Oberseminar Algebra, Zahlentheorie und Diskrete Mathematik
Sommersemester 2025
Donnerstags, 14:15-15:15 Uhr
Seminarraum A410 im Welfenschloss (Hauptgebäude, Welfengarten 1)
| Datum | Vortragende/r | Vortragstitel |
|---|---|---|
| Do 10.4.2025 | Vorbesprechung | |
| Do 8.5.2025 | Nils Wirries (LUH) | Plesken Lie algebras of associative algebras with involution |
| Do 15.5.2025, 13:50 | Loïs Faisant (IST Austria)
| Counting rational curves with prescribed tangency conditions: a motivic analogue via universal torsors Abstract: Given a smooth projective and geometrically irreducible curve C and a Mori Dream Space X, we present a general parametrisation of morphisms from C to X which allows us to express the Grothendieck motive of Hom (C,X) as a motivic function defined on some power of the scheme of effective divisors of C, generalising previous works of Bourqui. Such a parametrisation should be understood as lifting our morphisms to the universal torsor of X. |
| Do 15.5.2025, 15:10 | Victor Wang (IST Austria) | Average sizes of mixed character sums Abstract: In joint work with Max Xu, we prove that the average size of a certain smoothly weighted, mixed character sum of length x is on the order of sqrt(x), under a weak Diophantine genericity condition on the angle θ of the additive character e(nθ). Certain quadratic Diophantine equations play a key role. In contrast, it was proved by Harper that the average size is o(sqrt(x)) for rational θ. Some remaining open questions will be highlighted. |
Mo 19.5.2025 in Göttingen | 15:00 Maxim Gerspach (Göttingen) 16:30 Gunther Cornelissen (Utrecht) | Göttingen-Hannover Number Theory Workshop |
| Do 22.5.2025 | Johannes Schmitt (Bochum) | Towards the computation of minimal models of symplectic quotient singularities Abstract: A symplectic resolution - or more generally a minimal model - of asymplectic quotient singularity is a relative Mori dream space. This means that the Cox ring R(X) of such a resolution X is a finitely generated algebra and that we can construct X as a GIT quotient of the spectrum of R(X). In this talk, we present how one may turn this procedure into an algorithm. We show that a set of generators of R(X) is given by a certain Khovanskii basis. This enables us in particular to compute R(X) without knowledge of X. We further discuss what theoretical and practical obstacles have to be overcome to algorithmically construct the resolution from the Cox ring. |
| Do 26.6.2025 | Ulrich Derenthal (LUH) | 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. |
| Do 3.7.2025 | Efthymios Sofos (Glasgow) | Rational points on conic bundles Abstract: In upcoming joint work with Christopher Frei we prove the Hasse principle for random diagonal conic bundle surfaces over P^1. |
| Do 10.7.2025 | Sascha Wache (LUH) | Kohomologie von simplizialen Arrangements |
| Mi 16.7.2025, 14:15 in G117 | Marta Pieropan (Utrecht) | Campana’s orbifold base revisited Abstract: Given a morphism of varieties X->Y, or equivalently a function with polynomial coordinates, determining its image is a very difficult question in general. If X and Y are smooth and Y is a curve, Campana and Abramovich defined the orbifold base of the morphism and showed that the image of the set of rational points under the morphism is contained in the set of Campana points determined by the orbifold base. This talk explains how to extend their construction to higher dimensional Y and, most importantly, relaxing all regularity conditions on X and Y. The set of Campana points gives only a rough approximation of the image of the set of rational points. A better approximation is possible if the morphism is given by monomials, rather than general polynomials, in each coordinate. The final part of the talk will illustrate this concept and show how it can be extended to morphisms that are given by monomials in étale local charts, such as toroidal or log smooth ones. |
