Carlos Arreche

Professional Preparation

Ph.D. - Mathematics
City university of New York - 2014

M.Phil. - Mathematics
City University of New York - 2012

M.A.St. - Pure Mathematics
University of Cambridge - 2009

A.B. - Mathematics
Princeton University - 2008

Research Areas

Differential Algebraic Geometry

Symbolic Computation

Algebraic Theory of Differential and Difference Equations

Galois Theories

Publications

Complex reflection groups as differential Galois groups 2025 - Extended Abstract

Symmedians as Hyperbolic Barycenters (Symédianes comme barycentres hyperboliques) 2024 - Journal Article

Twisted Mahler Discrete Residues 2024 - Journal Article

Computing discrete residues of rational functions 2024 - Conference Paper

Normal Reflection Subgroups of Complex Reflection Groups 2023 - Journal Article

Computing differential Galois groups of second-order linear q-difference equations 2022 - Journal Article

Mahler Discrete Residues and Summability for Rational Functions 2022 - Conference Paper

Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions 2021 - Journal Article

1

Awards

Outstanding Teaching Award for Tenure-Track Faculty - School of Natural Sciences and Mathematics, The University of Texas at Dallas [2021]

ISSAC Distinguished Student Author Award - Special Interest Group in Symbolic and Algebraic Manipulation, Association for Computing Machinery [2014]

Appointments

Associate Professor of Mathematics
The University of Texas at Dallas [2024–Present]

Assistant Professor of Mathematics
The University of Texas at Dallas [2017–2024]

Postdoctoral Visitor
Fields Institute for Research in Mathematical Sciences [2015–2015]
Thematic Program in Computer Algebra: Fall 2015

NSF Alliance Postdoctoral Fellow
North Carolina State University [2014–2017]

Funding

Computation of functional relations among solutions of difference and differential equations

$203,416 - National Science Foundation [2018/10–2021/09]

This project will develop algorithms to automatically discover functional properties of solutions of differential or difference equations by looking for symmetries encoded in a geometric object called the Galois group.