School of Mathematics

Georgia Institute of Technology

686 Cherry Street

Atlanta, GA 30332

Office: Skiles 024

E-mail Address: bernstein [at] math [dot] gatech [dot] edu

I am a visiting assistant professor of mathematics
at Georgia Tech.

Research:

My research is in the fields of probability and combinatorics. This includes finding Markov chain mixing times, such as for random walks on the symmetric group

(also known as card shuffles), using tools from representation theory, algebraic combinatorics, and probability.

My thesis under Persi Diaconis titled Random Walks on the Symmetric Group, Likelihood Orders, and Involutions

My research is in the fields of probability and combinatorics. This includes finding Markov chain mixing times, such as for random walks on the symmetric group

(also known as card shuffles), using tools from representation theory, algebraic combinatorics, and probability.

- Cutoff for biased transpositions. M. Bernstein, N.
Bhatnagar, I. Pak. Submitted arxiv

- Analyzing Boltzmann Samplers for Bose-Einstein Condensates with Dirichlet Generating Functions. M. Bernstein, M. Fahrbach, D. Randall, Proceedings of ANALCO18 arxiv
- On sampling graphical Markov models. M. Bernstein, P. Tetali. Submitted arxiv
- Cutoff for random to random card shuffle. M. Bernstein, E. Nestoridi. Submitted arxiv
- A random walk on the symmetric group generated by random involutions. M. Bernstein. Accepted, to appear in Electronic Journal of Probability arxiv
- The Mixing Time for a Random Walk on the Symmetric Group
Generated by Random Involutions. M. Bernstein. Proceedings of the 28-th International
Conference on Formal Power Series and Algebraic Combinatorics [pdf]

- Likelihood orders for the p-cycle walks on the symmetric group. M. Bernstein. Accepted, to appear in Electronic Journal of Combinatorics [pdf]

My thesis under Persi Diaconis titled Random Walks on the Symmetric Group, Likelihood Orders, and Involutions

Teaching:

- Math 3670-D Spring 2018, Probability and Statistics with Applications

- Math 4221-A Fall 2017, Stochastic Processes
- Math 4032-A Spring 2017, Combinatorial Analysis
- Math 1552-G Fall 2016, Integral Calculus
- Math 3012-K Spring 2016, Applied Combinatorics
- Math
3012-C Fall 2015, Applied Combinatorics

- Handouts from Stanford's Math 51 Winter 2014