In this lecture Francis Brown (University of Oxford, LMS Distinguished Visiting Fellow at ICMU) will explain the work of a Ukrainian mathematician Georgy Voronyi from over a century ago on the minimal vectors of quadratic forms, and how this gives a decomposition of the space of symmetric matrices which is equivariant for the action of GLn(Z). This lecture will also demonstrate how this decomposition relates to recent work on the moduli space of tropical curves and abelian varieties, all from a very concrete perspective aimed at a level for students.

Francis Brown is an LMS Distinguished Visiting Fellow at ICMU. He has been a professor of mathematics  and a senior research fellow at All Souls College of the University of Oxford since 2015. Francis Brown studied at the University of Cambridge, École normale supérieure in Paris, and the University of Bordeaux. He obtained his PhD in 2006 under the guidance of Pierre Cartier. He then worked at the Institut de mathématiques de Jussieu – Paris Rive Gauche (2007-2012) and Institut des Hautes Études Scientifiques (2012-2015). His research interests cover various aspects of algebraic geometry and number theory, with applications to quantum field theory in mathematical physics.

On 26-29 November Francis Borown will give a course of lectures at ICMU entitled "Elementary recurrences, graph polynomials, and values of the Riemann zeta function".

The Ukrainian host is Masha Vlasenko, a professor at the Kyiv School of Economics and the Managing Director of ICMU.