Aktuelle Vorträge und Veranstaltungen

Sommersemester 2021

Das Seminar findet bis auf weiteres über Zoom statt. Der Link wird am Morgen des Seminartermins via Zoom an die Mitglieder der Arbeitsgruppe geschickt. Falls Sie die Emails unserer Arbeitsgruppe nicht bekommen, melden Sie sich bitte mit einer kurzen Email an ulirsch[at]math.uni-frankfurt.de an.

The Seminar will be held via Zoom for the foreseeable future. The link will be sent to all members of our working group on the morning of the seminar. If you do not receive the emails of our working group, please register with a short email to ulirsch[at]math.uni-frankfurt.de.

Mi, 21. April 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00 - 17:00: Noémie Combe (MPI Leipzig): The realm of Frobenius manifolds.
  • This talk will focus on different facets of so-called Frobenius manifolds, a mathematical object that arose in the process of axiomatisation of Topological Field Theory (TFT). Until 2019 there were three main classes: 1. Quantum cohomology, in relation to Gromov--Witten invariants. 2. Saito manifold (unfolding spaces of singularities), in relation to Landau--Ginzburg models. 3. The moduli space of solutions to Maurer--Cartan equations appearing in the Barannikov--Kontsevich theory, related to Gerstenhaber--Batalanin--Vilkoviskiy algebras. In a result 2020, in a joint work with Yu. Manin, we have proved that there exists a very unexpected bridge between algebraic geometry (involving moduli spaces of curves, Gromov--Witten invariants, unfolding spaces of isolated singularities, known as the Saito manifold) and statistical manifolds, central objects for machine learning, information geometry and decision theory. In this talk we will discuss different aspects of Frobenius manifolds in particular the Saito manifold (unfoldings of isolated singularities) and consider relations to Grothendieck—Teichmuller theory.

Mi, 28. April 2021, Bachelorabschlussvortrag (on Vidyo)

  • 14:00 - 15:00: Marcel Feth (Goethe-Universität Frankfurt): Aufbau, Funktionsweise und Sicherheit digitaler Signaturen am Beispiel von RSA und ElGamal.
    Die Arbeit behandelt den Aufbau der digitalen Signaturverfahren RSA und ElGamal unter Verwendung von Hashfunktionen und betrachtet mit der Faktorisierungsproblematik ganzer Zahlen und dem Problem des diskreten Logarithmus die den Verfahren zugrunde liegende Sicherheit.

    Den Zugangscode erhalten Sie bei Interesse per e-mail an "colmar@math.uni-frankfurt.de".

Mi, 05. Mai 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00 - 17:00: Marcin Lara (Krakow): tba.

Mi, 02. Juni 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00 - 17:00: Michael Groechenig (Toronto): Hypertoric Hitchin systems and p-adic integration.
    The first half of this talk will be devoted to a panoramic overview of p-adic integration for Hitchin systems. In particular, I will explain the main ideas that were used in joint work with Dimitri Wyss and Paul Ziegler to resolve the Hausel--Thaddeus conjecture.
    In the second half we will turn to concrete examples. A construction due to Hausel and Proudfoot associates to a graph a complex-analytic integrable system. In joint work with Michael McBreen we introduce a formal-algebraic analogue of their spaces and compute the p-adic volumes of the fibres in graph-theoretic terms.

Wintersemester 2020/21

Mi, 10. March 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: Sourav Das (Tata Institute of Fundamental Research, Mumbai): Log-symplectic structure on a degeneration of moduli of Higgs bundles
    Given a one parameter degeneration of a smooth projective curve to a nodal curve Balaji et. al. constructed a semistable degeneration of the moduli of Higgs bundles. In this talk, I will show that there exists a relative log-symplectic form on the total space of the degeneration whose restriction to the generic fibre is the known symplectic form. If time permits, I will also show that the special fibre is an example of an integrable system with normal-crossing singularities.

Fr., 12. March. 2021, Tropical Geometry in Zoom (TGiZ)-Seminar (on Zoom)

  • 14:00-15:00: Anthea Monod (Imperial College)
  • 15:15-16:15: Claudia He Yun (Brown University)
  • 16:30-17:30: Daniel Corey (University of Wisconsin)

Bereits gehaltene Vorträge im WiSe 2020/21:

Di, 6. Okt. 2020, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: David Leatham (Goethe-Universität Frankfurt): Tropical Geometry of Deep Neural Networks (Bachelorabschlussvortrag)

Mi, 4. Nov. 2020, Bachelorabschlussvortrag (on Vidyo)

  • 14:00 - 16:00: Florian Schröck (Goethe-Universität Frankfurt): Kryptographie mit elliptischen Kurven am Beispiel von WhatsApp                                          
  • Wie kann man ein Geheimnis austauschen, ohne im gleichen Raum zu sein? Vor dem Aufruf dieser Webseite haben Ihr Browser und der Webserver genau das getan und dabei eine elliptische Kurve benutzt. Im Rahmen des Vortrags werden die algebraisch-geometrischen Grundlagen elliptischer Kurven und ihrer Gruppenstruktur eingeführt, die kryptographisch vorteilhaften Montgomery-Kurven beleuchtet und dargestellt, wie sich Alice und Bob auf Basis des Signal-Protokolls in WhatsApp vertraulich unterhalten können.
  • Den Zugangscode erhalten Sie bei Interesse per e-mail an "colmar@math.uni-frankfurt.de".

Mi, 4. Nov. 2020, Oberseminar Algebra und Geometrie (on Zoom):

  • 16:00-17:00: Ming-Hao Quek (Brown University): Resolution of singularities via stacks and weighted blowings up
    One feature of Hironaka's resolution of singularities over a field k of characteristic zero is that the process is independent of choices of local embeddings, and hence, this allows us to reduce to the case of embedded resolution of singularities (namely, resolving the singularities of a reduced, finite type -scheme embedded in a smooth -scheme). I will explain recent work by Abramovich-Temkin-Włodarczyk and me, which revisits this topic of embedded resolution of singularities by considering stack-theoretic weighted blowings up. Doing so forces us to consider embeddings in (log) smooth Deligne-Mumford stacks over, instead of embeddings in a smooth -scheme. The result is a simpler and faster procedure to Hironaka's resolution of singularities in characteristic zero, although the end result is a smooth stack instead of a smooth scheme. We resolve that final problem by applying a de-stackification theorem due to Bergh-Rydh.

Do., 12. Nov. 2020, Oberseminar Algebra und Geometrie (on Zoom)

- DaFra-Seminar on Condensed Mathematics: Leitfaden & Getting condensed -

  • 15:00-16:00 (Talk 1)  Ingmar Metzler, "The condensed world"
  • 16:00-16:30: Coffee break
  • 16:30-17:30 (Talk 2) Theresa Kumpitsch, "Topological spaces as condensed sets"

Mi, 18. Nov. 2020, Oberseminar Algebra und Geometrie (on Zoom):

  • 16:00-17:00: Beatrice Pozzetti (University of Heidelberg): The real spectrum compactification of higher rank Teichmüller spaces
    After introducing and motivating the study of higher rank Teichmüller spaces, interesting connected components of character varieties of fundamental groups of surfaces in semisimple Lie groups, I will discuss joint work with Burger Iozzi and Parreau in which we use ideas from real algebraic geometry as well as non-Archimedean techniques to compactify these spaces and to give geometric characterizations of the boundary points.

Do., 26. Nov. 2020, Oberseminar Algebra und Geometrie (on Zoom)
DaFra-Seminar on Condensed Mathematics: 
Condensed abelian groups and their cohomology I 

  • 15:00-16:00 (Talk 3) Paola Chilla :"The category of condensed abelian groups" 
  • 16:00-16:30: Coffee break
  • 16:30-17:30 (Talk 4) Jakob Stix: "Digression: Computing cohomology via simplicial hypercovers" 

Mi, 2. Dez. 2020, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: Martin Schwald (University of Essen):
    Title: On the definition of irreducible holomorphic symplectic manifolds and their singular analogues

    Abstract: We show that in the definition of IHSM being simply connected can be replaced by vanishing irregularity. This fits well with the theory of singular symplectic varieties. The proof uses the decomposition theorem for compact Kähler manifolds with trivial canonical bundle as well as the representation theory of finite groups to analyze quotients of complex tori.

Do., 3. Dez. 2020, Oberseminar Algebra und Geometrie (on Zoom)
DaFra-Seminar on Condensed Mathematics:
Condensed abelian groups and their cohomology II 

  • 15:00-16:00 (Talk 5) Gabriele Bogo: "Computation of the cohomology of Z and of R"
  • 16:00-16:30: Coffee break
  • 16:30-17:30 (Talk 6) Matti Würthen:"Locally compact abelian groups as condensed abelian groups"  

Fr., 4. Dec. 2020, Tropical Geometry in Zoom (TGiZ)-Seminar (on Zoom)

  • 14:00-15:00: Xin Fang (Universität Köln)
  • 15:15-16:15: Man-Wai Cheung (Harvard University)
  • 16:30-17:30: Lara Bossinger (UNAM Oaxaca)

Mi, 16. Dez. 2020, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: Yajnaseni Dutta (University of Bonn): Holomorphic 1-forms and geometry
    Abstract: In this talk I will discuss various geometric consequences of the existence of zeros global holomorphic 1-forms on smooth projective varieties. Such geometry has been indicated by a plethora of results. I will present some old and new results in this direction.  Then I will discuss two sets of such 1-forms that arise out of both the generic vanishing theory and the decomposition theorem and present a new connection between the two. This connection gives us further geometric properties of the variety. This is an on-going joint work with Feng Hao and Yongqiang Liu.

Do., 17. Dez. 2020, Oberseminar Algebra und Geometrie (on Zoom)
DaFra-Seminar on Condensed Mathematics: Return of the Solids 

  • 15:00-16:00 (Talk 7) Milton Lin: "Solids I" 
  • 16:00-16:30: Coffee break
  • 16:30-17:30 (Talk 8) Patrick Bieker, "Solids II" 

Do., 14. Jan. 2021, Oberseminar Algebra und Geometrie (on Zoom)
DaFra-Seminar on Condensed Mathematics: Coherent duality 

  • 15:00-16:00 (Talk 9) Anton Güthge: "Analytic rings"
  • 16:00-16:30: Coffee break
  • 16:30-17:30 (Talk 10) Can Yaylali:"Local Serre duality" 

Mi., 20. Jan. 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: Dori Bejleri (Harvard University): Compact moduli of higher dimensional varieties
  • The Deligne-Mumford space of pointed stable curves and its cousin the space of stable maps are central objects in algebraic geometry with deep connections to many other fields. The higher dimensional analogue is the moduli space of stable log varieties or stable pairs. The existence of compact moduli spaces of such stable pairs in all dimensions is one of the crowning achievements of the last several decades of progress on the minimal model program. However, little is known about the structure of these moduli spaces in general and even the most basic computations of e.g. cohomology or enumerative invariants appear out of reach. In this talk I will give an introduction to the theory of stable log varieties and describe some recently developed tools for studying these spaces with a view toward possible applications.

Fr., 22. Jan. 2021, Tropical Geometry in Zoom (TGiZ)-Seminar (on Zoom)

  • 14:00-15:00: Alheydis Geiger (Universität Tübingen)
  • 15:15-16:15: Matt Baker (Georgia Institute of Technology)
  • 16:30-17:30: Daniel Litt (University of Georgia)

Mi., 27. Jan. 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: John Cristian Ottem (Univ. Oslo): Enriques surface fibrations of even index​.
  • Abstract: I will explain a geometric construction of an Enriques surface fibration over P^1 of even index. This answers a question of Colliot-Thelene and Voisin, and provides new counterexamples to the Integral Hodge conjecture. This is joint work with Fumiaki Suzuki.

Do., 28. Jan. 2021, Oberseminar Algebra und Geometrie (on Zoom)

DaFra-Seminar on Condensed MathematicsLiquids strike back 

  • 15:00-16:00 (Talk 11) Julian Quast: "Banach and Smith spaces I"  
  • 16:00-16:30: Coffee break
  • 16:30-17:30 (Talk 12) Martin Möller: "Banach and Smith spaces II" 

Di., 2. Feb. 2021, Interdisciplinary Seminar (on Zoom)

  • 15:00 - 17:00 Interdisciplinary Seminar on Topology in Condensed Matter Physics 
    Abstract: The idea of this seminar is to start off with an overview on the concepts from group theory and topology that enter the physical classification of electronic states in condensed matter. Moreover, we present some open problems and limitations of these tools.
    Organization: K. Zantout, R. Valentí and T. Weth

Mi, 3. Feb. 2021, Bachelorabschlussvortrag (on Zoom)

  • 14:30 - 15:30: Leonie Scherer (Goethe-Universität Frankfurt): Galoistheorie nach Grothendieck

Mi, 3. Feb. 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: Daniele Agostini (MPI Leipzig): On the irrationality of moduli spaces of K3 surfaces.
    Abstract: In this talk, we consider quantitative measures of irrationality for moduli spaces of polarized K3 surfaces of genus g. We show that, for infinitely many examples, the degree of irrationality is bounded polynomially in terms of g, so that these spaces become more irrational, but not too fast. The key insight is that the irrationality is bounded by the coefficients of a certain modular form of weight 11. This is joint work with Ignacio Barros and Kuan-Wen Lai.
Do, 18. Feb. 2021, Masterabschlussvortrag (on Vidyo. Link und Passwort erhalten Sie von colmar@math.uni-frankfurt.de)

  • 14:00 - 15:00: Anastasia Karathanasis (Goethe-Universität Frankfurt): Titel: Perfektoide Körper.
  • Abstract: Die von Peter Scholze entwickelte Theorie der Perfektoiden Räume zielt darauf ab, Probleme in gemischter Charakteristik (0,p) in Charakteristik p zu übersetzen. Ein Anfangspunkt dieser Theorie ist der Satz von Fontaine-Wintenberger, welcher erklärt, wie sich der Vergleich der lokalen Q_p und F_p((t)) auf ihre endlichen seperablen Körpererweiterungen fortsetzen lässt. Diese Aussage lässt sich verallgemeinern. In diesem Vortrag werden wir diesen Satz als eine sogenannte Tilting-Äquivalenz perfektoider Körper vorstellen. Der Beweis dieses Satzes basiert auf Faltings “Almost Mathematics”.
Do, 18. Feb. 2021, Bachelorabschlussvortrag (on Vidyo. Link und Passwort erhalten Sie von colmar@math.uni-frankfurt.de)

  • 15:15 - 16:15: Lucas Euler (Goethe-Universität Frankfurt): An outline of Almost Purity for perfectoid spaces.
  • Abstract: The Almost Purity theorem is a statement about étale ring morphisms and their counterpart in almost mathematics, which is the practice of assigning properties to rings and modules up to very small torsion. In 2011 Peter Scholze introduced a strong version of the original by Faltings which states that for his notion of perfectoid rings (topological rings that are very close to being perfect) étale and almost étale morphisms are equivalent and the proof relies on translating the problem to Huber’s adic spaces.

Fr., 19. Feb. 2021, Tropical Geometry in Zoom (TGiZ)-Seminar (on Zoom)
  • 14:00-15:00: John Christian Ottem (University of Oslo)
  • 15:15-16:15: Marco Pacini (Universidade Federal Fluminense)
  • 16:30-17:30: Laura Escobar (Washington University in St. Louis)

Mi, 24. Feb. 2021, Oberseminar Algebra und Geometrie (on Zoom)

  • 16:00-17:00: Eleonore Faber (University of Leeds): Grassmannian categories of infinite rank and rings of countable Cohen-Macaulay type
  • Abstract: We construct a categorification of the coordinate rings of Grassmannians of infinite rank in terms of graded maximal Cohen-Macaulay modules over a hypersurface singularity. This gives an infinite rank analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. We show that there is a structure preserving bijection between the generically free rank one modules in a Grassmannian category of infinite rank and the Plücker coordinates in a Grassmannian cluster algebra of infinite rank. In a special case, when the hypersurface singularity is a curve of countable Cohen-Macaulay type, our category has a combinatorial model by an ''infinity-gon'' and we can determine triangulations of this infinity-gon. This is joint work with Jenny August, Man-Wai Cheung, Sira Gratz, and Sibylle Schroll.