I am a PhD candidate in the Department of Mathematics at the University of Washington, Seattle advised by Rekha Thomas. My office is C20 PDL, and I can be reached by email at cbabecki(at)uw(dot)edu. I'm graduating in Spring 2023 and will be starting a postdoc at Caltech jointly supported by the Math and CMS departments in Fall 2023.

Here are my **CV** and **Research Statement**.

**Research Interests**: My research interests include combinatorics, discrete geometry, optimization, graph theory, spectral graph theory, and theoretical computer science.

**Teaching**: In Fall 2023, I will be teaching a special topics course on *Spectral Graph Theory (ACM 270)* in the CMS department at Caltech. Check out my CV for my past teaching & mentorship positions.

**Software**: I have written some Matlab code for computing graphical designs, which you can find at my GitHub. I host a gallery of graphical designs computed using this code.

**Structure and complexity of graphical designs for weighted graphs through eigenpolytopes** with David Shiroma

arXiv: 2209.06349

**What is... A graphical design?**

In the AMS Notices, October 2022.

PDF here

**Graphical designs and Gale duality** with Rekha Thomas. To appear in Mathematical Programming.

arxiv:2204.01873

**Codes, cubes, and graphical designs**. In the Journal of Fourier Analysis and Applications, 2021.

arxiv:2012.12376

**Higher order smallest parts functions and rank-crank moment inequalities from Bailey pairs** with Chris Jennings-Shaffer and Geoffrey Sangston. In Research in Number Theory, 2016.

arxiv:1608.08132

**The polyhedral structure of graphical designs**.

Presented at ICERM's Combinatorics and Optimization Workshop.

**Graphical designs and Gale duality**.

Presented at the University of Waterloo Algebraic Graph Theory Seminar.

**Codes, cubes, and graphical designs **.

Presented at the University of Washington Combinatorics and Geometry Seminar.

**Error correcting codes**.

Presented at the University of Washington Combinatorics and Geometry Pre-Seminar.