## Aktuelle Vorträge und Veranstaltungen

Wintersemester 2018/19

Mi, 07. November 2018 Oberseminar Algebra und Geometrie

• Kristin Shaw (Universität Oslo)
tba

Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (klein), Robert-Mayerstr. 10

Fr, 25. Januar 2019 Loewe-Vortragsreihe für ein allgemeines Publikum

• tba

Zeit und Ort: 18:00-20:00 Uhr im Hilbertraum 302, Robert-Mayerstr. 6-8

- bereits gehaltene Vorträge -

Sommersemester 2018

Do, 19. April 2018 Forschungs- und Oberseminar (Darmstadt - Frankfurt)

• Markus Rennig und Max Bieri
Fundamentals of positivity

Line bundles and Cartier divisors, intersection numbers á la Kleiman–Snapper, numerical equivalence of divisors, Néron–Severi space, the Riemann–Roch theorem and its asymptotic version, the theorem of Cartan–Grothendieck–Serre, first formal properties (restriction to irreducible components, behaviour under pullbacks, amplitude in families, etc.). Examples: Pn, P2 blown up at a point.
Zeit und Ort: 15:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

Mi, 25. April 2018 Abschlussseminar

• Adrian Rötzer (Vortrag über die Bachelorarbeit):
Über den Satz von Ostrowski

Die Bachelorarbeit behandelt die Originalarbeit aus dem Jahre 1916 von Ostrowski zum nach ihm benannten Satz in moderner Form.
Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (klein), Robert-Mayerstr. 10

Do, 17. Mai 2018 Forschungs- und Oberseminar (Darmstadt - Frankfurt)

• Paul Kiefer und Michaelis Neururer
Topological consequences of ampleness and vanishing theorems

Metric characterization of ampleness, Kodaira’s embedding theorem (without proof), topology of affine varieties (review), cohomological dimension, Lefschetz hyperplane theorem, Kodaira’s and Fujita’s vanishing theorems (if time permits, comparison with Serre).
Zeit und Ort: 15:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

Mi, 23. Mai 2018 Oberseminar Algebra und Geometrie

• Dr. Emre Sertöz (Max-Planck-Institut MiS, Leipzig):
Computing and using periods of hypersurfaces

The periods of a smooth complex projective variety X are complex numbers, typically expressed as integrals, which give an explicit representation of the Hodge structure on the cohomology of X. Although they provide great insight, periods are often very hard to compute. In the past 20 years, an algorithm for computing the periods existed only for plane curves. We will give a different algorithm which can compute the periods of any smooth projective hypersurface and can do so with much higher precision. As an application, we will demonstrate how to reliably guess the Picard rank of quartic K3 surfaces and the Hodge rank of cubic fourfolds from their periods.
Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (klein), Robert-Mayerstr. 10

Mi, 13. Juni 2018 Abschlussseminar

• Theresa Kumpitsch (Vortrag über die Masterarbeit):
Krull-Bewertungen auf Funktionenkörpern regulärer Flächen

Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (klein), Robert-Mayerstr. 10

Mo, 18. Juni 2018 Antrittsvorlesungen im Rahmen

• der Berufung von Prof. Dr. Martin Ulirsch
Geometrie algebraischer und tropischer Kurven

• des Habilitationsverfahrens von Dr. Gilles Evéquoz
Stationäre Lösungen der nichtlinearen Helmholtz-Gleichung

Zeit und Ort: 12:00 Uhr s.t., Raum 302 (Hilbertraum), Robert-Mayerst. 8

Mi, 20. Juni 2018 Oberseminar Algebra und Geometrie

• Florian Pop (UPenn, Philadelphia):
Recovering canonical inertia generators

Birational anabelian geometry is about (canonical) reconstruction of function fields K from Galois theoretical information. As a major step in the strategies to tackle the problem one recovers the divisor group Div(X) of "nice" models X of the function field K. It turns out that recovering Div(X) is equivalent to recovering "canonical" inertia generators. The aim of this talk is to explain the terms in detail, and report on work in progress concerning the recovering of canonical inertia generators.
Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (klein), Robert-Mayerstr. 10

Do, 28. Juni 2018 Forschungs- und Oberseminar (Darmstadt - Frankfurt) [Programm]

• Matteo Costantini und Matthias Nickel
Ample subschemes

Definition of ample subschemes, examples, the fact that ampleness does not respect rational equivalence, ampleness of the normal bundle, ample versus local complete intersection, regular section of ample vector bundles, intersections with divisors, cohomology of the complement and the Lefschetz hyperplane theorem, fundamental groups of ample subvarieties, the question of Kodaira vanishing for q-ample line bundles.
Zeit und Ort: 15:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

Di, 03. Juli 2018 Forschungs- und Oberseminar

• Dmitry Zakharov (Central Michigan University)
The double ramification cycle, relations in the tautological ring, and tropical geometry

The moduli space $\mathcal{M}_{g,n}$ parametrizes smooth algebraic curves of genus g with n marked points, and the Deligne—Mumford moduli space $\overline{\mathcal{M}}_{g,n}$ compactifies $\mathcal{M}_{g,n}$ by adding curves with nodal singularities. The spaces $\mathcal{M}_{g,n}$ and $\overline{\mathcal{M}}_{g,n}$ are the subject of a large body of work, however, their geometry is still far from being completely understood. The double ramification cycle is a family of codimension g loci in $\mathcal{M}_{g,n}$, parametrizing curves admitting a meromorphic function with prescribed zeroes and poles. A natural question is to construct its compactification in $\overline{\mathcal{M}}_{g,n}$, and to compute its class in the Chow or cohomology rings. Recently, a formula for the double ramification cycle compactified via relative stable maps was proved by Janda, Pandharipande, Pixton and Zvonkine. A related family of relations in the Chow ring of $\overline{\mathcal{M}}_{g,n}$ were proved by Clader and Janda. I will discuss the consequences of the relations of Clader and Janda, and show that they naturally reproduce classical vanishing results in the tautological ring of $\overline{\mathcal{M}}_{g,n}$. Furthermore, they give an effective algorithm for computing boundary formulas for classes that vanish on $\mathcal{M}_{g,n}$. I will also discuss upcoming work on a tropical analogue of the double ramification cycle. Joint work with Emily Clader, Samuel Grushevsky, Felix Janda and Martin Ulirsch.
Zeit und Ort: 16:00 c.t. im Raum 309, Robert-Mayerstr. 6