ERC Grants for Valentin Blomer and Georg Oberdieck

"Automorphic Forms and Arithmetic" (AuForA) - this is the name of the project led by Valentin Blomer is in the field of basic mathematical research. In this project, Blomer investigates connections between classical number-theoretic objects such as integer matrices or integer solutions of equations on the one hand and complex and highly structured functions, the so-called automorphic forms, on the other. At the center are three fundamental mathematical conjectures, unsolved for more than 15 years, whose conceptual common feature is the statistical behavior of automorphic forms in certain families. The project aims to help achieve substantial progress and solutions for these three conjectures. The ERC Advanced Grant will provide Blomer with approximately two million euros for his research over the next five years.

After studying mathematics and computer science at the University of Mainz, Valentin Blomer earned his doctorate at the University of Stuttgart in 2002 and habilitated three years later at the University of Göttingen, where he was an assistant professor from 2004 to 2005. He then moved to the University of Toronto, initially as an Assistant Professor, and later received a full professorship there. In 2009, he became a professor at the University of Göttingen, and since 2019 he has been at the University of Bonn. The Advanced Grant is not his first ERC funding: from 2010 to 2015, the specialist in analytic number theory already held a Starting Grant. Valentin Blomer is a member of the Hausdorff Center for Mathematics Cluster of Excellence and the Transdisciplinary Research Area "Modelling" at the University of Bonn.

Enumerative geometry is a classical area of mathematics that deals with the question of how many objects of a certain type exist on a given geometric space, or more precisely on an algebraic variety. Studying and possibly solving these counting problems helps to understand new aspects of the geometry of these spaces and often leads to interesting new algebraic structures as well as to new connections between geometry and other subfields of mathematics. In the project "Correspondences in enumerative geometry: Hilbert schemes, K3 surfaces and modular forms" (K3Mod) Georg Oberdieck investigates the enumerative geometry of algebraic surfaces, in particular the so-called K3-surface. The focus is on proving correspondences between different enumerative theories and thereby gaining new insights into these theories. A central goal is to determine the Gromov-Witten theory of Hilbert schemes of points on algebraic surfaces. Part of Oberdieck's approach is to prove symmetries of generating functions of invariants and thereby establish a connection to modular forms, a classical branch of number theory. This allows complicated structures to be computed by determining a few coefficients. The K3Mod project is part of algebraic geometry, but also features numerous connections with representation theory, number theory and physics. It is funded by the ERC Starting Grant with about 1.5 million euros.

After studying mathematics at ETH Zurich, Georg Oberdieck earned his PhD there in 2015 under Rahul Pandharipande, one of the leading experts in modern algebraic geometry. He then worked at the Massachusetts Institute of Technology (MIT) in the USA before becoming a Bonn Junior Fellow at the Hausdorff Center for Mathematics Cluster of Excellence at the University of Bonn in September 2018. In 2020, he received the prestigious Heinz Maier-Leibnitz Prize of the German Research Foundation.