I am currently a postdoctoral researcher at the Centro de Investigación en Matemáticas (CIMAT) in Guanajuato, Mexico, working with James Melbourne.
My research interests are in information theory, probability, combinatorics and convex geometry.
Actualmente soy posdoc en el Centro de Investigación en Matemáticas (CIMAT), Guanajuato, GTO México. Trabajo con James Melbourne.
Mi investigación centra en probabilidad, combinatoria, la teoría de información y la geometría convexa.
Entropic symmetrization resistance (with Mokshay Madiman), 2026+ (submitted).
Anti-concentration inequalities for log-concave variables on the real line (with Tulio Gaxiola, James Melbourne, Vincent Pigno). In XIV Symposium on Probability and Stochastic Processes. Springer, 2025. ISBN 978-3-031-96118-2.
Submodular function inequalities indexed by chordal graphs (with Mokshay Madiman), In proceedings of the 2023 IEEE International Symposium on Information Theory (ISIT), pages 2756–2761. IEEE, 2023.
A Study of Some Entropy Inequalities. PhD thesis, University of Delaware, 2023.
my CV.
Title:
Symmetrization Resistance
Abstract:
An asymmetric random variable X is said to be symmetrization resistant if every independent random variable Y that produces a symmetric sum X+Y has a greater variance than that of X. Asymmetric Bernoulli random variables were shown to be symmetrization resistant by Kagan, Mallows, Shepp, Vanderbei, and Vardi (1999); Pal (2008) gave a proof using stochastic calculus. Proving symmetrization resistance appears to be difficult: little is known about other asymmetric distributions. We introduce the notion of entropic symmetrization resistance which is the same as symmetrization resistance except that the entropy (rather than variance) of Y must exceed that of X. We show that Bernoulli random variables exhibit entropic symmetrization resistance exactly when they exhibit symmetrization resistance. We also extend the underlying entropy and variance inequalities to the hypercube. Finally, we explore the possibility of extensions to non-Bernoulli random variables. This talk is based on joint work with Mokshay Madiman.
Title:
Circularly Symmetric Complex Gaussian Random Vectors, Entropy, and Determinants
Abstract:
Circularly symmetric complex Gaussian (CSCG) random vectors are an elegant generalization of jointly Gaussian random vectors which have found use in communications engineering but seem to be little known to mathematicians. In this talk we will introduce jointly Gaussian and CSCG random vectors and cover some useful facts from the theory of CSCG random vectors. We will then briefly demonstrate two applications which link determinant inequalities for positive definite Hermitian matrices with information theory. This talk is intended to be accessible to first-year graduate students or advanced undergraduates, and is based on joint work with Mokshay Madiman (University of Delaware).
Single-Variable Calculus (Playlist)
Vector Calculus (Playlist)