Among the many sensibilities that humans have, two are very basic: the sensibility of the discrete, and that of the continuous. The sensibility of the discrete is at the basis of counting and hence of economics, while that of the continuous at the heart of drawing, or of art more generally. Many fundamental changes in mathematics have arisen from insights into how one sensibility could be understood in terms of the other.

Despite many great achievements, we are still missing a powerful geometric view unifying many special geometrical theories and visions. Progress in solving difficult problems often involves methods and constructions from seemingly unrelated areas. It is a manifestation of deep harmony in mathematics when the discovery of new structures leads to new explanations for phenomena or to the solution of complex long-standing problems.

The aim of the school is to present and discuss fundamental insights and approaches to several key types of geometries, and significant links between them. More specifically, the school will address, with top experts in central areas of contemporary mathematics, intra-disciplinary connections between algebraic, arithmetic, tropical, motivic, p-adic, adelic, anabelian, topos-theoretic and model-theoretic geometries. It is our hope that the school will contribute to stimulate new developments towards a unified geometric vision shedding light on some of the most challenging problems in modern mathematics.

Because of the pandemic, the school will be held entirely online, by using Zoom for the talks and Slack as a discussion platform; only the organizers and some speakers will be on site. In order to attend this event, you need to register.

The school poster can be downloaded here.

Organizers and school lecturers

Olivia Caramello (University of Insubria and IHES)
Ivan Fesenko (University of Nottingham)
Laurent Lafforgue (Huawei)

Supporting lecturers

Weronika Czerniawska (University of Geneva)
Paolo Dolce (Universities of Nottingham and Oxford)
Wojciech Porowski (University of Nottingham)
Riccardo Zanfa (University of Insubria)

Invited speakers

Alain Connes (IHES)
Misha Gromov (IHES and Courant Institute, N.Y.)
Ilia Itenberg (Sorbonne Université – Paris)
Maxim Kontsevich (IHES)
Kobi Kremnitzer (University of Oxford)
Barry Mazur (Harvard University)
Grigory Mikhalkin (University of Geneva)
Andras Szenes (University of Geneva)


We gratefully acknowledge the support of the Lake Como School of Advanced Studies, the University of Insubria and the EPSRC Programme Grant Symmetries and Correspondences.