Email: bahtoh ~at~ gatech.edu
Office: Skiles 260
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!
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).
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!
Currently advised students
Currently supervised postdocs
Past advised students
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
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).
- 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).
- 2017, Fall A Mathematical World (MATH 181), Primary Instructor.
- 2015, Spring Applied Linear Algebra (MATH 415), TA.
- 2014, Fall Applied Linear Algebra (MATH 415), TA.
School of Mathematics
Georgia Institute of Technology
College of Science