Email: bernsht2 _at_ illinois _dot_ edu
Office: 129 Altgeld Hall
Welcome!
I am a fourth year Ph.D. student in the Mathematics Department at the University of Illinois at UrbanaChampaign.
My advisers are Alexandr Kostochka and Anush Tserunyan.
You can find my CV here (last update: March 28, 2018).
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
 A. Bernshteyn. Multiplication of weak equivalence classes may be discontinuous. Preprint.
 A. Bernshteyn. Building large free subshifts using the Local Lemma. Preprint.
 A. Bernshteyn, A. Kostochka, and X. Zhu. Fractional DPcolorings of sparse graphs. Preprint.
 A. Bernshteyn, M. Delcourt, H. Towsner, and A. Tserunyan. A short nonalgorithmic proof of the containers theorem for hypergraphs. Preprint.
 A. Bernshteyn. On Baire measurable colorings of group actions. Preprint.
 A. Bernshteyn. The JohanssonMolloy Theorem for DPcoloring. Preprint.
 A. Bernshteyn and A. Kostochka. On differences between DPcoloring and list coloring. Preprint.
 A. Bernshteyn. Measurable versions of the Lovász Local Lemma and measurable graph colorings. Preprint.
 A. Bernshteyn and A. Kostochka. Sharp Dirac’s theorem for DPcritical graphs. Journal of Graph Theory, to appear.
 A. Bernshteyn, A. Kostochka, and X. Zhu. DPcolorings of graphs with high chromatic number. European Journal of Combinatorics (2017).
 A. Bernshteyn. The Local Cut Lemma. European Journal of Combinatorics (2017).
 A. Bernshteyn, A. Kostochka, and S. Pron. On DPcoloring of graphs and multigraphs (in Russian). Siberian Mathematical Journal (2017); English version.
 A. Bernshteyn. The asymptotic behavior of the correspondence chromatic number. Discrete Mathematics (2016).
 A. Bernshteyn. New bounds for the acyclic chromatic index. Discrete Mathematics (2016).
 A. Bernshteyn and A. Kostochka. On the number of edges in a graph with no (k+1)connected subgraphs. Discrete Mathematics (2016).
 A. Bernshteyn. 3Regular subgraphs and (3,1)colorings of 4regular pseudographs (in Russian). Discrete Analysis and Operations Research (2014).
 A. Bernshteyn and N. Shilov. Robots in Space Multiagent Problem: complexity, information and cryptographic aspects (in Russian). Modeling and Analysis of Information Systems (2013).
Expository Notes
Teaching
Current Teaching
Set Theory and Forcing (MATH 574), TA. Course website.
Past Teaching
Department of Mathematics
University of Illinois at UrbanaChampaign
College of Liberal Arts & Sciences
