The August Comprehensive Exams will be offered both in-person and online. If you wish to take the exam online, please contact Christine Gathman.

The Stony Brook Trustees Faculty Awards recognize early-career faculty whose research, creative activities, and scholarly achievements predict an exceptional trajectory.

Project: "Analytic Number Theory and Analysis of Discrete Structures"

Robert Hough is an Assistant Professor of Mathematics at Stony Brook University. His research focuses on analytic number theory and discrete probability.

Robert Hough is an Assistant Professor of Mathematics at SUNY Stony Brook. His research focuses on analytic number theory and discrete probability. His best known work solved one of Paul Erdos' favorite problems, the "minimum modulus problem for covering systems" and has appeared in the Annals of Mathematics. Dr. Hough won the Math Association of America's David P. Robbins Prize for this work. His current research concerns questions related to the enumeration of low degree number fields, extending some works cited in Manjul Bhargava's Fields medal, and studies the asymptotic mixing of large statistical physics models such as the abelian sandpile model and Kac model. A discussion of Dr. Hough's work on the 15-puzzle recently appeared in Quanta.

Percolation is a mathematical model for the filtering of a liquid through a porous material or the spread of a forest fire or an epidemic: the edges of some graph are declared open or closed depending on independent coin tosses, and then connected open clusters are studied. While simple to define, this model exhibits very complicated behavior, with non-trivial scaling exponents and dimensions.Centering on the 2D setting, we will discuss simple proofs of some important theorems, connection of percolation to other models,as well as remaining open questions. …

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March 2-6, 2020

The workshop will bring together experts in Analysis, Dynamics, Geometry and Probability. These fields have had fruitful interaction in the past and present. One example is the connection between Brownian motion, harmonic measure, analysis of singular integrals, and geometric properties of domains. Another example is dynamics interacting with geometric properties of quasiconformal mappings. Finally we mention the interaction between analytic and probabilistic methods and computational problems. The purpose of the workshop will be to share insights and foster further interaction between the fields. To this end, an emphasis will be given to talks being accessible to a broad audience of mathematicians and physicists. …

Sir Simon Donaldson, a permanent member of the Simons Center for Geometry and Physics (SCGP) and a professor in the Department of Mathematics, was recently named a recipient of the 2020 Wolf Prize in Mathematics for his contribution to differential geometry and topology. Professor Donaldson is jointly awarded the prize with Professor Yakov Eliashberg, Stanford University and Chairman of the Board of Trustees of the SCGP, for their outstanding contributions to mathematics over many years. …

This question was asked by mathematician Percy Diaconis in 1988 and was open until this year, when the solution was found by Robert Hough, assistant professor at mathematics department of SBU and Yang Chu, an undergraduate student working with Hough as part of Enhanced REU program sponsored by the Summer Math Foundation. They have posted a preprint in which they provide a full answer to this question.

Read more about it in this article in Quanta magazine.

Stony Brook University Distinguished Professor of Mathematics Mikhail Lyubich has been honored with membership to the elite American Academy of Arts and Sciences (AAAS), which recognizes the outstanding achievements of individuals in academia, the arts, business, government and public affairs.

A leader in the field of dynamical systems, Lyubich is Director of the Institute for Mathematical Sciences at Stony Brook. He is one of the founders of modern real and complex one-dimensional dynamics, having in many ways shaped the development of the field. …