Research Seminar Algebra, Number Theory and Discrete Mathematics
Winter term 2024/25
Thursdays, 14:15-15:15
Seminar room A410 in Welfenschloss (main building, Welfengarten 1)
Datum | Vortragende/r | Vortragstitel |
---|---|---|
Do 24.10.2024 | Guillaume Tahar | Simplicial arrangements and the geometry of planar cubic curves (online) In their solution to the orchard-planting problem, Green and Tao established a structure theorem which proves that in a line arrangement in the real projective plane with few double points, most lines are tangent to the dual curve of a cubic curve. We provide geometric arguments to prove that in the case of a simplicial arrangement, the aforementioned cubic curve cannot be irreducible. It follows that Grünbaum's conjectural asymptotic classification of simplicial arrangements holds under the additional hypothesis of a linear bound on the number of double points. This is a joint work with Dmitri Panov. |
Do 21.11.2024 | Anca Macinic | Freeness-type properties and combinatorics of line arrangements Abstract: We study the relation between freeness-adjacent properties and combinatorics, for arrangements of complex projective lines, via Ziegler restrictions. |
Fr 22.11.2024 | Opening RTG Colloquium (in Berlin) | |
Do 28.11.2024 | Seoyoung Kim (Göttingen) | Certain families of K3 surfaces and their modularity Abstract: We start with a double sextic family of K3 surfaces with four parameters with Picard number 16. Then by geometric reduction (top-to-bottom) processes, we obtain three, two and one parameter families of K3 surfaces of Picard number 17, 18 and 19 respectively. All these families turn out to be of hypergeometric type in the sense that their Picard--Fuch differential equations are given by hypergeometric or Heun functions. We will study the geometry of two parameter families in detail. |
Do 5.12.2024 | Jakob Glas (LUH) | Terminality of moduli spaces of curves on hypersurfaces via the circle method Abstract: I will explain how one can use tools from analytic number theory to study moduli spaces of curves on Fano varieties. In particular, I will report on joint work with Matthew Hase-Liu that shows that the moduli space of genus g curves of degree e on a smooth hypersurface of low degree only has terminal singularities, provided e is sufficiently large with respect to g. Using a spreading argument together with a result of Mustata, we reduce the problem to counting points over finite fields on the jet schemes of these moduli spaces. We solve this counting problem by developing a suitable version of the circle method. |
Do 12.12.2024 | Nuno Arala (LUH) | |
Do 19.12.2024 | Leon Eickhoff (LUH) | |
Do 9.1.2025 | Christopher Frei (Graz) | |
Do 16.1.2025 | ||
Do 23.1.2025 | Göttingen-Hannover Number Theory Workshop 15:00: Zhizhong Huang (CAS, Beijing) 16:30: Fabian Gundlach (Paderborn) | |
Do 30.1.2025 |