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: Here is my teaching schedule for the 2025-26 academic year (at Caltech!):
Fall: Math 2 (Practical) Differential Equations -- a fairly standard college ODEs class
Winter: Math 6b Intro to Discrete Mathematics -- a first undergraduate course in graph theory
Spring: ACM 11 Intro to Computer Science and Engineering -- an intro to practical numerical methods and how to implement them in Matlab
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. In Operations Research 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. PDF here
Graphical designs and Gale duality with Rekha Thomas. In Mathematical Programming.
Codes, cubes, and graphical designs. In the Journal of Fourier Analysis and Applications.
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.
The spectrahedral geometry of graph sparsifiers.
Presented at ICERM's reunion workshop Discrete Optimization: Mathematics, Algorithms, and Computation.
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.