GRK-Seminar
The Thursday morning seminar (10:15-11:45 in WSC-N-U-3.05) will be the “Research Training Group Seminar” where members of the RTG (PhD students, post-docs,…) present their results. Sometimes, we also have speakers from other places. Depending on the number of speakers and on the proposed topic, a speaker could use one or two sessions.
| Termin | Vortragende*r | Titel |
|---|---|---|
| 13.4.2023 | Workshop: Good Scientific Practice | |
| 27.4.2023 | Clémentine Lemarié- -Rieusset (Inst. Math. Bourgogne) | Motivic Knot Theory |
| 4.5.2023 | First Joint Symposium of GRKs 2240/2553 | |
| 25.5.2023 | Matthias Paulsen (Univ. Hannover) | The degree of algebraic cycles on hypersurfaces |
| 1.6.2023 | Neelam Kandhil (MPI Bonn) | On linear independence of Dirichlet L-values |
| 15.6.2023 | – | no talk |
| 22.6.2023 | – | no talk |
| 29.6.2023 | Anneloes Viergever | The quadratic Euler characteristic of a smooth projective same-degree complete intersection (to the end) |
| 6.7.2023 | Manuel Hoff | Deformation theory of parahoric $(\mathcal{G}, \mu)$-displays |
| 13.7.2023 | Rehearsal for ALGANT Thesis defences | ALGANT students |
Abstracts
Clémentine Lemarié- -Rieusset
In this talk I will present a new application of motivic homotopy theory: motivic knot theory. More specifically, I will present the quadratic linking degree, which is a counterpart in algebraic geometry of the linking number of two oriented disjoint knots (the number of times one of the knots turns around the other knot). I will first present the quadratic linking degree of oriented couples of closed immersions of the affine plane minus the origin in the affine 4-space minus the origin (with several examples). I will then explain what assumptions on F-schemes X and Y allow to define the quadratic linking degree of oriented couples of closed immersions of X in Y and apply this to the study of oriented couples of closed immersions of smooth models of motivic spheres (such as some families of affine quadrics for instance).
Matthias Paulsen
Let X be a very general hypersurface of dimension 3 and degree d at least 6. Griffiths and Harris conjectured in 1985 that the degree of every curve on X is divisible by d. Substantial progress on this conjecture was made by Kollár in 1991 via degeneration arguments. However, the conjecture of Griffiths and Harris remained open in any degree d. In this talk, I will explain how to prove this conjecture (and its higher-dimensional analogues) for infinitely many degrees d.
Neelam Kandhil
The study of linear independence of L(k,χ) for a fixed integer k > 1 and varying χ depends critically on the parity of k vis-à-vis χ. Several authors have explored this phenomenon for Dirichlet characters χ with fixed modulus and having the same parity as k. We extend this investigation to families of Dirichlet characters modulo distinct pairwise co-prime natural numbers across arbitrary number fields. In the process, we determine the dimension of the multi-dimensional generalization of cotangent values and the sum of generalized Chowla-Milnor spaces over the linearly disjoint number fields.
Anneloes Viergever
To any smooth projective scheme over a perfect field $k$ of which the characteristic is not equal to $2$, one can assign a quadratic Euler characteristic. These are quadratic forms over $k$, which carry a lot of information about the scheme inside of them. However they are in general hard to compute. In their paper from 2021, Levine, Srinivas and Lehalleur successfully compute the quadratic Euler characteristic of a smooth projective hypersurface. I will discuss some of the main results of my PhD thesis: an algorithm which can extend the results for a hypersurface to smooth projective complete intersections of hypersurfaces of the same degree. This talk could be viewed as a continuation of my talk during the PhD Days of 2021, but this time, the story will have an end.
Manuel Hoff
Dieudonné displays are a generalization of Dieudonné modules to complete Noetherian local base rings $R$ with perfect residue field. As in classical Dieudonné theory, there is a natural anti-equivalence between $p$-divisible groups over $R$ and Dieudonné displays over $R$. In this talk we discuss the notion of a Dieudonné display with $(\mathcal{G}, \mu)$-structure and then study the deformation theory of these objects.