Alperen A. Ergür- Personal Web Page

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 (with Claire Walton),
(3) a course on algorithmic foundations of data science
(4) s seminar style course on Reinforcement Learning
(5) abstract algebra series from a computational point of view (with Henry Chimal Dhuzul-under development),

Seminar I am involved in organizing our two freshly starting seminars: Algorithms Seminar, and Optimization seminar. For the moment, I am also part of Math Dept Colloquium organization.
In the past, with Grigoris Paouris and Petros Valettas we had a student friendly research seminar on Geometry, Probability, and Computing. Details about the seminar can be found here .

Creative Math Circle With Suleyman Tek and Rodrigo Velez we started a creative/competitive math circle for middle schoolers. Currently we only take 6th graders. Contact S. Tek if you are interested.

Mentoring I very much enjoy working with undergraduate researchers, graduate students, and postdoctoral researchers. If you find the topics below interesting; stop by my office to chat.

Research Interests I am interested in real algebraic geometry, convex geometry, randomized numerical algorithms, algebraic algorithms, optimization, theory of computing, and reinforcement learning. I love Combinatorics since high school :). My publications are divided into broad categories below.
Here are two podcasts that summarize my research according to AI: Summary 1 - Real Algebraic Geometry Focused , Summary 2 - Probability Focused Overview

Optimization

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

Probability

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
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
On the Number of Real Zeros of Random Sparse Polynomial Systems, Alperen A. Ergür, Máté L. Telek, Josué Tonelli-Cueto

Algorithms in Discrete, Algebraic, and Convex Geometry

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

Algebraic Geometry and Combinatorics

The Geometry of Rank Drop in a Class of Face-Splitting Matrix Products, Advances in Geometry, 2024 Journal version Erin Connely, Sameer Agarwal, Alperen A. Ergür, Rekha Thomas
The Multivariate Schwartz-Zippel Lemma, SIAM Journal of Discrete Mathematics, 2022. Journal version M. Levent Doğan, Alperen A. Ergür, Jake Mundo, Elias Tsigaridas
Tropical Varieties for Exponential Sums, Mathematische Annalen, 2020. Journal version Alperen Ergür, Grigoris Paouris, J. Maurice Rojas