Anton Bernshteyn

Email: bahtoh ~at~ gatech.edu
Office: Skiles 260

Welcome!

I am an Assistant Professor in the School of Mathematics at the Georgia Institute of Technology.

You can find my CV here (last update: Oct 26, 2023). Here's my Math Genealogy entry.

I am one of the organizers of the Atlanta Combinatorics Colloquium, a seminar in discrete mathematics jointly hosted by the combinatorics groups at the Georgia Institute of Technology, Georgia State University, and Emory University.

I am also currently co-organizing (together with Tom Kelly) the Georgia Tech Graph Theory/Combinatorics Seminars. Please shoot any of us an email if you'd like to give a talk!

Research

My main areas of research are combinatorics and descriptive set theory. Some particular topics I am interested in include: graph coloring, probabilistic methods, extremal combinatorics, and Borel/measurable combinatorics with applications to ergodic theory.

Papers and Preprints

With J. Anderson. Borel line graphs. Preprint (submitted).
With F. Weilacher. Borel versions of the Local Lemma and LOCAL algorithms for graphs of finite asymptotic separation index. Preprint (submitted).
With D. Dominik, H. Kaul, and J.A. Mudrock. DP-coloring of graphs from random covers. Preprint (submitted).
With A. Dhawan. Borel Vizing's theorem for graphs of subexponential growth. Preprint (submitted).
With A. Dhawan. Fast algorithms for Vizing's theorem on bounded degree graphs. Preprint (submitted).
With J. Yu. Large-scale geometry of Borel graphs of polynomial growth. Preprint (submitted).
With J. Anderson and A. Dhawan. Coloring graphs with forbidden almost bipartite subgraphs. Preprint (submitted).
Distributed algorithms, the Lovász Local Lemma, and descriptive combinatorics. Inventiones Mathematicae (2023).
With E. Lee. Weak degeneracy of graphs. Journal of Graph Theory (2023).
Equivariant maps to subshifts whose points have small stabilizers. Journal of Modern Dynamics (2023).
With T. Brazelton, R. Cao, and A. Kang. Counting colorings of triangle-free graphs. Journal of Combinatorial Theory, Series B (2023).
Probabilistic constructions in continuous combinatorics and a bridge to distributed algorithms. Advances in Mathematics (2023).
With J. Anderson and A. Dhawan. Coloring graphs with forbidden bipartite subgraphs. Combinatorics, Probability and Computing (2023).
Descriptive combinatorics and distributed algorithms. Notices of the American Mathematical Society, Feature Article (2022)
Borel fractional colorings of Schreier graphs. Annales Henri Lebesgue (2022).
With E. Lee. Searching for an intruder on graphs and their subdivisions. Electronic Journal of Combinatorics (2022).
With M. Delcourt and A. Tserunyan. Independent sets in algebraic hypergraphs. Journal of the European Mathematical Society (2022).
Local coloring problems on smooth graphs. Fundamenta Mathematicae (2022).
A fast distributed algorithm for (Δ+1)-edge-coloring. Journal of Combinatorial Theory, Series B (2022).
With C.T. Conley. Equitable colorings of Borel graphs. Forum of Mathemarics, Pi (2021).
On Baire measurable colorings of group actions. Ergodic Theory and Dynamical systems (2021).
A short proof of Bernoulli disjointness via the Local Lemma. Proceedings of the American Mathematical Society (2020).
Ergodic theorems for the shift action and pointwise versions of the Abért–Weiss theorem. Israel Journal of Mathematics (2020).
With O. Khormali, R.R. Martin, J. Rollin, D. Rorabaugh, S. Shan, and A.J. Uzzell. Regular colorings in regular graphs. Discussiones Mathematicae Graph Theory (2020).
With A. Kostochka and X. Zhu. Fractional DP-colorings of sparse graphs. Journal of Graph Theory (2020).
Multiplication of weak equivalence classes may be discontinuous. Transactions of the American Mathematical Society (2019).
Building large free subshifts using the Local Lemma. Groups, Geometry, and Dynamics (2019).
With A. Kostochka. DP-colorings of hypergraphs. European Journal of Combinatorics (2019).
With M. Tait. Improved lower bound for difference bases. Journal of Number Theory (2019).
Measurable versions of the Lovász Local Lemma and measurable graph colorings. Advances in Mathematics (2019).
The Johansson–Molloy Theorem for DP-coloring. Random Structures and Algorithms (2019).
With M. Delcourt, H. Towsner, and A. Tserunyan. A short nonalgorithmic proof of the containers theorem for hypergraphs. Proceedings of the American Mathematical Society (2019).
With A. Kostochka. On differences between DP-coloring and list coloring (in Russian). Matematicheskie Trudy (2018); English version.
With A. Kostochka. Sharp Dirac's theorem for DP-critical graphs. Journal of Graph Theory (2018).
With A. Kostochka and X. Zhu. DP-colorings of graphs with high chromatic number. European Journal of Combinatorics (2017).
The Local Cut Lemma. European Journal of Combinatorics (2017).
With A. Kostochka and S. Pron. On DP-coloring of graphs and multigraphs (in Russian). Siberian Mathematical Journal (2017); English version.
The asymptotic behavior of the correspondence chromatic number. Discrete Mathematics (2016).
New bounds for the acyclic chromatic index. Discrete Mathematics (2016).
With A. Kostochka. On the number of edges in a graph with no (k+1)-connected subgraphs. Discrete Mathematics (2016).
3-Regular subgraphs and (3,1)-colorings of 4-regular pseudographs (in Russian). Discrete Analysis and Operations Research (2014).
With N. Shilov. Robots in Space Multi-agent Problem: complexity, information and cryptographic aspects (in Russian). Modeling and Analysis of Information Systems (2013).

Other Writing

The \(\mathbb{G}_0\)-dichotomy.
An \(\ell_2\)-based proof of Gaboriau's theorem.
Linear Algebra (lecture notes).

Reading groups and seminars

I am currently co-organizing (together with Tom Kelly) the Georgia Tech Graph Theory/Combinatorics Seminars. Please shoot either of us an email if you'd like to give a talk!

Mentoring

Currently advised students

James Anderson, Ph.D.
Abhishek Dhawan (co-advised with Cheng Mao), Ph.D.
Jing Yu, Ph.D.

Currently supervised postdocs

Evelyne Smith-Roberge, 2022–present

Past advised students

Aaditya Raghavan, B.Sc, 2022
Eugene Lee, B.Sc./M.Sc, 2022

REUs, GRAs, etc.

Cameron Chang, Horace Fusco, Sarah Peterson, Faren Roth, and Henry Simmons, Georgia Tech REU, Summer 2022
Manuel Fernandez, GRA, Spring–Summer 2022
Tyler Brazelton, Ruijia Cao, and Akum Kang, undergraduate research project, Summer 2021

Teaching

Current Teaching

Applied Combinatorics (MATH 3012).

Highlights of Past Teaching

At Georgia Tech:

2023, Spring Probabilistic Combinatorics (MATH 7018).
2022, Fall Applied Combinatorics (MATH 3012) and Introduction to Graph Theory (MATH 4022).
2022, Spring Probabilistic Combinatorics (MATH 7018).
2021, Fall Descriptive Combinatorics (MATH 8803).
2021, Summer Undergraduate Research (MATH-2699 and MATH-4699).
2021, Spring Combinatorial Analysis (MATH 4032).
2020, Fall Introduction to Graph Theory (MATH 4022).

At CMU:

2019, Fall Combinatorics (21-301) and Algebraic Structures (21-373).
2019, Summer Research Topics in Combinatorics (21-499).
2019, Spring Set Theory (21-329).
2018, Fall Linear Algebra (21-341).

At UIUC:

2017, Fall A Mathematical World (MATH 181), Primary Instructor.
2015, Spring Applied Linear Algebra (MATH 415), TA.
- On List of Teachers Ranked as Excellent by Their Students.
2014, Fall Applied Linear Algebra (MATH 415), TA.
- On List of Teachers Ranked as Excellent by Their Students.

School of Mathematics Georgia Institute of Technology College of Science