# Alexander Ruys de Perez

Office: Blocker 629A alperez [AT] math.tamu.edu TR 2-4; W 12-2 here

### 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.

### 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 Fall
Math 142-201, 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