Carlos Arreche

Carlos Arreche

Assistant Professor - Mathematical Sciences
FO 2.408D
Personal webpage
Tags: differential algebraic geometry symbolic computation algebraic theory of differential and difference equations Galois theories

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


Computing differential Galois groups of second-order linear q-difference equations 2022 - Journal Article
Normal Reflection Subgroups of Complex Reflection Groups 2021 - Journal Article
Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions 2021 - Journal Article
Normal Reflection Subgroups 2020 - Conference Paper
Galois groups for integrable and projectively integrable linear difference equations 2017 - Journal Article
Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation 2016 - Journal Article
On the computation of the parameterized differential Galois group for a second-order linear differential equation with differential parameters 2016 - Journal Article
Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation 2014 - Journal Article


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]


Assistant Professor of Mathematics
The University of Texas at Dallas [2017–Present]
NSF Alliance Postdoctoral Fellow
North Carolina State University [2014–2017]


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.