Sonstige Veranstaltungen

Sonstige Veranstaltungen



The paramodular conjecture [Programm]
WiSe 2019/20
SoSe 2019
The Noether-Lefschetz conejcture"
(Frankfurt-Darmstadt) [Programm]
WiSe 2018/19
SoSe 2018
WiSe 2017/18
SoSe 2017
[Programm] WiSe 2016/17
„Rational points." (Darmstadt-Frankfurt-Mainz One)[Programm] WiSe 2016/17
arXiv-Seminar“ (Frankfurt-Darmstadt) [Programm] SoSe 2016
„Vertex algebras“ (Frankfurt-Darmstadt) WiSe 2015/16
„Arrangements, Kammerkomplexe und K(Π, 1)-Räume" (Frankfurt-Darmstadt) SoSe 2015
Prime-Gaps (Frankfurt-Darmstadt) WiSe 2014/15
Noether-Lefschetz und Gromov-Witten  (Frankfurt-Darmstadt) SoSe 2014
Die Birch-Swinnerton-Dyer-Vermutung und die Gross-Zagier-Formel       

WiSe 2013/14

Margulis' Superstarrheit und Arithmetizität  (Frankfurt-Darmstadt)  SoSe 2013
Arakelov-Theorie (Frankfurt-Darmstadt) WiSe 2012/13
„Selbergs 3/16 Theorem“ (Frankfurt-Darmstadt) SoSe 2012
Institutweites Forschungsseminar „Polynomielle Gleichungssysteme“ SoSe 2012
Berkovich-Räume und ihre Anwendungen WiSe 2011/12
Forschungsseminar über Expandergraphen SoSe 2011
Stationaere Maße auf Liegruppen nach Benoist und Quint   WiSe 2010/11

TGiF - Tropical Geometry in Frankfurt Seminar


Fr, 26. Juni 2020, TGiF-Seminar (on Zoom)

  • 14:00-15:00: Mark Gross (University of Cambridge):
  • 15:15-16:15: Luca Battistella (Ruprecht-Karls-Universität Heidelberg)
  • 16:30-17:30: Kalina Mincheva (Yale University)

Fr, 26. Mai 2020 TGiF-Tropical Geometry in Frankfurt - Second meeting in Summer Semester 2020

  • 14:00-15:00
    Ben Smith (University of Manchester):
    Faces of tropical polyhedra
  • 15:15-16:15
    Yue Ren (Swansea University):
    Tropical varieties of neural networks
  • 16:30-17:30
    Hannah Markwig (Eberhard-Karls-Universität Tübingen):
    The combinatorics and real lifting of tropical bitangents to plane quartics

Fr, 24. April 2020 TGiF-Tropical Geometry in Frankfurt - First meeting in Summer Semester 2020

  • 14:00-15:00
    Marta Panizzut (TU Berlin)

    15:00-15:30 - Coffee Break -

  • 15:30-16:30
    Alejandro Vargas (Universität Bern)

  • 16:45-17:45
    Prof. Dr. Jan Draisma (Universität Bern)

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.

    - 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.

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


  • Prof. Dr. Sam Payne (University of Texas, Austin):
    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.

Fr, 05. Juli 2019 TGiF-Tropical Geometry in Frankfurt - Second meeting in Summer Semester

  • Madeline Brandt (University of California at Berkeley)
    Matroids and their Dressians
    Abstract: In this talk we will explore Dressians of matroids. Dressians have many lives: they parametrize tropical linear spaces, their points induce regular matroid subdivisions of the matroid polytope, they parametrize valuations of a given matroid, and they are a tropical prevariety formed from certain Plücker equations. We show that initial matroids correspond to cells in regular matroid subdivisions of matroid polytopes, and we characterize matroids that do not admit any proper matroid subdivisions. An efficient algorithm for computing Dressians is presented, and its implementation is applied to a range of interesting matroids. If time permits, we will also discuss an ongoing project extending these ideas to flag matroids.
    Zeit und Ort: 13:15-14:15 Uhr im Raum 711 (groß), Robert-Mayerstr. 10
  • Dhruv Ranganathan (University of Cambridge)
    Tropical curves, stable maps, and singularities in genus one
    Abstract: In the early days of tropical geometry, Speyer identified an extremely subtle combinatorial condition that distinguished tropical elliptic space curves from arbitrary balanced genus one graphs. Just before this, Vakil and Zinger gave a very explicit desingularization of the moduli space of elliptic curves in projective space, with remarkable applications. Just after this, Smyth constructed new compactifications of moduli spaces of pointed elliptic curves, using worse-than-nodal singularities, as part of the Hasset-Keel program. A decade on, we understand these three results as part of a single story involving logarithmic structures and their tropicalizations. I will discuss this picture and how the unified framework extends all three results. This is joint work with Keli Santos-Parker and Jonathan Wise.
    Zeit und Ort: 14:45-15:45 Uhr im Raum 711 (groß), Robert-Mayerstr. 10
  • Yoav Len (Georgia Institute of Technology)
    Algebraic and Tropical Prym varieties
    Abstract: My talk will revolve around combinatorial aspects of Abelian varieties. I will focus on Pryms, a class of Abelian vari- eties that occurs in the presence of double covers, and have deep connections with torsion points of Jacobians, bi-tangent lines of curves, and spin structures. I will explain how problems concern- ing Pryms may be reduced, via tropical geometry, to problems on metric graphs. As a consequence, we obtain new results con- cerning the geometry of special algebraic curves, and bounds on dimensions of certain Brill–Noether loci. This is joint work with Martin Ulirsch.
    Zeit und Ort: 16:00-17:00 Uhr im Raum 711 (groß), Robert-Mayerstr. 10

Fr, 07. Juni 2019 TGiF-Tropical Geometry in Frankfurt - First meeting in Summer Semester

  • Margarida Melo (Università degli studi Roma Tre):
    Combinatorics and moduli of line bundles on stable curves.
    The moduli space of line bundles on smooth curves of given genus, the so called universal Jacobian, has a number of different compactifications over the moduli space of stable curves. These compactificatons have very interesting combinatorial properties, which can be used to describe their geometry. In the talk I will explain different features and applications of these interesting objects, focusing on properties which have a natural tropical counterpart.
  • Farbod Shokrieh (University of Copenhagen): 
    Heights and moments of abelian varieties
    We give a formula which, for a principally polarized abelian variety $(A,\lambda)$ over the field of algebraic numbers, relates the stable Faltings height of $A$ with the N\'eron-Tate height of $(A,\lambda)$. Our formula completes earlier results due to Bost, Hindry, Autissier and Wagener. We also discuss the case of Jacobians in some detail, where graphs and electrical networks will play a role.
    (Based on joint works with Robin de Jong.)
  • Philipp Jell (Universität Regensburg):
    The tropical Hodge conjecture for divisors
    The Hodge conjecture is one of the big open questions in algebraic geometry. Mikhalkin and Zharkov formulated a tropical analogue of this conjecture. In joint work with Johannes Rau and Kristin Shaw, we established this conjecture for divisors. I will introduce the notions that are necessary to state the tropical Hodge conjecture and then sketch the proof and further directions of research.


Süd-West-Arithmetik-Seminar„Quantum Unique Ergodicity" SoSe 2015
Süd-West-Arithmetik-Seminar (SWAS) 2014  SoSe 2014 

„Attaching Galois representations to modular forms“

SoSe 2012 


Mathematik-AG für Schülerinnen und Schüler

Mathematik-AG für Schülerinnen und Schüler  



Winter School on Enumerative Geometry and Modular Forms WiSe 18/19
Workshop: Recent advances on the geometry of valuations WiSe 17/18
Workshop: Non-Archimedean Geometry and Algebraic Groups WiSe 16/17
Workshop on Berkovich Spaces  SoSe 2011 
Workshop zur Diskreten, Tropischen und Algebraischen Geometrie SoSe 2011