Math

I enjoy building smooth 4-manifolds. In particular, I'm interested in using horizontal handles [LP22] to construct  fillings of 3-manifolds (which give rise to interesting embeddings, slice knots, etc.)

Spring 2026: Notes for my short presentation on the (purely) cosmetic surgery conjecture for Maggie Miller's topics course on open problems in low-dimensional topology.

Spring 2025: Illustrated the course notes written by Abhishek Shivkumar for Lisa Piccirillo's topics course on closed smooth 4-manifolds.

Upcoming

TBA

Past

April 25th, 2026: Graduate Student Topology and Geometry Conference (Rutgers), "Dehn Twister: Using Heegaard diagrams to construct 4-manifolds" (slides).

April 22nd, 2026: UT Austin Junior Topology Seminar, "Using Heegaard diagrams to construct 4-manifolds".

January 22, 2026: UT Austin, "Progress towards proving the (purely) cosmetic surgery conjecture" (notes).

November 18, 2025: UT Austin, "Horizontal handle decompositions and applications to embeddings" candidacy talk (slides).

April 2, 2025: UT Austin Junior Topology Seminar, "Horizontal Handle Decompositions and Fillings for S3p/q(K) ".

September 9, 2022: UT Austin Sophex Seminar, "Let's talk about SET" (slides).

August 9, 2019: YMC 2019, "Chebyshev Linearizations of Matrix Polynomials: Are They Well-Conditioned?" (poster on the same topic).

Talks

March 5, 2026: Temple College, "Drawing shapes for a living (while getting a PhD in mathematics)" invited outreach talk for a community college audience (slides).

Panels

June 26, 2026: "Graduate School Advice" panel discussion for students in the UT Summer Directed Reading Program

Aug. 28 & 29, 2024;  Jan. 15 & 16, 2025: "How to Succeed in UT Math Courses" panel discussions organized by the Sanger Learning Center

March 23, 2024: "Graduate Student Life at UT" panel discussion for admitted students