Email: abernsht ~at~ math.cmu.edu
Office: 7101 Wean Hall
Welcome!
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 UrbanaChampaign under the supervision of Alexandr Kostochka and Anush Tserunyan.
You can find my CV here (last update: January 22, 2020).
I currently serve as the organizer of the ACO Seminar.
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 C.T. Conley. Equitable colorings of Borel graphs. Preprint.
 A short proof of Bernoulli disjointness via the Local Lemma. 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 (to appear).
 Ergodic theorems for the shift action and pointwise versions of the Abért–Weiss theorem. Israel Journal of Mathematics (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).
 With A. Kostochka and X. Zhu. Fractional DPcolorings 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. DPcolorings 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 JohanssonMolloy Theorem for DPcoloring. 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 DPcoloring and list coloring (in Russian). Matematicheskie Trudy (2018); English version.
 With A. Kostochka. Sharp Dirac’s theorem for DPcritical graphs. Journal of Graph Theory (2018).
 With A. Kostochka and X. Zhu. DPcolorings 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 DPcoloring 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).
 3Regular subgraphs and (3,1)colorings of 4regular pseudographs (in Russian). Discrete Analysis and Operations Research (2014).
 With N. Shilov. Robots in Space Multiagent Problem: complexity, information and cryptographic aspects (in Russian). Modeling and Analysis of Information Systems (2013).
Expository Writing
Reading groups and seminars
I currently serve as the organizer of the ACO Seminar. If you would like to give a talk or have questions or suggestions about the seminar, please email me!
This semester (Spring 2020) we are running a reading group on topics related to Szemerédi's theorem. Regular meetings are scheduled to be on Fridays at 4:45–6:00pm in 7201 Wean Hall. Please let me know if you would like to be added to the mailing list!
Teaching
Current Teaching
I am not teaching this semester (Spring 2020).
Highlights of Past Teaching
At CMU:
At UIUC:
Department of Mathematical Sciences
Carnegie Mellon University
Mellon College of Science
