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

I am an assistant professor in University of Texas at San Antonio Mathematics Department.

I am interested in discrete and convex geometry, real algebraic geometry, convex optimization, randomized numerical analysis, and theory of computing.

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 .

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

I think context and contemporary connections matter for teaching timeless math wisdom.

So far I'm involved in designing:

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

(2) An course on introduction to discrete and continuous optimization,

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

**Interests.** Discrete and Convex Geometry, Real Algebraic Geometry, Convex Optimization, Randomized Numerics, Theory of Computation

- Multihomogenous Nonnegative Polynomials and Sums of Squares, Discrete and Computational Geometry, 2018. Journal version Alperen Ergür
- 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
- Approximating Nonnegative Polynomials via Spectral Sparsification, SIAM Journal on Optimization (SIOPT), 2019. Journal version Alperen Ergür
- Tropical Varieties for Exponential Sums, Mathematische Annalen, 2020. Journal version Alperen Ergür, Grigoris Paouris, J. Maurice Rojas
- On the Complexity of the Plantinga-Vegter Algorithm, ACM Symposium on Symbolic and Algebraic Computation (ISSAC), 2019. Conference version , Discrete & Computational Geometry, 2022. Journal Version Felipe Cucker, Alperen Ergür, Josue Tonelli-Cueto
- 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
- Smoothed Analysis for the Condition Number of Structured Real Polynomial Systems Mathematics of Computation, 2021. Journal version Alperen Ergür, Grigoris Paouris, J. Maurice Rojas
- The Rank of Sparse Random Matrices, ACM-SIAM Symposium on Discrete Algorithms (SODA), 2020. Conference version , Random Structures and Algorithms, 2022. Journal Version Amin Coja-Oghlan, Alperen A. Ergür, Pu Gao, Samuel Hetterich, Maurice Rolvien
- The Multivariate Schwartz-Zippel Lemma, SIAM Journal of Discrete Mathematics, 2022. Journal version M. Levent Doğan, Alperen A. Ergür, Jake Mundo, Elias Tsigaridas
- A Polyhedral Homotopy Algorithm for Real Zeros, Minor Revision @ Arnold Mathematical Journal Alperen A. Ergür, Timo de Wolff
- Functional Norms, Condition Numbers, and Numerical Algorithms in Algebraic Geometry, Accepted @ Forum Mathematics Sigma 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. Conference version Alperen A. Ergür, Josue Tonelli-Cueto, Elias Tsigaridas
- On the Bit Complexity of Computing Chow Forms, M. Levent Doğan, Alperen A. Ergür, Elias Tsigaridas
- Approximate Low-Rank Decomposition for Real Symmetric Tensors, Python implementation of Energy Increment Algorithm Juypter Notebook Alperen A. Ergür, Jesus Rebollo Bueno, Petros Valettas