Monday, February 26, 2024

8:00 AM (Los Angeles), 11:00 AM (Toronto, New York), 5:00 PM (Zurich, Paris) 6:00 PM (Tel-Aviv)

Richard Borcherds

UC Berkeley

Vinberg's Algorithm and Kac-Moody algebras


Vinberg’s algorithm was introduced by Vinberg in order to calculate the fundamental domains of hyperbolic reflection groups, especially those coming from Lorentzian lattices. We will show how to use it to calculate the automorphism groups of some lattices, culminating in Conway’s spectacular discovery that the Dynkin diagram of the 26-dimensional even unimodular Lorentzian lattice  is the Leech lattice. We will then discuss some of the Kac-Moody algebras associated with Vinberg’s Dynkin diagrams.

Additional lectures on this topic:

About the Speaker

“In 1992 Borcherds was one of the first recipients of the EMS prizes awarded at the first European Congress of Mathematics in Paris, and in 1994 he was an invited speaker at the International Congress of Mathematicians in Zurich. In 1994, he was elected to be a Fellow of the Royal Society. In 1998 at the 23rd International Congress of Mathematicians in Berlin, Germany he received the Fields Medal together with Maxim KontsevichWilliam Timothy Gowers and Curtis T. McMullen. The award cited him “for his contributions to algebra, the theory of automorphic forms, and mathematical physics, including the introduction of vertex algebras and Borcherds’ Lie algebras, the proof of the Conway-Norton moonshine conjecture[14] and the discovery of a new class of automorphic infinite products.” In 2012 he became a fellow of the American Mathematical Society, and in 2014 he was elected to the National Academy of Sciences.”  (From Wikipedia)

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Vinberg Distinguished Lecture Series Scientific Committee

Nikolay Bogachev​

Sasha Kolpakov​

Alex Kontorovich

University of Toronto, Canada

University of Neuchâtel, Switzerland

Rutgers University, USA