# Wochenplan der Fakultät für Mathematik

**Dienstag, 16.07.2024**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Jan Bohr (Bonn), "On transport twistor spaces"****Abstract:**

Transport twistor spaces are complex surfaces that are tailored to the geodesic flow (magnetic flow,...) over a Riemannian surface and capture many interesting features of the flow in complex geometric language. For Zoll geodesic flows a cousin (or rather a quotient) of this construction is at the heart of LeBrun-Masons work on Zoll deformations. More recently, it was discovered that transport twistor spaces provide a unifying picture to several developments in geometric inverse problems, allowing to organise and reinterpret various older results, while at the same time posing new intriguing challenges. In the talk I will sketch the aforementioned picture in more detail and report on some recent work with F. Monard and G.P. Paternain that locally recovers LeBrun-Masons desingularisation of twistor space for arbitrary metrics.

**Montag 15.07.2024**

**16:15 Uhr IA 1/135**

## Oberseminar Arrangements and Symmetries

**Sven Wiesner (RUB): "Free multiderivations of connected subgraph arrangements" ****Abstract:** Recently Cuntz and Kühne introduced a new class of arrangements coming from undirected graphs. In their work they classified all graphs which give a free simple arrangement. In this talk I will discuss joint work with Paul Mücksch and Gerhard Röhrle, where we extend this result to the multiarrangement case by classifying all graphs that (for some multiplicity) give a free multiarrangement.

**Freitag 12.07.2024**

**ID 03/401**

**10:30 - 11:30 Uhr **B. Liu

**11:45 - 12:45 Uhr **S. Cupit-Foutou

**14:30 - 15:30 Uhr **J. Schürmann

## Joint Seminar on Complex Algebraic Geometry and Complex Analysis

Das Joint Seminar findet als nächstes in Bochum mit den folgenden Gästen statt:

**Stéphanie Cupit-Foutou (Bochum), Toric quantum stacks: some review, a generalisation**

**Bingxiao Liu (Köln), Toeplitz-Fubini-Study forms and lowest eigenvalues of Toeplitz operators**

**Jörg Schürmann (Münster), Equivariant toric geometry and Euler-Maclaurin formulae**

Nähere Informationen entnehmen Sie bitte folgender Webseite: (link).

**Dienstag, 09.07.2024**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Levin Maier (Heidelberg), "On Mañé's critical value for the two-component Hunter-Saxton system"****Abstract:**

In this talk, we will introduce Mañé's critical value for a Hamiltonian PDE,

the two-component Hunter-Saxton system. We will introduce the magnetic two-component

Hunter-Saxton system (M2HS), which is a magnetic geodesic equation on an infinite-dimensional Lie group. We prove that this magnetic system is magnetic isomorphic to a magnetic system on an infinite-dimensional sphere. Surprisingly each magnetic geodesic is tangent to the 3-sphere obtained by intersecting the ambient sphere with a complex plane. We use this geometric description of the (M2HS) to give explicit criteria for blow-ups and prove the existence of global weak solutions.

**Montag 08.07.2024**

**14:15 Uhr IA 1/75**

## Oberseminar Lie-Theorie

**Alexander Ivanov (RUB): "An introduction to the Langlands correspondences" ****Abstract:** I will try to explain some basics of the Langlands program, with as few prerequisites as possible. More concretely, I will concentrate on the case of number fields (the original case, where Langlands program took its origin) and discuss in detail the one-dimensional case --that is, global class field theory. Then I will sketch the n-dimensional conjecture.

## BACH Seminar

**14:30 Uhr, IA 01/473, Marco Mazzucchelli (ENS Lyon)**

Title: LOCALLY MAXIMAL CLOSED ORBITS OF REEB FLOWS

Abstract: A compact invariant set of a flow is called locally maximal when it is the largest invariant set in some neighborhood. In this talk, based on joint work with Erman Cineli, Viktor Ginzburg, and Basak Gurel, I will present a "forced existence" result for the closed orbits of certain Reeb flows on spheres of arbitrary odd dimension:

- If the contact form is non-degenerate and dynamically convex, the presence of a locally maximal closed orbit implies the existence of infinitely many closed orbits.

- If the locally maximal closed orbit is hyperbolic, the assertion of the previous point also holds without the non-degeneracy and with a milder dynamically convexity assumption.

These statements extend to the Reeb setting earlier results of Le Calvez-Yoccoz for surface diffeomorphisms, and of Ginzburg-Gurel for Hamiltonian diffeomorphisms of certain closed symplectic manifolds.

**15:30 Uhr, HIA Foyer**, Kaffeepause

**16:15 Uhr, IA 01/473, Nicola Gigli (SISSA)**

Title: Trading linearity for ellipticity - a novel approach to global Lorentzian geometry

Abstract: The concepts of Sobolev functions, elliptic operators and Banach spaces are central in modern geometric analysis. In the setting of Lorentzian geometry, however, unless one restricts the attention to Cauchy hypersurfaces these do not have a clear analogue, due to the signature of the metric tensor. Aim of the talk is to discuss some recent observations in this direction centered around the fact that for \(p<1\) the \(p\)-D’Alambertian is elliptic on the space of time functions.

The talk is mostly based on joint project with Beran, Braun, Calisti, McCann, Ohanyan, Rott, Saemann.

**Donnerstag 4.7.2024**

**16:00 Uhr IB 3/73**

## Oberseminar Topologie

**Sven Möller (Universität Hamburg), "Sheaves of Vertex Algebras over Symplectic Resolutions"****Abstract:**

Symplectic singularities (and their resolutions) appear prominently in

(geometric) representation theory. In physics, they arise as the Higgs

branch of 3d and 4d superconformal quantum field theories.

Vertex algebras are mathematical structures that axiomatise 2d conformal

field theories. The associated Poisson variety, a certain geometric

invariant defined by a vertex algebra, is often a symplectic

singularity. In that case, the vertex algebra can be regarded as a

"chiral quantisation" of the latter.

The 4d/2d correspondence in physics (Beem et al.) proposes vertex

algebras as invariants of 4d superconformal theories. Crucially, it is

conjectured that the Higgs branch of the 4d theory can be recovered as

the associated variety of the vertex algebra. Therefore, all vertex

algebras arising from 4d theories are supposed to be chiral

quantisations of singular symplectic varieties.

I will report on work where we construct these vertex algebras as global

sections of sheaves of vertex algebras over the resolution of the

symplectic varieties.

**Donnerstag, 04.07.2024**

**16:15 Uhr IA 1/177**

## Oberseminar Dynamische Systeme

**Hans-Bert Rademacher (Leipzig), "Closed geodesics and orthogonal geodesic chords without self-intersections"****Abstract:**

We show that for a generic Riemannian metric on a compact manifold of dimension at least three all closed geodesics do not have self-intersections. Similar results are possible for geodesic loops and orthogonal geodesic chords.

**Donnerstag 27.6.2024**

**16:00 Uhr IB 3/73**

## Oberseminar Topologie

**Markus Szymik (Sheffield University), "Quandles - an algebraic theory not only for knots"****Abstract:** Knot theory, a classical topic in topology, sets the stage for our discussion. I will first outline the classification of knots in a formulation by Joyce and Matveev, which builds upon the earlier work of Burde and Waldhausen. The necessary algebraic structure, often overlooked, is pervasive throughout mathematics and finds applications in geometry, number theory, logic, and computation. Then, I will present new results that offer fresh insights into the homotopy theory and homological algebra of these structures. Part of this is joint work with Tyler Lawson.

**Donnerstag, 27.06.2024**

**14:15 Uhr IA 1/177**

## Oberseminar Dynamische Systeme

**Monika Yadav (Gandhinagar, India), "Jones polynomial and its categorification for Legendrian knots in \((\mathbb{R}^3,\xi_{st})\)** **"****Abstract: **

In this talk, I will talk about the joint work with Dr. Dheeraj Kulkarni. The goal of this talk is to define a new invariant of Legendrian knots in \(\mathbb{R}^3\) with the standard tight contact structure.

We will start by recalling some background on Legendrian knots and the Jones polynomial invariant for smooth knots. I will define two invariants of the Legendrian knot type, namely, the Legendrian Jones polynomial and the Legendrian Khovanov homology. We will see that both of these invariants are natural generalizations of the Jones polynomial and the Khovanov homology for smooth knots to the setting of Legendrian knots. In other words, for a Legendrian knot K, the Legendrian Jones polynomial P_{K}(A, r) reduces to the Jones polynomial of the underlying smooth knot after substituting r = 1. We will also see that the Thurston-Bennequin number which is a classical invariant of the Legendrian knot type, occurs as a grade shift in the Legendrian Khovanov homology.

**Dienstag, 25.06.2024**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**David Bechara Senior (Aachen), "The asymptotic action of area preserving disk maps and some of its properties"****Abstract: **

Given a diffeomorphism of the disk that preserves the standard symplectic form, I will introduce the asymptotic action associated to this map. I will then show a pointwise formula relating the asymptotic action to the asymptotic winding number of pairs of points. As a corollary one obtains a generalization for a well known result by A. Fathi which gives a formula for the Calabi invariant of a disk map in terms of its mean winding numbers. Additionally I will focus on how this formula can be used to study symplectic dynamical information for irrational pseudo-rotations of the disk. This talk includes joint work with Patrice Le Calvez and Abror Pirnapasov.

**Donnerstag, 20.06.2024****HZO 90**

**15:00-16:00** D. Calegari - *"A new family of algebraic K(π,1)s I"***16:00-17:00** Coffee break (in front of the HIA)**17:00-18:00** A. Neves - *"Recent developments in minimal surfaces I"*

**Freitag, 21.06.2024 IA 01/473**

**09:30-10:30**A. Neves -

*"Recent developments in minimal surfaces II"*

**10:30 - 11:30**Coffee break (in front of the HIA)

**11:30-12:30**D. Calegari -

*"A new family of algebraic K(π,1)s II"*

## Floer Lectures 2024

We are delighted to have **Danny Calegari** (University of Chicago) and **André Neves** (University of Chicago) as our two speakers. They will each give two talks.

This is a workshop hosted by the Floer Center of Geometry and funded by the Bochum-Cologne-Heidelberg collaboration program **CRC/TRR 191 "Symplectic Structures in Geometry, Algebra and Dynamics”**.

Anyone is welcome to attend!

There is no formal registration, but please send an email to Frau Minzlaff (Corina Minzlaff) so that we can estimate the number of participants.

We hope to see you there!

**Donnerstag 13.6.2024**

**16:00 Uhr IB 1/177**

## Oberseminar Topologie

**Jesse Cohen (Universität Hamburg), "Bordered Floer theory, Hochschild homology, and links in S^1\times S^2"****Abstract:** An early paper of Ozsváth--Szabó establishes the existence of a spectral sequence from the reduced Khovanov homology of the mirror of a link to the Heegaard Floer homology of its branched double cover. We will describe an analogue of this spectral sequence from Rozansky's categorified stable SU(2) Witten--Reshetikhin--Turaev invariant of links in S^1\times S^2 to the Hochschild homology of an A_\infty-bimodule defined using bordered Floer homology. Along the way, we will see that the algebras over which these bimodules are defined are nontrivial A_\infty-deformations of Khovanov's arc algebras.

**Donnerstag 13.6.2024**

**17:00 Uhr IB 1/177**

## Oberseminar Topologie

**Paolo Tomasini (MPIM**)**, "Equivariant elliptic cohomology and mapping stacks"****Abstract:** In this talk we will introduce a model of complexified equivariant elliptic cohomology via mapping stacks. After reviewing Grojnowski's definition of equivariant elliptic cohomology, we will introduce a notion of equivariant elliptic Hochschild homology for schemes with an action of algebraic tori, via a suitable stack of quasi-constant maps from an elliptic curve. A Tate construction converts this version of Hochschild homology into the equivariant elliptic cohomology of the analytification of the scheme. Joint with Nicolò Sibilla.

**Dienstag, 11.06.2024**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Comlan Edmond Koudjinan (Vienna), "On the Birkhoff conjecture for nearly centrally symmetric domains"****Abstract: **In this talk, I will discuss a recent advance on Birkhoff conjecture, namely a proof that : an integrable, nearly centrally symmetric Birkhoff billiard table is necessarily an ellipse. This is done by combining recent breakthroughs by Bialy-Mironov (who prove the conjecture for centrally symmetric Birkhoff billiard tables) and by Kaloshin-Sorrentino (who prove the conjecture for Birkhoff billiard tables close to ellipses). In particular, we shall discuss the use of nonstandard generating functions discovered by Bialy-Mironov. This is a joint work with Ke Zhang and V. Kaloshin.

**Monday 10.06.24**

and**Tuesday 11.06.24**

**14:00 - 15:00**

and**16:00 - 17:00 **

**ID 03/653**

## Lecture Series "Matroidal polynomials and their singularities''

A lecture series by**Uli Walther (Purdue University, USA)**

to be held at Ruhr-University Bochum within the DFG Priority Programme 2458 "Synergies in Combinatorics"

**Topics to be covered:**

- Matroids, matroidal polynomials, examples of these, including Kirchhoff polynomials, configuration polynomials, multivariable Tutte polynomials, matroid support polynomials.
- Feynman diagrams and Feynman integrands (which are also matroidal). A discussion on torus actions on these hypersurfaces. The singular locus of certain matroidal polynomials: for configuration polynomials when the matroid is sufficiently connected, discuss irreducibility, size of singular locus, comparison between Jacobian ideal and a certain corank 2 determinantal ideal, Cohen-Macaulayness of these. The special case of the free resolution of the singular locus of the Kirchhoff polynomial of a complete graph.
- For matroidal polynomials in general, it will be explained that they have rational singularities, and in the homogeneous case that they are F-regular.
- Time permitting there will also be a discussion about the resolution of singularities.

**Dienstag, 04.06.2024**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Umberto Hryniewicz (Aachen), "Proof of Hofer-Wysocki-Zehnder’s two or infinity conjecture"****Abstract: **In this talk we will describe the main steps in the proof that the Reeb flow of a contact form on a closed connected 3-manifold has exactly two or infinitely many periodic orbits, under the assumption that the first Chern class of the associated contact structure is torsion. This is joint work with Cristofaro-Gardiner, Hutchings and Liu.

**Montag 03.06.2024**

**14:15 Uhr IA 1/75**

## Oberseminar Lie-Theorie

**Jakub Löwit (IST): "On modular p-adic Deligne--Lusztig theory for GL_n" ****Abstract:** In 1976, Deligne--Lusztig realized the characteristic zero representation theory of finite groups of Lie type inside cohomology of certain algebraic varieties. This picture has two interesting generalizations. In one direction, one can replace finite groups by p-adic groups. In another direction, one can consider modular coefficients. After recalling the key players, I will discuss what happens in the p-adic case with modular coefficients for GL_n. In particular, I will explain how to deduce such results from the case of characteristic zero coefficients.

**Dienstag, 21.05.2024**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Robert Cardona (Barcelona), "Contact topology and time-dependent hydrodynamics"****Abstract: **More than twenty years ago, Etnyre and Ghrist established a connection between Reeb fields and a class of stationary solutions to the 3D Euler equations for ideal fluids. In this talk, we present a new framework that allows assigning contact/symplectic invariants to large sets of *time-dependent* solutions to the Euler equations on any three-manifold with an arbitrary fixed Riemannian metric, thus broadening the scope of contact topological methods in hydrodynamics. We use it to prove a rather general non-mixing result for the infinite-dimensional dynamical system defined by the equation and to show the existence of new conserved quantities obtained from embedded contact homology spectral invariants. This is joint work with Francisco Torres de Lizaur.

**Donnerstag, 02.05.2024**

**16:15 Uhr IA 1/177**

## Oberseminar Dynamische Systeme

**Agustin Moreno (Heidelberg), "Symplectic structures from almost symplectic structures"****Abstract:** In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures. Given a formal symplectic manifold, i.e. a closed manifold M with a non-degenerate 2-form and a non-degenerate second cohomology class, we investigate when its natural stabilization to M x T^2 can be realized by a symplectic form.

We show that this can be done whenever the formal symplectic manifold admits a positive symplectic divisor. It follows that if a formal symplectic 4-manifold, which either satisfies that its positive/negative second betti numbers are both at least 2, or that is simply connected, then M x T^2 is symplectic.

This is joint work with Fabio Gironella, Fran Presas, Lauran Touissant.

**Montag 29.04.2024**

**16:15 Uhr IA 1/135**

## Oberseminar Arrangements and Symmetries

**Daniel Bath (KU Leuven): "Bernstein—Sato polynomials of Hyperplane Arrangements in C^3" ****Abstract:** The roots of Bernstein—Sato polynomial of a hypersurface manages to simultaneously contain most classical singularity invariants. Alas, computing these roots is mostly infeasible. For hyperplane arrangements in C^3, one can hope the roots of its Bernstein—Sato polynomial are combinatorially determined. Alas, things are more subtle. Walther demonstrated two arrangements with the same intersection lattice but whose respective Bernstein—Sato polynomials differ by exactly one root. We will show this is the only pathology possible. For arrangements in C^3, we prove that all but one root are (easily) combinatorially determined. We also give several equivalent criterion for the outlier, -2 + (2/deg), to in fact be a root of the Bernstein—Sato polynomial. These involve local cohomology data of the Milnor algebra and the non-formality of the arrangement.

This is an application of a study of Bernstein—Sato polynomials for a larger class of C^3 divisors than just arrangements. We will discuss Bernstein—Sato polynomials at large, our general strategy for divisor class, our main results, and how the promised formula for hyperplane arrangements appears.

**Donnerstag 25.04.2024**

**16:00 Uhr IB 3/73**

## Oberseminar Topologie

**Kaif Hilman (MPIM), "Equivariant Poincaré duality for finite groups and fixed points methods"****Abstract:** In this talk, I will introduce the notion of Poincare duality spaces in the equivariant setting for finite groups and discuss an approach relating equivariant Poincare duality with Poincare duality on the fixed points via a categorical basechange. Time permitting, I will also indicate how one can use the theory to give a new, purely homotopical, proof of an old theorem of Atiyah-Bott and Conner-Floyd. This is joint work with Dominik Kirstein and Christian Kremer.

**Mittwoch 17.04.2024**

**12:00 Uhr IA 1/109**

## Oberseminar über komplexe Geometrie

**Shang Li (Paris), "Wonderful compactification over an arbitrary base scheme"****Abstract:** Wonderful compactifications of adjoint reductive groups over an algebraically closed field play an important role in algebraic geometry and representation theory. In this talk, we will construct an equivariant compactification for adjoint reductive groups over arbitrary base schemes, which parameterize classical wonderful compactifications of De Concini and Procesi as geometric fibers. Our construction is based on a variant of the Artin–Weil method of birational group laws. In particular, our construction gives a new intrinsic construction of wonderful compactifications. If time permits, we will also discuss several applications of our compactification in the study of torsors under reductive group schemes.

**Dienstag 16.04.2024**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Karla Leipold (Cologne), "Computing the EHZ-capacity is NP-hard"****Abstract:** We show that computing the EHZ capacity of polytopes is NP-hard. For this we reduce the feedback arc set problem in bipartite tournaments to computing the EHZ capacity of simplices.

**Montag 15.04.2024**

**14:15 Uhr IA 1/75**

## Oberseminar Lie-Theorie

**David Schwein (University of Bonn), "Tame supercuspidals at very small primes"****Abstract:** Supercuspidal representations are the elementary particles in the representation theory of reductive p-adic groups. Constructing such representations explicitly, via (compact) induction, is a longstanding open problem, solved when p is large. When p is small, the remaining supercuspidals are expected to have an arithmetic source: wildly ramified field extensions. In this talk I'll discuss ongoing work joint with Jessica Fintzen that identifies a second, Lie-theoretic, source of new (tame!) supercuspidals: special features of reductive groups at very small primes. We'll summarize some of these features and explain how they contribute to the construction of supercuspidals.

**Dienstag **

**20.02.2024**

**16:15 Uhr IA 1/53**

## Oberseminar Dynamische Systeme

**Karim Mosani (Tübingen), "Geometry of trapped photon region in a class of stationary spacetimes"****Abstract:** In Einstein’s general relativity, extremely strong gravity can trap light. In a spacetime admitting a singularity, we say that light (or a “photon”) is trapped if it neither escapes to spatial infinity nor falls into the singularity. Null geodesics govern the trajectories of light. In the Schwarzschild spacetime with posi- tive mass M, there exist (unstable) circular orbits of trapped photons at the Schwarzschild radius r = 3M, outside the black hole horizon at r = 2M. These orbits fill a three-dimensional submanifold of topology S2 ×R called the photon sphere of the Schwarzschild spacetime. In general, a region in spacetime that is a union of all trapped null geodesics is called the Trapped Photon Region (TPR) of the spacetime. In this talk, we will consider a particular stationary space-time class constructed by the Newman-Jenis algorithm. We will see that, unlike the TPR of Schwarzschild spacetime, the TPR in such spacetimes is not a submanifold of the spacetime in general. However, the lift of TPR in the phase space is a five-dimensional submanifold. This result has applications in various problems in mathematical relativity (This work is an extension of the similar result but in Kerr spacetime, by Cederbaum and Jahns- 2019). This is a joint work with Carla Cederbaum.

**Dienstag 13.02.2024**

**16:15 Uhr IA 1/53**

## Oberseminar Dynamische Systeme

**James Farre (Leipzig), "Horospheres, Lipschitz maps, and laminations"**

**Abstract:**

Every horocycle in a closed hyperbolic surface is dense, and this has been known since the 1940's. We study the behavior of horocycle orbit closures in Z-covers of closed surfaces, and obtain a fairly complete classification of their topology and geometry. The main tool is a solution of a surprisingly delicate geometric optimization problem: finding an optimal Lipschitz map to the circle and the associated lamination of maximal stretch. This is joint work with Yair Minsky and Or Landesberg.

**08.-10.02.2024**

## CAST in Bochum

## BACH Seminar

**14:30 Uhr, IA 01/473**, Marco Radeschi (Torino), „Reading topological ellipticity of G-manifolds from their quotients”

**15:30 Uhr, HIA Foyer**, Kaffeepause

**16:15 Uhr, IA 01/473**, Lei Zhao (Augsburg), „*z* ↦ *z*^{2}“

**MIttwoch 10.01.2024**

**14:15 Uhr ID 03/653**

## Antrittsvorlesungen

**14:15 Uhr, ID 03/653**, Jun.-Prof. Dr. Luca Asselle, „Morse theory in infinite dimension old and new”

**15:15 Uhr, ID 03/471**, Kaffeepause

**16:15 Uhr, ID 03/653**, Prof. Dr. Alexander Ivanov, „Meromorphe Vektorbündel auf der Fargues--Fontaine Kurve“

**Donnerstag 11.1.2024**

**16:00 Uhr IB 3/73**

## Oberseminar Topologie

**Julian Brüggemann, "**On discrete Morse theory in persistent topology**"**

**Abstract: **Discrete Morse theory is a versatile tool in combinatorial algebraic topology for the investigation of cell complexes of many different flavors. Persistent topology is the study of filtered spaces using topological techniques, which are ubiquitous in topological data analysis. In this talk, I will give a brief introduction to persistent topology and motivate the subject with topological data analysis. After that I will present results from my PhD thesis: an investigation of the inverse problem between discrete Morse functions on graphs and their induced (generalized) merge trees, as well as a novel model for the moduli space of discrete Morse functions and its relationship to smooth Morse theory, discrete Morse matchings, merge trees, and barcodes. In these projects, I mostly use concepts from graph theory, poset theory, combinatorial topology, combinatorial geometry, differential topology, and differential geometry.

**Dienstag 16.1.2024**

**14:00 Uhr IB 3/73**

## Oberseminar Topologie

**Leo Ryvkin, "Differentiation of simplicial manifolds"**

**Abstract: ** Kan simplicial manifolds provide a very explicit model for $L_\infty$-groupoids. Pavol Severa proposed a procedure of differentiation for these objects, yielding an $L_\infty$-algebroid, (an NQ-manifold). In the talk I will report on joint work with Du Li, Arne Wessel and Chenchang Zhu, where we have proven that this procedure always works.

**Mittwoch 17.01.2024**

**10:00 Uhr IA 1/75**

## Oberseminar über Komplexe Geometrie

**Johanna Bimmermann, "Capacities of disk tangent bundles"**

**Abstract: **In general rather little is known about symplectic capacities of open subsets of cotangent bundles. In this talk I will discuss methods to compute the Gromov width and the Hofer—Zehnder capacity of disk tangent bundles and demonstrate these methods for certain homogenous spaces (namely spheres and projective spaces). The key observation is that in these cases the disk bundle sits as complement of a divisor inside a coadjoint orbit. This makes it possible to explicitly construct symplectic embeddings of balls for the lower bound and find non-vanishing Gromov—Witten invariants for the upper bound.

**Donnerstag 07.12.2023**

**15:00 Uhr HIB **

**Freitag 08.12.2023**

**09:30 Uhr HZO 20**

## Floer Lectures

**Thursday (HIB):**

15:00-16:00 Gigliola Staffilani - *"A small window on wave turbulence theory I"*

16:00-17:00 Coffee break

17:00-18:00 Alessio Figalli - *"Quantitative stability in geometric and functional inequalities I"*

**Friday (HZO 20):**

09:30-10:30 Alessio Figalli - *"Quantitative stability in geometric and functional inequalities II"*

10:30 - 11:30 Coffee break

11:30-12:30 Gigliola Staffilani - *"A small window on wave turbulence theory II" *

**Abstracts:**

Gigliola Staffilani - *"A small window on wave turbulence theory"*

Wave turbulence theory is a vast subject and its goal is to formulate for us a global

picture of wave interactions. Phenomena involving interactions of waves happen at different

scales and in different media: from gravitational waves to the waves on the surface of the

ocean, from our milk and coffee in the morning to infinitesimal particles that behave like

wave packets in quantum physics. These phenomena are difficult to study in a rigorous

mathematical manner, but maybe because of this challenge mathematicians have developed

interdisciplinary approaches that are powerful and beautiful. I will describe some of these

approaches and show for example how the need to understand certain multilinear and periodic

interactions gave also the tools to prove a famous conjecture in number theory, or how

classical tools in probability gave the right framework to still have viable theories behind

certain deterministic counterexamples.

Alessio Figalli - *"Quantitative stability in geometric and functional inequalities"*

Geometric and functional inequalities play a crucial role in several problems in analysis and

geometry. The sharpness of a constant and the characterization of minimizers is a classical

and essential question. More recently, there has been a growing interest in studying the

stability of such inequalities. The basic question one wants to address is the following:

Suppose we are given a functional inequality for which minimizers are known. Can we

quantitatively show that if a function “almost attains the equality,” then it is close to one of

the minimizers?

In these lectures, I will first overview this beautiful topic and then discuss recent results

concerning the Sobolev, isoperimetric, and Brunn–Minkowski inequalities.

**Dienstag 05.12.2023**

**16:15 Uhr IA 1/53**

## Oberseminar Dynamische Systeme

**Álvaro del Pino (Utrecht), "Convex integration with avoidance"**

**Abstract:**

Convex integration is one of the most important tools in the construction of solutions of partial differential relations. It was first introduced by J. Nash in his work on C^1 isometric embeddings and later generalised by M. Gromov to deal with a large class of differential relations satisfying a geometric condition called ampleness.

Gromov developed various flavours of ampleness to which convex integration applies. Roughly speaking, there is an "easy" to check version (ampleness in all principal directions) that is limited in its applications, and an "impossible" to check version (ampleness via convex hull extensions) that is extremely general.

This will motivate me to discuss a new version of convex integration and a corresponding notion of ampleness, called ampleness up to avoidance. This notion is checkable in practice and applies in more generality than ampleness in all principal directions. This is joint work with F.J. Martínez Aguinaga.

**Dienstag 28.11.2023**

**16:15 Uhr IA 1/53**

## Oberseminar Dynamische Systeme

**Valerio Assenza (Heidelberg), "Geometrical aspects of magnetic flows"**

**Abstract: **To a Riemannian manifold endowed with a magnetic form we associate an operator called Magnetic Curvature. Such an operator encodes the geometrical properties of the Riemannian structure together with terms of perturbation due to the magnetic interaction and carries relevant information about the magnetic dynamics. In the first part of the talk we will see how a level of the energy positively curved in a magnetic sense carries a contractible periodic orbit. The second part is devoted to the generalization of the Hopf’s rigidity to the magnetic case and to the notion of magnetic flatness.

**Dienstag 14.11.2023**

**16:15 Uhr IA 1/53**

## Oberseminar Dynamische Systeme

**Michael Rothgang (Berlin-Humboldt), "Equivariant transversality for holomorphic curves"**

**Abstract: **We study closed holomorphic curves in symplectic G-manifolds, with respect to a G-equivariant almost complex structure. We should not expect the moduli space of such curves to be a manifold (after all, transversality and symmetry are famously incompatible). However, we can hope for a clean intersection condition: the moduli space decomposes into disjoint strata which are smooth manifolds; the dimensions of the strata are explicitly computable.

I'll present this decomposition for simple curves and indicate how to extend this to multiple covers. These are the first steps towards a well-behaved theory of equivariant holomorphic curves.

**Donnerstag 16.11.2023**

**16:00 Uhr IB 3/73**

## Oberseminar Topologie

Yuqing Shi (Universität Bonn) spricht über:

**A universal property of the Bousfield—Kuhn functor**

Abstract: Stable chromatic homotopy theory provides us with a filtration of the category of p-local spectra, for a fixed prime number p. The associated graded of this filtration, known as the monochromatic layer of height h (with h ∈ ℕ), is given by the category of vₕ-periodic spectra, i.e. the localisation of the category of p-local spectra on the set of so-called vₕ-periodic equivalences. The layer of height 0 recovers the rational spectra. In a similar way, Bousfield constructs the unstable monochromatic layer, which is the localisation of the category of p-local homotopy types on the set of vₕ-periodic equivalences. The Bousfield—Kuhn functor Φₕ, mapping from the unstable to the stable monochromatic layer of height h, serves as an important bridge between unstable and stable chromatic homotopy theory. For example, it is shown by Heuts that Φₕ exhibits vₕ-periodic homotopy types as spectral Lie algebras in vₕ-periodic spectra, generalising Quillen's Lie algebra model for simply connected rational homotopy types. In this talk we will present a universal property of the Bousfield—Kuhn functor, exhibiting the stable monochromatic layer as a costabilisation of the unstable monochromatic layer.

Guests are very welcome!

**Mittwoch 08.11.2023**

**15:00 Uhr IB 1/103**

## Women in math

**Welcome event**

Join us in welcoming all Women and Gender Minorities of the Math Faculty, as we kick off the Winter Semester at RUB.

Connect with fellow mathematicians and learn about their

field of research, while enjoying delicious cake and drinks.

DATE: 8 November 2023

TIME: 15.00

LOCATION: Friedrich-Sommer-Raum IB 1/103

Spread the word, and see you there!

**Donnerstag 02.11.2023**

**09:30 - 16:30 Uhr TBA**

**Freitag 03.11.2023**

**09:00 - 17:00 Uhr IA 02/445**

## Workshop in memory of Dmitri Akhiezer

**Lie Group Actions in Complex Analysis**

You can find more detailed information on the following website:

https://sites.google.com/view/workshop-dmitri-akhiezer/home

**Mittwoch 27.09.2023**

**10:15 Uhr IA 1/135**

## Oberseminar Komplexe Geometrie

**Dr. Valdemar Tsanov (Bulgarian Academy of Sciences), "Mackey Lie algebras and universal tensor categories"**

Abstract:

A known source of problems in infinite dimensional linear algebra is the fact that the dual space V* to an infinite dimensional vector space V has dimension (the cardinality of a basis) strictly larger than that of V. A recently defined class of algebras - Mackey Lie algebras, or the related Mackey groups - offer a way to study V* and discover some interesting structures. In this talk, based on joint work with Ivan Penkov, I will define Mackey Lie algebras and explain the classification of their ideals, simple tensor modules, and a generalization of Schur-Weyl duality. I will also describe a category of Mackey modules with a universality property similar to the universality property of a tensor product.

**Mittwoch 20.09.2023**

**10:15 Uhr IA 1/109**

## Oberseminar Komplexe Geometrie

**Dr. Valdemar Tsanov (Bulgarian Academy of Sciences), "Partial convex hulls of coadjoint orbits"**

Abstract:

The coadjoint orbits of compact Lie groups, equipped with their Kostant-Kirillov-Sourieau Kähler structures, represent models for all simply connected compact homogeneous Kähler manifolds. The integral orbits admit embeddings as projective algebraic varieties corresponding to the irreducible unitary representations of the group. Several representation theoretic concepts are related to properties of the convex hull of the orbit, and to its projections to subalgebras. I will introduce the notion of partial convex hulls in this context and indicate some of its relations to representation theory and invariant theory.

**Mittwoch 13.09.2023**

**10:15 Uhr IA 1/109**

## Oberseminar Komplexe Geometrie

**Dr. Valdemar Tsanov (Bulgarian Academy of Sciences), "On the nonconvexity of momentum map images"**

Abstract:

A classical theorem of Atiyah asserts that the image of a momentum map for a Hamiltonian action of a connected compact Lie group on a compact Kähler manifold is a convex polytope, whenever the group is abelian. For a nonabelian group, a convex polytope is obtained by intersecting the image with a Weyl chamber, but the entire image may or may not be convex. In this talk, I will discuss some phenomena causing nonconvexity, and derive sufficient conditions for convexity of the entire image. In particular, I will present a structural characterization of the compact connected subgroups of a compact group, for which all coadjoint orbits of the larger group have convex momentum images under the subgroup.

**Mittwoch 16.08.2023**

**10.00 Uhr IA 1/53**

## Vortrag

**PD Dr. Stéphanie Cupit-Foutou**, „Eine Verallgemeinerung des Sylvester'schen Trägheitssatzes“

Alle Interessenten sind herzlich eingeladen.

**Dienstag 11.07.2023**

**10:00 Uhr ID 03/653**

## Mini Workshop "Random graphs"

**10:00 - 11:00 Uhr, **Tara Trauthwein: Normal approximation of Poisson functionals via generalized p-Poincaré inequalities

**11:30 - 12:30 Uhr, **Matthias Linenau: Large components in the subcritical Norros-Reittu model

**14:30 - 15:30 Uhr, **Benedikt Rednoß: Normal approximation for subgraph counts

**Mittwoch 05.07.2023**

**12:15 Uhr IA 1/109**

## Oberseminar Komplexe Geometrie

**Oliver Brammen (RUB), "Intersections between harmonic manifolds and complex geometry"**

Abstract:

The aim of this talk is to highlight connections between the study of harmonic manifolds and Grauert tubes and pose some questions arising from this connection. To this end, I will give an introduction to harmonic manifolds and informally present results from R.M Aguilarand M.B. Stenzel about the characteristics of their Grauert tube, in case of their existence. Furthermore, I will discuss questions regarding the isometry group of harmonic manifolds.

**Mittwoch 21.06.2023**

**14.15 Uhr ID 03/445**

## Antrittsvorlesungen

**Katharina Kormann**, „Approximation und Struktur - Numerik schnell und zuverlässig“

Alle Interessenten sind anschliessend zu Kaffee/Tee/Kuchen eingeladen.

**Dienstag 20.06.2023**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Filip Broćić (Montreal), "Riemannian distance and symplectic embeddings in cotangent bundle"**

Abstract In the talk, I will define a distance-like function d_W on the zero section N of the cotangent bundle T*N. The function d_W is defined using certain symplectic embeddings from the standard ball to the open neighborhood W of the zero section. Using such a function, one can define a length structure on the zero section. The main result of the talk is that in the case when W is equal to the unit disc-cotangent bundle with respect to some Riemannian metric g, the length structure is equal to the Riemannian length. In the process of explaining the proof I will present some results related to the relative type of Gromov width in T*N, and I will give the proof of the strong Viterbo conjecture for the product of two Lagrangian discs in R^{2n}. In the joint work with Dylan Cant, we were able to give a sharper bound on the relative Gromov width, under some constraints, using bordism classes in the free loop space. We also prove the existence of periodic orbits for a large class of Hamiltonians using the same technic. Time permitting, I will present how to use bordism classes to prove these results.

**Freitag 16.06.2023**

** IA 01/473**

## BACH Seminar

14:30 - 15:30 Jakob Hedicke (Montreal)

15:30 - 16:15 coffee break

16:15 - 17:15 Fabian Ziltener (Utrecht)

Jakob Hedicke:

**Title: A causal**** ****characterisation**** ****of positively elliptic elements in**** ****Sp(2n)**

Abstract: We will use the unique bi-invariant proper closed convex cone structure on the linear symplectic group to characterise the set of Krein-positively elliptic elements in terms of causality.

In particular we will show that the positively elliptic region is globally hyperbolic.

These results can be applied to study the causal geodesics and the Lorentzian distance of a bi-invariant Lorentz-Finsler metric on Sp(2n) and its universal cover, recently introduced by Abbondandolo, Benedetti and Polterovich.

Fabian Ziltener:

**Title: Capacities as a complete**** ****symplectic**** ****invariant**

Abstract: This talk is about joint work with Yann Guggisberg. The main result is that the set of generalized symplectic capacities is a complete invariant for every symplectic category whose objects are of the form $(M,\omega)$, such that $M$ is compact and 1-connected, $\omega$ is exact, and there exists a boundary component of $M$ with negative helicity. This answers a question of Cieliebak, Hofer, Latschev, and Schlenk. It appears to be the first result concerning this question, except for results for manifolds of dimension 2, ellipsoids, and polydiscs in $\mathbb{R}^4$.

If time permits, then I will also present some answers to the following question and problem of Cieliebak, Hofer, Latschev, and Schlenk:

Question: Which symplectic capacities are connectedly target-representable?

Problem: Find a minimal generating set of symplectic capacities.

**Donnerstag 15.06.2023**

**16:15 Uhr IB 3/73**

## Oberseminar Topologie

"Eine topologische Tour durch Datenanalyse und Neurale Netze"

Damian Dadanovic

Dieser Vortrag ist eine Einführung in neurale Netze, mit Fokus auf "Convolutional Neural Networks" (CNNs), und eine Einführung in Topologische Datenanalyse (TDA). Anwendungsbeispiele von TDA sind die Analyse von Bildern bzw. Pixel-patche und die Entwicklung von CNNs für Bilderkennung. Gegebenenfalls auch in diesem Vortrag ist eine Erklärung, welche Rolle die Kleinschen Flasche im Kontext der Bilderkennung spielt.

**Dienstag 13.06.2023**

**16:15 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Roman Golovko (Prague), "On non-geometric augmentations of Chekanov-Eliashberg algebras"**

Abstract: Legendrian contact homology is a modern invariant of Legendrian submanifolds of contact manifolds defined by Eliashberg–Givental–Hofer and Chekanov, and developed by Ekholm–Etnyre–Sullivan for the case of the standard contact vector space.

It is defined to be the homology of the Chekanov-Eliashberg algebra of a given Legendrian submanifold. This invariant is difficult to compute, and, in order to make it computable, one needs to use augmentations. Some augmentations come from certain geometric objects called exact

Lagrangian fillings, some do not. We will discuss non-geometric augmentations for high dimensional Legendrian submanifolds. Along the way, we prove a Künneth formula for (linearized) Legendrian contact homology for high spuns of Legendrian submanifolds. If time permits, we will also discuss whether algebraic torsion appears in Legendrian contact homology.

**Dienstag 13.06.2023**

**17:30 Uhr IA 1/181**

## Oberseminar Dynamische Systeme

**Sayani Bera (IACS, Calcutta) ), "On non-autonomous attracting basins"**

Abstract: The goal of this talk is to discuss briefly the idea of the proof of the Bedford's conjecture (formulated by Fornæss-Stensønes in 2004), on uniform non-autonomous attracting basins of automorphisms of C^k, k \ge 2 and Fatou-Bieberbach domains.

Thus we also affirmatively answer Bedford's question (2000) on uniformizations of the stable manifolds, corresponding to a hyperbolic compact invariant subset of a complex manifold.

This is a joint work with Dr. Kaushal Verma.

**Mittwoch 24.05.2023**

**13:00 Uhr ID 03/445**

## Studiengangsbezogene Lehrveranstaltung

**Dr. Martin Kroll, „Der χ^2-Anpassungstext"**

**Mittwoch 17.05.2023**

**12:15 Uhr IB 01/103**

## Frauenvollversammlung

Alle Professorinnen, Mitarbeiterinnen und Studentinnen der Fakultät für Mathematik sind herzlich zur Frauenvollversammlung eingeladen.

Tagesordnung: Nachwahl dezentrale Gleichstellungsbeauftragte, siehe Wahlordnung hierzu:

https://www.chancengleich.ruhr-uni-bochum.de/cg/chancen/dezentral.html.de

**Donnerstag 11.05.2023**

**14:15 Uhr IA 01/177**

## Oberseminar Dynamische Systeme

**Stefano Baranzini (Turin), "Morse Index Theorems for Graphs"**

Abstract: The classical N-centre problem of Celestial Mechanics describes the behaviour of a point particle under the attraction of a finite number of motionless bodies. Considered as a limit case of a (N+1)-body problem, it has been the object of several results concerning integrability, investigation of chaos and existence of periodic orbits, mostly when the motion is constrained to the Euclidean plane. In particular, variational approaches are convincing in this situation and have produced classes of collision-less periodic solutions, after imposing topological constraints of different natures. Looking for genuine solutions of second order differential equations, the most delicate step resides in avoiding collisions with the centres. Picturing a more realistic situation, a natural extension of these results could be the one in which the motion is constrained to a prescribed Riemannian surface. In this talk we state the N-centre problem on orientable surfaces and we show how it is possible to use variational arguments in order to produce collision-less periodic solutions. Such trajectories will be found among homotopy classes of loops, and their variational and topological properties will be described. This is a joint work with Stefano Baranzini.

**Mittwoch 10.05.2023**

**14:15 Uhr ID 03/445**

## Wissenschaftlicher Vortrag

**Dr. Martin Kroll, „Approximation positiv definiter Funktionen auf kompakten Gruppen“**

**Dienstag 09.05.2023**

**16:15 Uhr IA 01/181**

## Oberseminar Dynamische Systeme

**Gian Marco Canneori (Turin), "The N-centre problem on Riemannian surfaces: a variational approach"**

Abstract: The classical N-centre problem of Celestial Mechanics describes the behaviour of a point particle under the attraction of a finite number of motionless bodies. Considered as a limit case of a (N+1)-body problem, it has been the object of several results concerning integrability, investigation of chaos and existence of periodic orbits, mostly when the motion is constrained to the Euclidean plane. In particular, variational approaches are convincing in this situation and have produced classes of collision-less periodic solutions, after imposing topological constraints of different natures. Looking for genuine solutions of second order differential equations, the most delicate step resides in avoiding collisions with the centres. Picturing a more realistic situation, a natural extension of these results could be the one in which the motion is constrained to a prescribed Riemannian surface. In this talk we state the N-centre problem on orientable surfaces and we show how it is possible to use variational arguments in order to produce collision-less periodic solutions. Such trajectories will be found among homotopy classes of loops, and their variational and topological properties will be described. This is a joint work with Stefano Baranzini.

**Mittwoch 03.05.2023**

**14:15 Uhr IA 02/445**

## Antrittsvorlesungen

**14:15 Uhr, Prof. Dr. Kai Zehmisch**, „Komplexe Suche nach reellen Lösungen“

15:15 Uhr, Kaffeepause, IA 02/480/481

**16:00 Uhr, Prof. Dr. Patrick Henning**, „Mehrskalenprobleme und deren numerische Behandlung“