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

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

** Reasonable person policy ** I like (some quotes ) and 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 (still under development),

(4) a course on algorithmic foundations of data science: ad , syllabus

** 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, high school researchers, masters students, and postdoctoral researchers. If you find the topics
above interesting and already a student at UTSA feel free to come talk to me.

** Research Interests ** I am interested in real algebraic geometry, convex geometry, randomized numerical algorithms,
optimization, and theory of computing. Combinatorics is natural and beatiful to me, so I dabble into it time to time.
My publications are divided into broad categories below.

- 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, Arnold Mathematical Journal, 2023. Journal version Python implementation of Energy Increment Algorithm 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
- On the Number of Real Zeros of Random Sparse Polynomial Systems, Alperen A. Ergür, Máté L. Telek, Josué Tonelli-Cueto

- 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
- On the Number of Iterations of the DBA Algorithm, SIAM Conference on Data Mining, 2024. Conference version Frederik Brüning, Anne Driemel, Alperen Ergür, Heiko Röglin

- 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 An implementation of this algorithm by Lee, Lindberg, Rogriguez Realhomotopy.jl Alperen A. Ergür, Timo de Wolff
- On the Complexity of the Plantinga-Vegter Algorithm, Discrete & Computational Geometry, 2022. Journal Version , ACM Symposium on Symbolic 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 Computation (ISSAC), 2022. Extended Abstract Alperen A. Ergür, Josue Tonelli-Cueto, Elias Tsigaridas
- On the complexity of Chow and Hurwitz forms, ACM Communications in Computer Algebra Journal version M. Levent Doğan, Alperen A. Ergür, Elias Tsigaridas
- The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products, Advances in Geometry (to appear) Erin Connely, Sameer Agarwal, Alperen A. Ergür, Rekha Thomas