We also have a Google calendar of the seminar.
Seminars Calendar
Tuesday April 28, 2026 - 14:30 - 2AB40 - Johannes Sprang (University of Duisburg-Essen)
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Tuesday March 31, 2026 - 14:30 - 1BC45 - Dante Bonolis (TU Graz)
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Tuesday March 10, 2026 - 14:30 - 2AB40 - Rosa Winter (Albert-Ludwigs-Universität Freiburg)
Many rational points on del Pezzo surfaces of low degree
Abstract: Let X be an algebraic variety over a number field k. In arithmetic geometry we are interested in the set X(k) of k-rational points on X. Questions one might ask are, is X(k) empty or not? And if it is not empty, how `large' is X(k)? Del Pezzo surfaces are surfaces classified by their degree d, which is an integer between 1 and 9 (for d at least 3, these are the smooth surfaces of degree d in P^d). The lower the degree, the less is known about the set of rational points on the surface. I will give an overview of different notions of `many' rational points, go over several results for rational points on del Pezzo surfaces of degree 1 and 2, and show how these relate to some of the major open questions on the arithmetic of surfaces.
Tuesday March 3, 2026 - 14:30 - 2AB40 - Aleksander Horawa (University of Bonn)
The arithmetic of Fourier coefficients of automorphic forms on G2
Abstract: In 1973, Shimura discovered a way to associate a holomorphic half-integral weight modular form h with a classical cusp form f. Subsequently, in the 1980s, Waldspurger proved a remarkable formula relating squares of the Fourier coefficients of h and quadratic twists of L-values of f. In the spirit of these results, we prove that one can associate "quaternionic" modular forms on the group G2 with dihedral cusp forms f, whose Fourier coefficients are explicitly related to cubic twists of L-values of f. This gives the first examples where a conjecture of Gross from 2000 has been fully verified. (Joint work with Petar Bakić, Siyan Daniel Li-Huerta, and Naomi Sweeting).
Tuesday February 17, 2026 - 14:30 - 2AB45 - Jaume Amoròs (UPC Barcelona)
Holomorphic tangent vector fields in compact Kaehler manifolds
Abstract: The existence of holomorphic tangent vector fields is a very particular feature in complex projective manifolds. The birational classification of such manifolds was established by F. Severi, R. Hall and D. Lieberman. Using holomorphic foliation techniques and Kuranishi deformation theory, one may find the biholomorphic classification of such manifolds, and the classification up to deformation of complex structure in the compact Kaehler case. A consequence is that the study of the dynamics of holomorphic tangent fields in compact Kaehler manifolds reduces to the case of rational varieties.
Tuesday February 3, 2026 - 14:30 - 1BC45 - Ernesto Mistretta (Università di Padova)
Semiample bundles, abelian varieties, fundamental groups
Abstract: We describe 2 non equivalent definitions of semiample vector bundles, and see how to obtain geometric characterizations when these notions are applied to the holomorphic cotangent bundle of a compact complex manifold. We relate these constructions to the finiteness of the fundamental group, and give a conjecture on compact complex manifolds with semiample cotangent bundle. This conjecture is related to some proven or conjectured statements when the manifold is Kähler or projective. This is a joint work with Francesco Esposito.
Tuesday January 20, 2026 - 14:30 - 2AB45 - Remke Kloosterman (Università di Padova)
The average Mordell--Weil rank of elliptic surfaces over number fields
Abstract: Let K be a number field and let n be a non-negative integer. In this talk we determine the average (arithmetic) Mordell--Weil rank of elliptic surfaces over K with base curve P^1 and geometric genus n, hereby proving a conjecture of Alex Cowan. The proof consists of two parts, the first part relies on work by Andr\'e and Maulik--Poonen on the jump loci of the Picard Number in flat families. This is sufficient to prove that the average Mordell--Weil in the family equals the Mordell--Weil rank of the generic fiber. The second part of the proof uses an argument involving quadratic twists in order to show that the generic Mordell--Weil rank of elliptic surfaces over a number field with fixed topological invariants equals zero.
Tuesday December 16, 2025 - 14:30 - 2AB45 - Andrea Gallese (SNS Pisa)
How to compute the connected monodromy field of a CM abelian variety
Abstract: Let A be an abelian variety defined over a number field k. The connected monodromy field k(eA) is the minimal extension of k over which every ell-adic Galois representation attached to A has connected image. Equivalently, it is the smallest field over which all Tate classes on self-products A^r are defined. When the extension k(eA)/k(End A) has positive degree, one finds “exotic’’ Tate classes on certain powers A^r. In this talk, I will explain how to compute the connected monodromy field for the Jacobian A of a curve with complex multiplication. After computing the endomorphism ring of A, we use CM theory to describe the algebra of Tate classes on all powers of A. We make the Galois action on this algebra explicit in terms of periods -- suitable integrals of algebraic differential forms. Although periods are generally transcendental, those attached to Tate classes are algebraic, hence computing k(eA) amounts to identifying these periods as exact algebraic numbers. This can be done numerically and, in the case of Fermat curves, via explicit algebraic identities.
Tuesday December 2, 2025 - 14:30 - 1BC45 - Andrea Ricolfi (SISSA Trieste)
Moduli spaces of semiorthogonal decompositions
Abstract: The bounded derived category of coherent sheaves on a smooth projective variety X is a sensible and somewhat subtle invariant of X. Its study is tightly related to rationality problems, MMP, Mirror Symmetry, Enumerative Geometry. Semiorthogonal decompositions (SODs) are a gadget allowing one to "decompose" this category into smaller pieces. Proving the very existence of SODs is often a delicate question. In this talk we shall explain how to construct a "moduli space of SODs" attached to a smooth proper morphism of schemes; we will also discuss its main properties, and how to use it to detect indecomposability of derived categories of some smooth projective varieties. Joint work with Pieter Belmans and Shinnosuke Okawa.
Tuesday November 18, 2025 - 13:15 - 1BC45 - Sergej Monavari (Università di Padova)
Partitions, motives and Hilbert schemes
Abstract: Counting the number of higher dimensional partitions is a hard classical problem. Computing the motive of the Hilbert schemes of points is even harder. I will discuss some structural formulas for the generating series of both problems, their stabilisation properties when the dimension grows very large and how to apply all of this to obtain (infinite) new examples of motives of singular Hilbert schemes. This is joint work with M. Graffeo, R. Moschetti and A. Ricolfi.
Tuesday November 4, 2025 - 14:30 - 2AB45 - Julian Demeio (Hamburg University)
The Grunwald Problem for solvable groups
Abstract: Let $K$ be a number field. The Grunwald problem for a finite group (scheme) G/K asks what is the closure of the image of $H^1(K,G) \to \prod_{v \in M_K} H^1(K_v,G)$. For a general G, there is a Brauer—Manin obstruction (BMO) to the problem, and this is conjectured to be the only one. In 2017, Harpaz and Wittenberg introduced a technique that managed to give a positive answer (BMO is the only one) for supersolvable groups. I will present a new fibration theorem over quasi-trivial tori that, combined with the approach of Harpaz and Wittenberg, gives a positive answer for all solvable groups.
Work group on -- A RH-correspondence in positive characteristic -- by Bhatt-Lurie. First semester 2025/2026
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