During his visit to Kyiv, Francis Brown (University of Oxford) will give a series of accessible lectures introducing several themes on the crossroads of number theory and quantum physics:

• recurrences arising from elementary families of integrals

• graph polynomials

• counting solutions to algebraic equations over finite fields

"I will use examples of certain elementary families of integrals, of the style discovered by Apery in his famous proof of the irrationality of ζ(3), to show how all the above themes connect to each other. In brief, certain families of integrals give rise to a polynomial recurrence relation which relate to many different fields of mathematics. The solutions to this recurrence relation may be used, via the so-called Apery limit, to reconstruct the values of the integral via a sequence of rational approximations. Running the recurrence in the negative direction gives a sequence of integers related to the number of solutions over finite fields of polynomial equations. Applying these ideas to the integrals which arise in quantum field theory leads to interesting new invariants of graphs, a connection with modular forms, and a resolution of a question posed by Kontsevich regarding the appearance of zeta values in particle physics."

On Monday, 2nd of December, Francis Brown will also give a colloquium lecture at ICMU entitled "Voronoi diagrams, tropical curves and the cohomology of the general linear group of integers". Everyone is welcome!

Francis Brown is an LMS Distinguished Visiting Fellow at ICMU. He is 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.


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

The image on this page is a fragment of a wall mosaic composition "Plachta" by Ivan Marchuk, circa 1970, Bogolyubov Institute for Theoretical Physics in Kyiv.