Alexander Ruys de Perez
Research
My interests are in algebraic and combinatorial applications to mathematical biology. Currently, I am working on ways to determine the convexity or nonconvexity of a neural code through the study of a related simplicial complex called the factor complex, the details of which are given in the paper below.
Papers

Neural codes and the factor complex, with Laura Matusevich and Anne Shiu. To appear in Advances in Applied Mathematics.
Talks
 "Max intersection completeness in the neural ideal",
 AMS Spring Southeastern Sectional Meeting, March 2019
 Graduate Students Organization Seminar at Texas A&M University, March 2019
 "Neural codes and convexity",
 Gathering in Graduate Expository Mathematics, February 2019
 "Standard form for neural codes",
 Graduate Students Organization Seminar at Texas A&M University, April 2018
Posters
 "Max intersection completeness in the neural ideal",
 Meeting on Applied Algebraic Geometry, April 2019
 Southwest Local Algebra Meeting, February 2019
 "A canonical form for neural codes",
 NSF/CBMS Regional Conference on Applications of Polynomial Systems, June 2018
 Texas Algebraic Geometry Symposium, April 2018
 Southwest Local Algebra Meeting, February 2018
Teaching
Math 150, 2019 FallMath 142201, 2019 Summer Session II
 MATH 220 Grader, Fall 2015
 MATH 308 Help Session, Spring 2016
 MATH 152 Recitation and Lab, Fall 2016
 MATH 152 Lab, MATH 251 Help Session, Spring 2017
 MATH 308 Grader, Summer 2017
 MATH 431 Grader, Fall 2017
 MATH 152 Recitation and Lab, Spring 2018
 Algebra Qualifying Exam Prep Course Instructor, Summer 2018
 MATH 151 Recitation and Lab, Fall 2018
 MATH 152 Recitation and Lab, Spring 2019
Algebra Qualifying Exam
For anyone studying for the algebra qualifying exam, I have compiled solutions to problems from the exams between January 2013 and January 2018. The solutions are below, organized by subject matter (e.g. ''Finite and Simple Groups'' contains all the problems related to Sylow theory). In the documents the problems are designated using the format ''month year.number''; for example J17.6 denotes Problem 6 from the January 2017 qual. Please email me if you think you've found any mistakes or typos.
Solutions to Algebra Qualifying Exam Problems by Subject: 

Finite and Simple Groups 
Group Theory 
Ring Theory 
Modules 
General Galois Theory 
More Galois Theory 
Linear Algebra 
Tensor Products 
Finite Fields and Random Problems 