Jérémy Guéré is currently an Associate Professor in Mathematics at the University of Grenoble in France. He was  a PhD student at theUniversity Paris 6 under the supervision of Professor Alessandro Chiodo and then a Postdoc at Humboldt Universität zu Berlin under the supervision of Professors Gavril Farkas and Rahul Pandharipande. He works in algebraic geometry, specifically on Gromov–Witten theory and related areas. Some keywords: moduli spaces of curves, K-theory, log-geometry, Gromov-Witten and Fan-Jarvis-Ruan-Witten theories, mirror symmetry, integrable hierarchies, rationality

Abstract: In the first lecture, I will review the construction of atoms, beginning with an overview at the formal level before addressing the technical difficulties that necessitate the use of non-Archimedean fields. I will also discuss the behavior of the Hodge structure under Iritani’s blow-up formula.

In the second lecture, I will introduce the new atomic invariant and provide the proof for the following theorem: if a smooth complex cubic fourfold is rational, then its primitive cohomology is isomorphic, as a Hodge structure, to the shifted middle cohomology of a projective K3 surface. The proof relies on explicit computations for surfaces that I will present.