On June 27th, the Colloquium of the CRC-TRR 358 will take place at the Department of Mathematics, Paderborn. The speakers are Prof. Ulrich Derenthal (Hannover) and Prof. Christian Lehn (Bochum).
Program:
14:00 - 15:00 Prof. Ulrich Derenthal (Hannover)
15:00 - 15:40 Coffee / Tea
15:40 - 16:40 Prof. Christian Lehn (Bochum)
16:40 Reception / Buffet
Location:
The talks will be held in lecture room D2, the coffee break and reception will take place in room J2.138.
Here is a link to our campus map.
Prof. Ulrich Derenthal (Hannover):
Title: Rational points of bounded height on the chordal cubic fourfold
Abstract: Cubic hypersurfaces over the rational numbers often contain infinitely many rational points. In this situation, the asymptotic behavior of the number of rational points of bounded height is predicted by conjectures of Manin and Peyre. After reviewing previous results, we discuss the chordal cubic fourfold, which is the secant variety of the Veronese surface. Since it is isomorphic to the symmetric square of the projective plane, a result of W. M. Schmidt for quadratic points on the projective plane can be applied. We prove that this is compatible with the conjectures of Manin and Peyre once a thin subset with exceptionally many rational points is excluded from the count.
Prof. Christian Lehn (Bochum):
Title: A Hodge-theoretic journey from geometry to arithmetic via representation theory
Abstract: The Tannakian formalism gives a powerful tool to extract information from geometric situations via the theory of algebraic groups. In a joint work with Javanpeykar, Krämer and Maculan, we apply this to the study of the monodromy of subvarieties of abelian varieties. Complicated questions about those subvarieties can then be formulated as questions about the representation theory of groups like SL_n, Sp_n or SO_n. Also more exotic groups like E_6 show up together with the famous connection to the beautiful geometry of cubic equations in 5 variables. These results lead to applications to the Shafarevich conjecture in arithmetic geometry about the finiteness of subvarieties defined over a number field. For the proof, we extend the topological formalism of Krämer-Weissauer to a Hodge theoretic setup, a theory that began in the 1930s with the study of harmonic integrals and has experienced major developments in the last decades.
