Aktuelle Vorträge und Veranstaltungen

Wintersemester 2019/2020

Do, 16. Januar 2020 Darmstadt-Frankfurt Seminar: The paramodular conjecture (Forschungsseminar Algebra und Geometrie)

  • Dr. Michalis Neururer
    Special cases of paramodularity

  • Dr. Jolanta Marzec
    Galois representations associated to Siegel modular forms


    Zeit und Ort: 15:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

Mi, 22. Januar 2019 Vortrag im Abschlussseminar

  • Johannes Schwab
    Picardgruppen von Hurwitzräumen (Abschlussvortrag Masterarbeit)
    Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (kl.), Robert-Mayerstr. 10

Do, 23. January 2019 Oberseminar Algebra und Geometrie

  • Dr. Lorenzo Fantini (Goethe-Universität Frankfurt)
    Non-archimedean links of singularities
    Zeit und Ort: 14:15-15:15 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

    I will discuss several instances in which valuations play an important role in the study of singularities and of their resolutions, a context where Berkovich's theory of non-archimedean analytic spaces can be extremely fruitful. The main character of this (quite informal!) talk will be a non-archimedean version of the link of a singularity. In particular, if time allows I will explain how this objects provides a concrete bridge between resolution of singularities of surfaces over a field k and semi-stable reduction of curves over k((t)).

Fr, 24. Januar 2020 TGiF-Tropical Geometry in Frankfurt - Second meeting in Winter Semester

  • 13:15-14:15 
    Dr. Karl Christ (Ben-Gurion University)
    Title: Severi problem and tropical geometry

    Abstract: The classical Severi problem is to show that the space of reduced and irreducible plane curves of fixed geometric genus and degree is irreducible. In case of characteristic zero, this longstanding problem was settled by Harris in 1986. In the first part of my talk I will give a brief overview of the ideas involved. Then, I will describe a tropical approach to studying degenerations of plane curves, which is the main ingredient to a new proof of irreducibility obtained in collaboration with Xiang He and Ilya Tyomkin. The main feature of the construction is that it works in positive characteristic, where the other known techniques fail.

    14:15-15:00
    - Coffee Break -

  • 15:00-16:00
    Prof. Dr. Oliver Lorscheid (IMPA Rio de Janeiro/MPI Bonn)
    Title: Towards a cohomological understanding of the tropical Riemann Roch theorem

    Abstract: In this talk, we outline a program of developing a cohomological understanding of the tropical Riemann Roch theorem and discuss the first established steps in detail. In particular, we highlight the role of the tropical hyperfield and explain why ordered blue schemes provide a satisfying framework for tropical scheme theory.
    In the last part of the talk, we turn to the notion of matroid bundles, which we hope to be the right tool to set up sheaf cohomology for tropical schemes. This is based on a joint work with Matthew Baker.

  • 16:15-17:15
    Prof. Dr. Diane Maclagan (University of Warwick)
    Title: Connectivity of tropical varieties

    Abstract: The structure theorem for tropical geometry states that the tropicalization of an irreducible subvariety of the algebraic torus over an algebraically closed field is the support of a pure polyhedral complex that is connected through codimension one. This means that the hypergraph whose vertices correspond to facets of the complex, and whose hyperedges correspond to the ridges, is connected. In this talk I will discuss joint work with Josephine Yu showing that this hypergraph is in fact d-connected (when the complex has no lineality space). This can be thought of as a generalization of Balinski's theorem on the d-connectivity of the edge graph of a d-polytope. A key ingredient of the proof is a toric Bertini theorem of Fuchs, Mantova, and Zannier, plus additions of Amoroso and Sombra.

    Ort: Raum 309 (Ecksaal), Robert-Mayerstr. 6-8

Mi, 29. Januar 2020  Frankfurter Seminar - Kolloquium des Instituts für Mathematik

  • Ginkgo-Seminar - Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende
    Adrien Schertzer
    Stochastische Homogenisierung

    Zeit und Ort: 15.00 Uhr (c.t.) im Raum 711 (gr.), Robert-Mayerstr. 10

    - Tee 16.15 - 16.45 Uhr -
  • Prof. Dr. Felix Otto (MPI Leipzig)
    Effective behavior of random media
    Zeit und Ort: 16:45 Uhr im Raum 711 (gr.), Robert-Mayer-Str. 10

Do, 6. Februar 2019 Oberseminar Algebra und Geometrie

  • Prof. Dr. Cecília Salgado (MPI Bonn/Universidade Federal do Rio de Janeiro)
    tba
    Zeit und Ort: 14:00-16:00 Uhr im Raum 711 (gr.), Robert-Mayer-Str. 10

Do, 13. Februar 2020 Darmstadt-Frankfurt Seminar: The paramodular conjecture (Forschungsseminar Algebra und Geometrie)

  • Thomas Driscoll-Spittler
    Computing Hecke eigenvalues of Siegel modular forms

  • tba
    Paramodularity at level N = 277 and beyond


    Zeit und Ort: 15:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayer-Str. 10

Bereits gehaltene Vorträge im WiSe 2019/20

Mi, 15. Januar 2020  Frankfurter Seminar - Kolloquium des Instituts für Mathematik

  • Ginkgo-Seminar - Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende
    Theresa Kumpitsch (Goethe-Universität Frankfurt)
    Die Grad-Geschlecht Formel für komplex-projektive Kurven
    Zeit und Ort: 15.00 Uhr (c.t.) im Raum 711 (gr.), Robert-Mayerstr. 10

    - Tee 16.15 - 16.45 Uhr -
  • Prof. Dr. Hansjörg Geiges (Universität zu Köln)
    The topology of global surfaces of section
    Zeit und Ort: 16:45 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

Do, 19. Dezember 2019 Oberseminar Algebra und Geometrie

  • Prof. Dr. Mariá Angélica Cueto (Ohio State University)
    Anticanonical tropical del Pezzo cubic surfaces contain exactly 27 lines.
    Zeit und Ort: 14:00-16:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

    Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-known statement "any smooth surface of degree three in P^3 contains exactly 27 lines'' is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP^3.
    In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P^44 via its anticanonical bundle. The combinatorics of the root system of type E_6 and a tropical notion of convexity will play a central role in the construction. This is joint work with Anand Deopurkar (arXiv: 1906.08196)

Mi, 18. Dezember 2019 Oberseminar Algebra und Geometrie

  • Dr. Chiara Damiolini (Princeton University)
    Conformal blocks defined by modules over vertex algebras of CohFT-type
    Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (kl.), Robert-Mayerstr. 10

    In this talk I will discuss properties of certain vector bundles on the moduli space of stable n-pointed curves which arise from finitely generated admissible modules over certain vertex algebras. I will in particular describe conditions on the vertex algebra that guarantee that the factorization property holds for these vector bundles and discuss its consequences.  This is based on a joint work with A. Gibney and N. Tarasca.

Do, 5. Dezember 2019 Vortrag im Bachelor Abschlussseminar

  • Leon Goertz
    Konstruktion und Eigenschaften der Mathieugruppen
    Zeit und Ort: 15:00-16:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

Mi, 4. Dezember 2019 Oberseminar Algebra und Geometrie

  • Dr. Mirko Mauri (MPI Bonn)
    Dual complexes of log Calabi-Yau pairs and Mori fibre spaces
    Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (kl.), Robert-Mayerstr. 10
  • Dual complexes are CW-complexes, encoding the combinatorial data of how the irreducible components of a simple normal crossing pair intersect. They have been finding useful applications for instance in the study of degenerations of projective varieties, mirror symmetry and nonabelian Hodge theory. In particular, Kollár and Xu conjectures that the dual complex of a log Calabi-Yau pair should be a sphere or a finite quotient of a sphere. It is natural to ask whether the conjecture holds on the end products of minimal model programs. In this talk, we will validate the conjecture for Mori fibre spaces of Picard rank two

Mi, 27. November 2019  Frankfurter Seminar - Kolloquium des Instituts für Mathematik

  • Ginkgo-Seminar - Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende
    Zeit und Ort: 15.00 Uhr (c.t.) im Raum 711 (gr.), Robert-Mayerstr. 10
    tba

    - Tee 16.15 - 16.45 Uhr -
  • Prof. Dr. Mohab Safey El Din (Sorbonne Université)
    On solving polynomial systems over the reals and applications in robotics
    Zeit und Ort: 16:45 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

    Polynomial systems arise in many areas of engineering and computer sciences such as signal theory, cryptography, biology and robotics. In this talk, we will focus on the analysis of kinematic singularities in robotics, which is a fundamental problem in mechanism design. This analysis boils down to a core algorithmic issue in effective real algebraic geometry: given a polynomial system with real coefficients, how to count the number of connected components of their real solution set (or answer connectivity queries on this set)? We will review recent (mathematical and algorithmic) results which yield practically efficient algorithms to solve these problems using computer algebra methods and report on their implementations which can already solve concrete problems in robotics

Do, 21. November 2019 Darmstadt-Frankfurt Seminar: The paramodular conjecture (Forschungsseminar Algebra und Geometrie)

  • Riccardo Zuffetti
    Paramodular forms

  • Priyanka Majumder
    Yoshida lifting

    Zeit und Ort: 15:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

Do, 31. Oktober 2019 TGiF-Tropical Geometry in Frankfurt - First meeting in Winter Semester

           Schedule

  • Prof. Dr. Sam Payne (University of Texas, Austin):
    tba.
    Zeit und Ort: 14:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10
  • Enrica Mazzon (MPI Bonn):
    Tropical affine manifolds in mirror symmetry
    Zeit und Ort: 14:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

    Abstract: Mirror symmetry is a fast-moving research area at the boundary between mathematics and theoretical physics. Originated from observations in string theory, it suggests that certain geometrical objects (complex Calabi-Yau manifolds) should come in pairs, in the sense that each of them has a mirror partner and the two share interesting geometrical properties. In this talk I will introduce some notions relating mirror symmetry to tropical geometry, inspired by the work of Kontsevich-Soibelman and Gross-Siebert. In particular, I will focus on the construction of a so-called “tropical affine manifold” using methods of non-archimedean geometry, and the guiding example will be the case of K3 surfaces and some hyper-Kähler varieties. This is based on a joint work with Morgan Brown and a work in progress with Léonard Pille-Schneider.

  • Christoph Goldner (Tübingen):
    Tropical mirror symmetry for ExP^1
    Zeit und Ort: 14:00-18:00 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

    We recall some results of tropical mirror symmetry that relate the generating series of tropical Gromov-Witten invariants of an elliptic curve E to sums of Feynman integrals. After that, we present an approach to tropical mirror symmetry in case of ExP^1. The approach is based on the floor decomposition of tropical curves which is a degeneration technique that allows us to apply the results of the elliptic curve case. The new results are joint work with Janko Böhm and Hannah Markwig.

Mi, 30. Oktober 2019  Frankfurter Seminar - Kolloquium des Instituts für Mathematik

  • Ginkgo-Seminar - Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende
    Felix Röhrle (Goethe-Universität Frankfurt)
    Moduli Spaces of Tropical Curves
    Zeit und Ort: 15.00 Uhr (c.t.) im Raum 711 (gr.), Robert-Mayerstr. 10

    - Tee 16.15 - 16.45 Uhr -

  • Prof. Dr. Sam Payne (University of Texas, Austin)
    Tropical curves, graph homology, and top weight cohomology of M_g
    Zeit und Ort: 16:45 Uhr im Raum 711 (gr.), Robert-Mayerstr. 10

    I will discuss the topology of a space of stable tropical curves of genus g with volume 1. The reduced rational homology of this space is canonically identified with the top weight cohomology of M_g and also with the homology of Kontsevich's graph complex. As one application, we show that H^{4g-6}(M_g) is nonzero for infinitely many g. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of a recent theorem of Willwacher, that homology of the graph complex vanishes in negative degrees, using the identifications above and known vanishing results for M_g. And we prove a formula for the S_n-equivariant Euler characteristic of M_{g,n}, which was conjectured by Zagier.

Mi, 23. Oktober 2019 Oberseminar Algebra und Geometrie

  • Dr. Giulio Bresciani (FU Berlin)
    On the (birational) section conjecture over finitely generated fields
    Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (kl.), Robert-Mayerstr. 10

    We prove that, if the section conjecture holds over number fields, then it holds for every curve X over a field finitely generated over Q with a non-constant morphism to an abelian variety which is defined over a number field. Our method also gives an independent proof of the recent result by Saidi-Tyler of the fact that the birational section conjecture over number fields implies it over fields finitely generated over Q.