA Tech Topology Conference, December 2023.

Twisted Trisections (notes)

Temple GTA conference, May 2022.
UGA graduate student topology seminar, February 2022.

Slice Knots and an interestingly uninteresting example

GT GAPS, August 2020.

When is a^n+1 the sum of two squares? (with Kylie Hess and Emily Stamm) 

Joint math meetings (Atlanta, GA),  Jan 2017.
UGA mock AMS conference, July 2016.

Expository talks: 

Exotic phenomena in dimension 4

UGA graduate student topology seminar, September 2023.

What is spin? 

UGA graduate student topology seminar, February 2023.

Visualizing knotted surfaces in 4-space (with Geunyoung Kim)

UGA graduate student topology seminar, August 2022.

Knot Floer Homology and Concordance Invariants 

UGA Heegaard Floer Reading Seminar May 2022.

The secret life of the contractible 4-manifold 

UGA student topology seminar, November 2021. 

Strong corks (with Siddhi Krishna)

AIM Reading Seminar, May 2021.

The Conway knot is not slice (notes)

UGA oral exam, November 2020.

Complex tangencies of a Stein manifold (notes)

UGA student topology seminar, March 2020.

Slice knots and related topics

UGA graduate student seminar, November 2019.

Heegaard Diagrams and Knot Floer Homology 

Heegaard Floer reading seminar, September 2019.

Categorification of the Jones polynomial (notes)

UGA graduate student seminar, March 2019.

Introduction to contact topology (notes)

UGA student topology seminar, February 2019.

What makes a metric super? 

UGA mock AMS conference, July 2018.

Fantastic primes and how to find them

UGA graduate student seminar, March 2018.

Past Conferences/Workshops:

AMS Central Sectional meeting, October 2023.

Trisectors Worskhop 2023: Connections with Symplectic Topology at UC Davis, June 2023.

Georgia Topology Conference at UGA, May 2023.

Cornell Topology Festival at Cornell, May 2023.

Log Cabin Conference on Concordance and Knotted Surfaces in Sedona, March 2023.

Morphisms in Low Dimensions  at Oberwolfach, January 2023.

Topology in Dimension 4.5 at BIRS, November 2022.

AMS Western Sectional Meeting, October 2022.

AMS Southeast Sectional Meeting, October 2022.

Tech Topology Student Workshop, at GA Tech, July 2022.

Trisectors Workshop, at Western Washington University, June 2022.

Temple GTA conference, May 2022.

Georgia Topology Conference at UGA, May 2022.

Grad Student Geometry and Topology Conference, at GA Tech, April 2022.

Tech Topology Conference, at GA Tech, Dec 2021.

Tech Topology Summer School (virtually), July 2021.

PCMI Illustrating Math (virtually), July 2021.

Georgia Topology Conference (virtually), at UGA, June 2021.

Summer Trisectors Workshop (virtually), June 2021.

Graduate Student Topology and Geometry Conference (virtually), April 2021.

Winter Trisectors Workshop (virtually), December 2020.

Tech Topology Conference (virtually), December 2020.

GOATS (virtually), April 2020.

Tech Topology Conference, December 2019.

MPIM Workshop on 4-manifolds, September 2019.

Four Manifolds: Confluence of High and Low Dimensions, July 2019.

LG&TBQ, June 2019.

Graduate Student Conference in Algebra, Geometry, and Topology, June 2019.

Spring Trisectors Meeting, April 2019.

Virginia Topology Conference, December 2018.

Tech Topology Conference, December 2018.

Open Questions in Cryptography and Number Theory, Sept 2018.

Thirteenth Algorithmic Number Theory Symposium, July 2018.

Connecticut Summer School in Number Theory, June 2018.

Joint Math Meetings (Atlanta, GA), Jan 2017.

Wake/Davidson Experience in Number Theory Research (REU), May 2016. 


Publications and preprints:

G. Dresden, K. Hess, S. Islam, J. Rouse, A. Schmitt, E. Stamm, T. Warren, P. Yue, "When is an + 1 the sum of two squares?", Involve 12 (2019), no. 4, 585-605.