Email: abernsht ~at~ math.cmu.edu
Office: 7101 Wean Hall
I am a Postdoctoral Associate in the Department of Mathematical Sciences at Carnegie Mellon University.
I did my Ph.D. at the University of Illinois at Urbana-Champaign under the supervision of Alexandr Kostochka and Anush Tserunyan.
You can find my CV here (last update: June 18, 2019).
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 M. Delcourt and A. Tserunyan. Independent sets in algebraic hypergraphs. Preprint.
- On Baire measurable colorings of group actions. Preprint.
- With A. Kostochka and X. Zhu. Fractional DP-colorings of sparse graphs. Journal of Graph Theory (to appear).
- Measurable versions of the Lovász Local Lemma and measurable graph colorings. Advances in Mathematics (to appear).
- With M. Tait. Improved lower bound for difference bases. Journal of Number Theory (to appear).
- Ergodic theorems for the shift action and pointwise versions of the Abért–Weiss theorem. Israel Journal of Mathematics (to appear).
- Multiplication of weak equivalence classes may be discontinuous. Transactions of the American Mathematical Society (to appear).
- Building large free subshifts using the Local Lemma. Groups, Geometry, and Dynamics (to appear).
- With A. Kostochka. DP-colorings of hypergraphs. European Journal of Combinatorics (to appear).
- 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 (to appear).
- 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).
Research Topics in Combinatorics (21-499). Course website.
Highlights of Past Teaching
Department of Mathematical Sciences
Carnegie Mellon University
Mellon College of Science