This Conference will pay tribute to the great discovery made by Feigenbaum in the mid 1970s and its ramifications (mostly in math) in the past 45 years. It will also serve as an introduction to the SCGP Workshop Many faces of renormalization held during the following week (June 1–5). Both events are part of the Program: Renormalization and universality in Conformal Geometry, Dynamics, Random Processes, and Field Theory: February 22 – March 19, 2021

Claude LeBrun is one of the foremost geometers in the world today. His original and profoundly influential research over the past forty years has consistently changed the landscape of the field. He has used ideas from physics, such as Penrose’s twistor theory, the Gibbons-Hawking Ansatz, and Seiberg-Witten invariants, to establish results that no one expected, and at the same time to disprove long-standing conjectures. His deep mathematical knowledge and talent has enabled him to make transformative contributions to a wide range of subjects. He has been at Stony Brook since 1983, and is a leading member of the differential geometry group in our department.

Stony Brook University

October 23-25, 2020

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. …