Professors József Balogh and Yuliy Baryshnikov were recently named 2024 Simons Fellows in Mathematics by the Simons Foundation.

According to a recent press release from the Simons Foundation, “The Simons Fellows program extends academic leaves from one term to a full year, enabling recipients to focus solely on research for the long periods often necessary for significant advances.”

Prof. Jozsef Balogh, who works primarily in combinatorics, will pursue research advancing “the container method” during his fellowship. Many problems in combinatorics can be formulated as questions about independent sets in graphs and hypergraphs; applying the container method to these graphs helps illuminate patterns or extremal properties of those independent sets.

In fall 2023, Balogh was jointly awarded a prestigious Steele Prize for his work on the container method over the last decade.

For his fellowship, Prof. Yuliy Baryshnikov will work in two areas: analytic combinatorics and applied and stochastic topology. He plans to investigate outstanding topological issues involving the singular loci of meromorphic generating functions and the asymptotic behavior of their coefficients. He will also work on spaces of directed obstacle-avoiding paths and on the “stochastic phases” for general ergodic diffusions.

Last spring, Baryshnikov was jointly awarded grant funding from the U.S. Department of Defense to develop mathematical methods to analyze hybrid dynamics.