CRC 326 - GAUS

Stable infinity categories I
2022-03-16 14:00 - 15:30 (Europe/Berlin) | Darmstadt and Zoom
Katharina Hübner

Model categories II
2022-03-16 11:00 - 12:30 | Darmstadt and Zoom
Claudius Heyer

Model categories I
2022-03-16 09:00 - 10:30 | Darmstadt and Zoom
Rizacan Ciloǧlu (TU Darmstadt)

Cones of special cycles and unfolding of the Kudla-Millson lift
2022-03-15 10:30 - 12:30 | Frankfurt and Zoom
Riccardo Zuffetti (Universität Frankfurt)
Disputation

Vertex gluings and Demazure products
2022-02-23 16:00 - 17:00 | Frankfurt and Zoom
Oberseminar Algebra und Geometrie
Nathan Pflueger (Amherst College)
Abstract:
Finite graphs and metric graphs provide useful combinatorial analogs of algebraic curves. Since the work of Cools-Draisma-Payne Robeva, it has been known that chains of loops are particularly useful graphs in this regard. I will describe a new perspective on these chains of loops, by describing a version of Brill-Noether theory for curves or graphs with two marked points. Divisors on twice-marked graphs are associated with permutations; the extent to which a divisor is special is measured by the inversions of the permutation. This twice-marked Brill-Noether theory is well-suited to inductive arguments; when two twice-marked graphs are glued together, permutations are combined by an operation called the Demazure product. I will describe how this framework provides a short proof of some of the results of Cools-Draisma-Payne Robeva, as well as more recent results on tropical Hurwitz-Brill-Noether theory, and may provide a route to identifying new classes of Brill-Noether-General graphs.

The S_n action on the homology groups of M_{0,n}-bar
2022-02-18 16:30 - 17:30 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (Second meeting)
Rohini Ramadas (University of Warwick)
Abstract:
The symmetric group on n letters acts on M_{0,n}-bar, and thus on its (co-)homology groups. The induced actions on (co-)homology have been studied by, eg., Getzler, Bergstrom-Minabe, Castravet-Tevelev. We ask: does H_{2k}(M_{0,n}-bar) admit an equivariant basis, i.e. one that is permuted by S_n? We describe progress towards answering this question. This talk includes joint work with Rob Silversmith.

Cut-and-paste invariants of moduli spaces of relative stable maps to P^1
2022-02-18 15:15 - 16:15 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (Second meeting)
Siddarth Kannan (Brown University)
Abstract:
I will discuss ongoing work studying moduli spaces of genus zero stable maps to P^1, with fixed ramification profiles over 0 and infinity. I will describe a chamber decomposition of the space of ramification data such that the Grothendieck class of the moduli space is constant on the chambers. Finally, for the sequence of ramification data corresponding to maximal ramification over 0 and no ramification over infinity, I will describe a recursive algorithm to compute the generating function for Euler characteristics of these spaces.

Patchworks of real algebraic varieties in higher codimension
2022-02-18 14:00 - 15:00 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (Second meeting)
Johannes Rau (Universidad de los Andes)
Abstract:
I will present a combinatorial setup, based on smooth tropical varieties and real phase structures, which after “unfolding” produces a certain class of PL-manifolds (called patchworks). We have two motivations in mind: Firstly, in the spirit of Viro’s combinatorial patchwoking for hypersurfaces, these patchworks can be used to describe the topology of real algebraic varieties close to the tropical limit. Secondly, even if not “realisable” by real algebraic varieties, real phase structures provide a geometric framework for combinatorial structures such as oriented matroids. Joint work with Arthur Renaudineau and Kris Shaw.

Hodge theory of matroids (Session 7)
2022-02-17 15:00 - 18:00 | Frankfurt and Zoom
This semester’s topic in our joint research seminar is Hodge theory of matroids. The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.
Last meeting: Discussion of topics for the next seminar

Dissipation of Correlations of Automorphic Forms
2022-02-16 16:00 - 17:00 | Frankfurt and Zoom
Oberseminar Algebra und Geometrie
Petru Constantinescu (MPIM Bonn)
Abstract:
Mass equidistribution of eigenfunctions is a central topic in quantum chaos and number theory. In this talk we highlight a generalisation of the Quantum Unique Ergodicity for holomorphic cusp forms in the weight aspect. We show that correlations of masses coming from off-diagonal terms dissipate as the weight tends to infinity. This corresponds to classifying the possible quantum limits along any sequence of Hecke eigenforms of increasing weight.

Suslin homology
2022-02-16 09:30 - 11:00 | Heidelberg, MATHEMATIKON, SR 4, INF 205, Heidelberg, Germany

A Main Conjecture in non-commutative Iwasawa theory
2022-02-11 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream

Graph potentials, TQFTs and mirror partners
2022-02-09 16:00 - 17:00 | Frankfurt and Zoom
Oberseminar Algebra und Geometrie
Talk by Pieter Belmans (Université du Luxembourg)
Graph potentials, TQFTs and mirror partners
Abstract: In a joint work with Sergey Galkin and Swarnava Mukhopadhyay we introduced a class of Laurent polynomials associated to decorated trivalent graphs which we called graph potentials. These Laurent polynomials satisfy interesting symmetry and compatibility properties, leading to the construction of a topological quantum field theory which efficiently computes the classical periods as the partition function.
Under mirror symmetry graph potentials are related to moduli spaces of rank 2 bundles (with fixed determinant of odd degree) on a curve of genus $ggeq 2$, which is a class of Fano varieties of dimension $3g-3$. I will discuss how enumerative mirror symmetry relates classical periods to quantum periods in this setting. Time permitting I will touch upon aspects of homological mirror symmetry for these Fano varieties and their mirror partners.

Comparison with Čech cohomology, adic version (Part 2)
2022-02-09 09:30 - 11:00 | Heidelberg, MATHEMATIKON, SR 4, INF 205, Heidelberg, Germany
Christian Dahlhausen

Numerical experiments with plectic Darmon points (online)
2022-02-04 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream

Hodge theory of matroids (Session 6) / CRC-Colloquium
2022-02-03 15:00 - 18:00 | Frankfurt and Zoom
This semester’s topic in our joint research seminar is Hodge theory of matroids. The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.
Talk 11: June Huh (Princeton University): Kazhdan-Lusztig and singular Hodge theory for matroids
Abstract: There is a remarkable parallel between the theory of Coxeter groups (think of the symmetric group or the dihedral group) and matroids (think of your favorite graph or vector configuration). After giving an overview of the similarity, I will report proofs of two combinatorial conjectures, the nonnegativity conjecture for Kazhdan-Lusztig coefficients and the top-heavy conjecture for the number of flats of matroids. The key step is to formulate and prove an analogue of the decomposition theorem for a resolution of singularities in a combinatorial setup, which is closely related to the validity of the hard Lefschetz theorem and the Hodge-Riemann relations for what would be an intersection Chow cohomology in realizable cases. The talk should be enjoyable without specialized knowledge. Joint work with Tom Braden, Jacob Matherne, Nick Proudfoot, and Botong Wang.

Christin Bibby: A generating function approach to new representation stability phenomena in orbit configuration spaces
2022-02-02 16:00 - 17:00 | Frankfurt and Zoom
Oberseminar Algebra und Geometrie
Talk by Christin Bibby (Louisiana State University)
A generating function approach to new representation stability phenomena in orbit configuration spaces
Abstract: As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces: using the notion of twisted commutative algebras, which essentially categorify exponential generating functions. This idea allows for a factorization of the orbit configuration space “generating function” into an infinite product, whose terms are surprisingly easy to understand. Beyond the intrinsic aesthetic of this decomposition and its quantitative consequences, it reveals a sequence of primary, secondary, and higher representation stability phenomena. This is joint work with Nir Gadish.

Comparison with Čech cohomology, adic version (Part 1)
2022-02-02 09:30 - 11:00 | Heidelberg, MATHEMATIKON, SR 4, INF 205, Heidelberg, Germany

Tyler Kelly: An Open Enumerative Theory for Landau-Ginzburg models.
2022-01-26 16:00 - 17:00 | Frankfurt and Zoom
Oberseminar Algebra und Geometrie
Talk by Tyler Kelly (Birmingham)
An Open Enumerative Theory for Landau-Ginzburg models.
Abstract: Landau-Ginzburg models consist of a pair (W, G) where W is a potential (that is, a complex valued regular function from a quasi-affine variety X) and G is a group acting on X so that W is invariant. In the context of mirror symmetry, oftentimes they can be viewed as a noncommutative symplectic deformation of a symplectic manifold. Over the past couple of decades there has been work in establishing an enumerative theory for a Landau-Ginzburg model, akin to Gromov-Witten theory. Recently, a few of us have aimed to create an open enumerative theory for Landau-Ginzburg models. In the end, we can construct the mirror Landau-Ginzburg model’s potential function as a generating function of open enumerative invariants. This provides the Landau-Ginzburg analogue to Maslov index two discs / tropical discs for a symplectic manifold. This is joint work with Mark Gross and Ran Tessler.

Joins of Henselian Huber pairs (Part 2)
2022-01-26 09:30 - 11:00 | Heidelberg, MATHEMATIKON, SR 4, INF 205, Heidelberg, Germany
M. Amine Koubaa

Uniform bounds for torsion packets on tropical curves
2022-01-21 16:30 - 17:30 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2021/22)
Harry Richman (University of Washington)
Abstract:
Say two points x, y on an algebraic curve are in the same torsion packet if [x – y] is a torsion element of the Jacobian. In genus 0 and 1, torsion packets have infinitely many points. In higher genus, a theorem of Raynaud states that all torsion packets are finite. It was long conjectured, and only recently proven*, that the size of a torsion packet is bounded uniformly in terms of the genus of the underlying curve. We study the tropical analogue of this construction for a metric graph. On a higher genus metric graph, torsion packets are not always finite, but they are finite under an additional “genericity” assumption on the edge lengths. Under this genericity assumption, the torsion packets satisfy a uniform bound in terms of the genus of the underlying graph. (*by Kuehne and Looper-Silverman-Wilmes in 2021)

Applications of tropical geometry to irreducibility problems in algebraic geometry
2022-01-21 15:15 - 16:15 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2021/22)
15:15-16:15 Ilya Tyomkin (Ben Gurion University)
Abstract:
In my talk, I will discuss a novel tropical approach to classical irreducibility problems of Severi varieties and of Hurwitz schemes. I will explain how to prove such irreducibility results by investigating the properties of tropicalizations of one-parameter families of curves and of the induced maps to the tropical moduli space of parametrized tropical curves. The talk is based on a series of joint works with Karl Christ and Xiang He.

Orders and polytropes: matrices from valuations
2022-01-21 14:00 - 15:00 | Frankfurt and Zoom
TGiZ-Seminar: Tropical geometry in Zoom (First meeting Winter Semester 2021/22)
14:00-15:00 Mima Stanojkovski (RWTH Aachen)
Abstract:
Let K be a discretely valued field with ring of integers R. To a d-by-d matrix M with integral coefficients one can associate an R-module, in K^{d x d}, and a polytope, in the Euclidean space of dimension d-1. We will look at the interplay between these two objects, from the point of view of tropical geometry and building on work of Plesken and Zassenhaus. This is joint work with Y. El Maazouz, M. A. Hahn, G. Nebe, and B. Sturmfels.

Higher Hida theory and p-adic L-functions for Hilbert modular forms
2022-01-21 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream

Hodge theory of matroids (Session 5)
2022-01-20 15:00 - 18:00 | Frankfurt and Zoom
This semester’s topic in our joint research seminar is Hodge theory of matroids. The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.
Talk 9: Bergman fans and the permutohedral variety (Stefan Rettenmayr)
Talk 10: Intersection theory on the permutohedral variety (Andreas Gross)

Joins of Henselian Huber pairs (Part 1)
2022-01-19 09:30 - 11:00 | Heidelberg, MATHEMATIKON, SR 4, INF 205, Heidelberg, Germany

Topological Hochschild homology and Zeta-values
2022-01-14 13:30 - 15:00

Oishee Banerjee: Filtration of cohomology via symmetric (semi-)simplicial spaces
2022-01-12 16:00 - 17:00 | Frankfurt and Zoom
Oberseminar Algebra und Geometrie
Talk by Oishee Banerjee (University of Bonn)
Filtration of cohomology via symmetric (semi-)simplicial spaces
Abstract: Inspired by Deligne’s use of the simplicial theory of hypercoverings in defining mixed Hodge structures we replace the indexing category ∆ by the symmetric simplicial category ∆S and study (a class of) ∆S-hypercoverings, which we call spaces admitting symmetric (semi)simplicial filtration. For ∆S-hypercoverings we construct a spectral sequence, somewhat like the Cˇech-to-derived category spectral sequence. The advantage of working on ∆S is that all of the combinatorial com- plexities that come with working on ∆ are bypassed, giving simpler, unified proof of known results like the computation of (in some cases, stable) singular cohomol- ogy (with rational coefficients) and étale cohomology (with Q_l coefficients) of the moduli space of degree n maps C to a projective space , C a smooth projective curve of genus g, of unordered configuration spaces, that of the moduli space of smooth sections of a fixed gdr that is m-very ample etc.

Comparison with étale cohomology and finiteness in dimension
2022-01-12 09:30 - 11:00

Extending exodromy
2021-12-17 13:30 - 15:00 | Heidelberg, Mathematikon, SR A and Livestream
