Anton Bernshteyn

Email: bahtoh ~at~ gatech.edu
Office: Skiles 221

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: April 20, 2021). Here's my Math Genealogy entry.

I am currently co-organizing (together with Zhiyu Wang and Xingxing Yu) the Georgia Tech Graph Theory Seminar. Please shoot any of us an email if you'd like to give a talk! I am also maintaining a list of online lectures and talks in mathematical logic and related areas.

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 E. Lee. Searching for an intruder on graphs and their subdivisions. Preprint.
Probabilistic constructions in continuous combinatorics and a bridge to distributed algorithms. Preprint.
Local coloring problems on smooth graphs. Preprint.
A fast distributed algorithm for (Δ+1)-edge-coloring. Preprint.
Distributed algorithms, the Lovász Local Lemma, and descriptive combinatorics. Preprint.
With C.T. Conley. Equitable colorings of Borel graphs. Preprint.
With M. Delcourt and A. Tserunyan. Independent sets in algebraic hypergraphs. Journal of the European Mathematical Society (to appear).
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

An \(\ell_2\)-based proof of Gaboriau's theorem.
Linear Algebra (lecture notes).

Reading groups and seminars

I am currently co-organizing (together with Zhiyu Wang and Xingxing Yu) the Georgia Tech Graph Theory Seminar. Please shoot any of us an email if you'd like to give a talk! I am also maintaining a list of online lectures and talks in mathematical logic and related areas. Here are some other resources for online talks:

Teaching

Current Teaching

Combinatorial Analysis (MATH 4032).
Reading course on descriptive combinatorics and related topics (MATH-8900-BER)

Highlights of Past Teaching

At Georgia Tech:

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