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 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 Fall 2023, I am 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.
Sparse graphical designs via linear programming with J. Carlos Martínez Mori and Hessa Al-Thani
arXiv: 2309.00765
Spectrahedral geometry of graph sparsifiers with Rekha Thomas and Stefan Steinerberger
arXiv: 2306.06204
Eigenpolytope universality and graphical designs with David Shiroma
arXiv: 2209.06349 To appear 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.