An Invitation to Enumerative Geometric Combinatorics (Andrés R. Vindas Meléndez, Harvey Mudd College)

Speaker: Andrés R. Vindas Meléndez, Assistant Professor of Mathematics, Harvey Mudd College, Claremont CA

Title: An Invitation to Enumerative Geometric Combinatorics

Abstract: Enumerative geometric combinatorics is an area of mathematics concerned with counting properties of geometric objects described by a finite set of building blocks. Lattice polytopes are geometric objects that can be formed by taking the convex hull of finitely many integral points. In this talk I will present background on polytopes, lattice-point enumeration, and share some results on special families and properties of polytopes that can be further studied. Throughout the talk I will present questions and open problems.

Bio:  Andrés R. Vindas Meléndez,  is an Assistant Professor of Mathematics at Harvey Mudd College. His research interests are in algebraic, enumerative, and geometric combinatorics. His scholarly interests have also expanded to include mathematical & computational approaches and applications of data science and mathematics for social justice. He has also been a research member for the SLMath Fall 2023 program on Algorithms, Fairness, & Equity and a research scholar at the Institute for Computational and Experimental Research Mathematics [ICERM] for the program on Data Science & Social Justice: Networks, Policy, & Education during the Summers of 2022 and 2023.

Prof. Andrés strives to create community in order to build mathematics users’ confidence in spite of society’s negative messages and stigma about mathematics. He also aims to build meaningful and empowering experiences with mathematics, while also challenging others to think about the power structures that are present in and outside mathematical spaces.