- Postdoc, Carnegie Mellon University
- aergur@cs.cmu.edu

I am a postdoctoral researcher in CMU Theory of Computation group . My gracious hosts are Venkat Gruswami and Pravesh Kothari .

Before September 2019, I was used to discuss randomized numerics with Felipe Cucker
at Berlin, where we were hosted by
Peter Bürgisser .

I was also very fortunate to learn some very cool things in real algebraic and tropical geometry from Cynthia Vinzant .

I have learned high dimensional probability and convex geometry from Grigoris Paouris , toric geometry and computational algebraic geometry from J. Maurice Rojas . Maurice and Grigoris approved my PhD dissertation on August 2016.

I am originally from Denizli , Turkey . I still hope that one day, Turkish people will not be scared to dissent.

My research interests revolve around real algebraic geometry, discrete and convex geometry, optimization, high dimensional phenomena (such as concentration of measure), and connections of these topics with algorithms and complexity theory.

A statement of my research interests is here , and an informal summary of my writings is here .

- Probabilistic Condition Number Estimates For Real Polynomial Systems I: A Broader Family Of Distributions, Foundations of Computational Mathematics (FOCM), 2018. Alperen Ergür, J. Maurice Rojas, Grigoris Paouris
- Multihomogenous Nonnegative Polynomials and Sums of Squares, Discrete and Computational Geometry, 2018. Alperen Ergür
- Approximating Nonnegative Polynomials via Spectral Sparsification, SIAM Journal on Optimization (SIOPT), 2019. Alperen Ergür
- Tropical Varieties for Exponential Sums, Mathematische Annalen, 2019. Alperen Ergür, J. Maurice Rojas, Grigoris Paouris
- Plantinga-Vegter Algorithm Takes Average Polynomial Time, ACM Symposium on Symbolic and Algebraic Computation (ISSAC), 2019, (Journal version submission @ Discrete & Computational Geometry). Felipe Cucker, Alperen Ergür, Josue Tonelli-Cueto
- On the Number of Real Zeros of Random Fewnomials, Arxiv preprint, Accepted to SIAM Journal of Applied Algebra and Geometry (SIAGA). Peter Bürgisser, Alperen Ergür, Josue Tonelli-Cueto
- Probabilistic Condition Number Estimates For Real Polynomial Systems II: Structure and Smoothed Analysis, Arxiv preprint, Minor revision submitted to Mathematics of Computation. Alperen Ergür, J. Maurice Rojas, Grigoris Paouris
- The Rank of Sparse Random Matrices, Arxiv preprint, Accepted to ACM-SIAM Symposium on Discrete Algorithms (SODA), 2020, (Journal version submission @ Advances in Mathematics). Amin Coja-Oghlan, Alperen A. Ergür, Pu Gao, Samuel Hetterich, Maurice Rolvien
- The Multivariate Schwartz-Zippel Lemma, Arxiv preprint. Note: We noticed an error in Lemma 4.3, and found a way to fix it. This doesn't effect the results of the paper, so the lemma will be updated whenever we do a final revision (likely in Summer 2020). M. Levent Doğan, Alperen A. Ergür, Jake Mundo, Elias Tsigaridas
- A Polyhedral Homotopy Algorithm for Real Zeros, Arxiv preprint. Alperen A. Ergür, Timo de Wolff