I am an Olga Taussky and John Todd - Von Kármán Postdoctoral Scholar Teaching Fellow at Caltech, jointly supported by the Mathematics and CMS departments. I am mentored by Venkat Chandrasekaran and Leonard Schulman in CMS and David Conlon in Math. I received a PhD from the Department of Mathematics at the University of Washington, Seattle in June 2023, advised by Rekha Thomas. I can be reached by email at cbabecki(at)caltech(dot)edu.

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 Winter 2025, I will be teaching Math 6b: Intro to Discrete Mathematics and Math 121b: Combinatorial Analysis in the Math 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.

**Sparse graphical designs via linear programming** with J. Carlos Martínez Mori and Hessa Al-Thani

arXiv: 2309.00765. To appear in OR Letters

**Spectrahedral geometry of graph sparsifiers** with Rekha Thomas and Stefan Steinerberger

arXiv: 2306.06204

**Eigenpolytope universality and graphical designs** with David Shiroma

In SIDMA.

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

In the AMS Notices, October 2022.

PDF here

**Graphical designs and Gale duality** with Rekha Thomas. 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.