Serge Lang was a frequent visitor to our department. He spent many summers in Berkeley and often gave lectures to the Math Undergraduate Student Association (MUSA) after students returned to campus at the end of August. Each year from 1999 to 2005, Serge gave a MUSA lecture at 4PM on the first day of classes. MUSA and the Department of Mathematics continue the tradition by hosting a Serge Lang Undergraduate Lecture each fall (or occasionally spring).
The 2025 Serge Lang Undergraduate Lecture will be given on Thursday September 18th by Professor Federico Ardila-Mantilla - San Francisco State University
Room 60 - Evans Hall, 4 p.m. - 5 p.m.
Title: Inequalities for trees and matroids
Abstract: In their 1971 study of telephone switching circuitry, 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 bound the size of the addresses in their scheme. 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. Along the way we uncover a surprising appearance of Lorentzian polynomials in optimization and economics.
This is joint work with Sergio Cristancho, Graham Denham, Chris Eur, June Huh, and Botong Wang. The talk will assume no previous knowledge of these topics; it will be accessible to anyone with some knowledge of linear algebra.
Past Serge Lang Undergraduate Lecturers
2025-26 Federico Ardila-Mantilla
2024-25 Stefan Steinerberger
2023-24 Ken Ono
2022-23 Jeffrey Lagarias
2021-22 Stephon Alexander
2020-21 Steven Strogatz
2019-20 Persi Diaconis
2018-19 Helene Barcelo
2017-18 Keith Devlin
2016-17 Ravi Vakil
2015-16 Brian Conrad
2014-15 Tony DeRose
2013-14 Bjorn Poonen
2012-13 John Baez
2011-12 Jordan Ellenberg
2010-11 Andrew Granville
2009-10 Benedict H. (Dick) Gross
2008-09 Peter W. Jones
2007-08 John H. Conway
2006-07 William Stein