- Faculty, University of Texas at San Antonio
- alperen.ergur@utsa.edu

I am an assistant professor in University of Texas at San Antonio Computer Science and Mathematics Departments.

** Reasonable person policy ** I like CMU SCS reasonable person policy:

Everyone will be reasonable

Everyone expects everyone else to be reasonable

No one is special

Do not be offended if someone suggests you are not being reasonable

** Teaching Interests ** My goal is to empower students with modern mathematical and computational skills, and cultivate algorithmic thinking.
So far I'm involved in designing the following courses:

(1) a probability theory course delivered in algorithmic context,

(2) an undergrad level introduction to optimization,

(3) two course abstract algebra series from a computational point of view.

** Seminar ** With Grigoris Paouris (TAMU) and Petros Valettas (Mizzou) we are running a student friendly research seminar
on Geometry, Probability, and Computing. Details about the seminar can be found here .

** Mentoring ** I very much enjoy working with undergraduate researchers. If you are a UTSA undergrad in Math, CS, or ECE, and find the topics of the seminar
above interesting, feel free to come talk to me. If you are UTSA grad student in CS or Math and interested in theory of computing, computational geometry, optimization, computational algebra
or randomized algorithms feel free to come talk to me.

** Research Interests (Low resolution)** I am interested in algorithms and complexity in algebra, geometry, combinatorics, and optimization. I focus on
probabilistic and numerical methods. My publications are divided into broad categories below.

** Research Interests (Higher resolution) ** I am interested in developing a geometric perspective on design and analysis of numerical algorithms. Geometry is vast and deep.
I understand/use bits from convex geometry, real algebraic geometry, discrete geometry, and geometry of high-dimensional linear spaces.

I am also interested in developing an algorithmic theory of real polynomials;
the goal is to be able to infer computational complexity of a problem from its description given by polynomial equations/inequalities.

- Multihomogenous Nonnegative Polynomials and Sums of Squares, Discrete and Computational Geometry, 2018. Journal version Alperen Ergür
- Approximating Nonnegative Polynomials via Spectral Sparsification, SIAM Journal on Optimization (SIOPT), 2019. Journal version Alperen Ergür
- Approximate Real Symmetric Tensor Rank, Python implementation of Energy Increment Algorithm Juypter Notebook Alperen A. Ergür, Jesus Rebollo Bueno, Petros Valettas

- On the Number of Real Zeros of Random Fewnomials, SIAM Journal on Applied Algebra and Geometry (SIAGA), 2019. Journal version Peter Bürgisser, Alperen Ergür, Josue Tonelli-Cueto
- The Rank of Sparse Random Matrices, Random Structures and Algorithms, 2022 Journal Version , ACM-SIAM Symposium on Discrete Algorithms (SODA), 2020. Extended Abstract Amin Coja-Oghlan, Alperen A. Ergür, Pu Gao, Samuel Hetterich, Maurice Rolvien

- Tropical Varieties for Exponential Sums, Mathematische Annalen, 2020. Journal version Alperen Ergür, Grigoris Paouris, J. Maurice Rojas
- The Multivariate Schwartz-Zippel Lemma, SIAM Journal of Discrete Mathematics, 2022. Journal version M. Levent Doğan, Alperen A. Ergür, Jake Mundo, Elias Tsigaridas

- Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions, Foundations of Computational Mathematics (FOCM), 2019. Journal version Alperen Ergür, Grigoris Paouris, J. Maurice Rojas
- Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems Mathematics of Computation, 2021. Journal version Alperen Ergür, Grigoris Paouris, J. Maurice Rojas
- A Polyhedral Homotopy Algorithm for Real Zeros, Arnold Mathematical Journal, 2022, Journal version Alperen A. Ergür, Timo de Wolff
- On the Complexity of the Plantinga-Vegter Algorithm, Discrete & Computational Geometry, 2022. Journal Version , ACM Symposium on Symbolic and Algebraic Computation (ISSAC), 2019. Extended Abstract Felipe Cucker, Alperen Ergür, Josue Tonelli-Cueto
- Functional Norms, Condition Numbers, and Numerical Algorithms in Algebraic Geometry, Forum Mathematics Sigma, 2022, Journal version Felipe Cucker, Alperen A. Ergür, Josue Tonelli-Cueto
- Beyond Worst-Case Analysis for Root Isolation Algorithms, ACM Symposium on Symbolic and Algebraic Computation (ISSAC), 2022. Extended Abstract Alperen A. Ergür, Josue Tonelli-Cueto, Elias Tsigaridas

- On the complexity of Chow and Hurwitz forms, M. Levent Doğan, Alperen A. Ergür, Elias Tsigaridas
- The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products, Erin Connely, Sameer Agarwal, Alperen A. Ergür, Rekha Thomas