Details

In their 1971 study of telephone circuits, Graham and Pollak designed a novel addressing scheme that was better suited for the faster communication required by computers. They introduced the distance matrix of a graph, and used its eigenvalues to determine how short the addresses can be. We continue their investigation, obtaining more precise spectral information about tree distance matrices. These results, combined with the theory of Lorentzian polynomials, allow us to prove some conjectural inequalities about graphs and matroids that are very easy to state but have taken decades to prove.

Speaker

Federico Ardila-Mantilla is a Colombian-American mathematician and musician. He obtained his PhD from MIT in 2003 and has been a professor of mathematics at San Francisco State University since 2005. In his research, Ardila-Mantilla investigates objects in algebra, geometry, topology and applications by understanding their underlying combinatorial structure. His interests include polytopes, matroids, hyperplane arrangements, Lie and Coxeter combinatorics, Hopf algebras and tropical geometry.

Ardila-Mantilla loves working with and learning from students: he has advised over 50 thesis students. He founded the SFSU-Colombia Combinatorics Initiative, an international research and educational collaboration that also hosts more than 200 hours of free combinatorics lectures on YouTube. He also co-directed the Mathematical Sciences Research Institute Undergraduate Program in Berkeley, California, a summer research program designed to increase the participation of minoritized racial groups in mathematics.

He is a winner of the National Science Foundation CAREER Award for research, the Mathematical Association of America's National Haimo Award for Teaching and the American Mathematical Society's "Mathematics Programs that Make a Difference" Award for service. He is also a Fellow of the American Mathematical Society and the Colombian Academy of Science and an Invited Speaker at the International Congress of Mathematicians.

Federico is always searching for ways to grow and foster an increasingly diverse, equitable and welcoming community of mathematicians that empowers and serves the needs of all. His efforts are grounded on the following axioms:

1. Mathematical potential is equally present among different groups, irrespective of geographic, demographic, and economic boundaries.
2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
4. Every student deserves to be treated with dignity and respect.