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Mehtaab Sawhney

Mehtaab Sawhney will receive his PhD from the Massachusetts Institute of Technology in 2024, under the supervision of Yufei Zhao.

While still a graduate student, Sawhney has achieved a stunning number of breakthroughs on fundamental problems across extremal combinatorics, probability theory, and theoretical computer science. He is a highly collaborative researcher whose partnership with Ashwin Sah has been particularly fruitful. His remarkable body of work has already transformed swathes of combinatorics. For example, working with Kwan, Sah and Simkin, he proved a 1973 conjecture of Erdős on the existence of high-girth Steiner triple systems; with Keevash and Sah he established the existence of subspace designs; with Jain and Sah he established sharp estimates for the singularity probability in a wide class of discrete random matrices; with Sah and Sahasrabudhe he showed the existence of the spectral distribution of sparse directed Erdős–Rényi graphs; and with Kwan, Sah and Sauermann, he developed highly novel tools in anti-concentration in order to prove the Erdős- McKay conjecture concerning edge statistics in Ramsey graphs.

Mehtaab was appointed as a Clay Research Fellow for a term of five years from 1 July 2024.

Photo: Mehtaab Sawhney

Ishan Levy

Ishan Levy will receive his PhD from the Massachusetts Institute of Technology in 2024, under the supervision of Michael Hopkins.

Levy is known for his deep and ingenious contributions to homotopy theory. His new techniques in algebraic K-theory have led to solutions of many old problems. In joint work with Burklund he established the rational convergence of the “Waldhausen tower” interpolating between the K-theory of the integers and one of the most important moduli spaces in the study of high dimensional manifolds, A(pt). He is most renowned for his work Ravenel’s “Telescope Conjecture.”

In the late 1970s Ravenel made a series of deep conjectures outlining a rich conceptual vision of stable homotopy. By the mid 1980s all but the Telescope Conjecture had been proved. For over 40 years this remained the most important problem in this part of homotopy theory. Levy’s methods in K-theory led him, Burklund, Hahn and Schlank, to the construction of counterexamples, and, in joint work with Burklund, Carmeli, Hahn, Schlank and Yanovski, to an estimate of the growth rate of the stable homotopy groups of spheres that was completely untouchable by previous methods.

Ishan was appointed as a Clay Research Fellow for a term of five years from 1 July 2024.

Photo: Archives of the Mathematisches Forschungsinstitut Oberwolfach