### November 2024

**Location: **HIM lecture hall (Poppelsdorfer Allee 45, Bonn)

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Location: **Room: 0.003 (Endenicher Allee 60)**Abstract:** A representation of a set is a surjection from a subset of Baire space onto this set. Equipping a set with a representation can be seen as giving it ‘a notion of computability’. In this context, computability is seen as a refinement of topology, as continuous functions are the functions that are computable modulo ‘some oracle’. I will introduce the natural representation associated to groups given by the solution to their word problem, and discuss two problems: the existence of natural group properties that are open but not computably

open, and the comparison of ‘residual maps’, like the abelianization or the residually finite image, in the Weihrauch lattice, which gives a way to classify how discontinuous these functions are.

**Location: **Großer Hörsaal, Wegelerstraße 10, Bonn

**Location:** MPIM Lecture Hall

**This talk will be online via Zoom, Meeting ID: 63202654583, Passcode: 404412**

**Abstract: **We discuss the quantitative long-time convergence behavior of several kinetic dynamics for sampling, including the (underdamped) Langevin dynamics, randomized Hamiltonian Monte Carlo, and the zig-zag sampler. We will show how the growth of the potential impacts the convergence rates of the dynamics, via the Poincaré inequality or its weak variants, and draw the link between the convergence rates of similar dynamics for sampling and for optimization. The analysis is based on the Armstrong-Mourrat variational framework for hypocoercivity which combines a Poincaré-type inequality in time-augmented state space and an L^2 energy estimate.

Location: MPIM Seminar Room

**Abstract:** Bridgeland stability conditions have been constructed on curves, surfaces, and in some higher dimensional examples. In several cases, there are only so-called "geometric" stability conditions, which are constructed using slope stability for sheaves, whereas in other cases, there are more (for example if there is an equivalence with quiver representations). Lie Fu, Chunyi Li, and Xiaolei Zhao were the first to provide a general result explaining this phenomenon. In particular, they showed that if a variety has a finite map to an abelian variety, then all stability conditions are geometric. In this talk, we test the converse in two ways on surfaces that arise as free quotients by finite groups. One method is via Le Potier functions which characterize the existence of slope-semistable sheaves. The second method uses equivariant categories. This is joint work with Edmund Heng and Anthony Licata, based on arxiv:2307.00815 and arxiv:2311.06857.

**Location:** Max Planck Institut - Hörsaal

**Location:** MPIM Lecture Hall

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Location: **MPIM Lecture Hall

**Location:** MPIM Lecture Hall

**Abstract:** Arising in various contexts, such as e.g. quantum symmetric pairs and categorical actions on category O, module categories over monoidal categories are a natural part of the general setting of categorical representation theory. A common way to study, construct and classify module categories over a rigid monoidal category C is by "reconstructing" them as categories of modules for an algebra object in C. In absence of rigidity, e.g. for categories of crystals, monoid representations, and, more generally, modules over non-Hopf bialgebras, it is easy to provide examples where reconstruction fails. In this talk, I will present reconstruction results for module categories over non-rigid categories, where algebra objects are replaced by certain monads on C. I will also explain how these results can be used to obtain an algebraic description of module categories for categories of modules over non-Hopf bialgebras via certain Hopf modules (so-called Hopf trimodules), and present further applications.

**Location:** Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Raum 1.008.

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Abstract**: Given a (possibly non-linear) differential equation, how can we tell if there is an algebraic solution? I will discuss two elementary problems which are motivated by this question, and their solutions, which require some input from modern algebraic geometry. The first is a classification of algebraic solutions to a system of differential equations, known as the Schlesinger system, generalizing the corresponding classification for the Painlevé VI equation; equivalently, this is a classification of the finite orbits of the braid group action on (rank two) character varieties. The second is a conjectural arithmetic criterion for detecting algebraic solutions to differential equations, which is a converse to the last theorem of Eisenstein's: I'll discuss the proof of this conjecture in cases of "geometric origin".

This is based on joint works with Litt, and Landesman--Litt

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Location:** Lipschitzsaal

**Location:** MPIM Seminar Room

**Location:** MPIM Lecture Hall**Link:** https://www.mpim-bonn.mpg.de/UHT

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Location:** Lipschitz-Saal, Endenicher Allee 60

**Location:** MPIM Seminar Room

**Location**:

Room: Zoom meeting 641 6780 5250

https://uni-bonn.zoom-x.de/j/64167805250, password is the seminar name

(3 letters, lowercase)

**Abstract:**

For d≥4 and p a sufficiently large prime, we construct a lattice Γ≤PSp2d(ℚp), such that its universal central extension cannot be sofic if Γ satisfies some weak form of stability in permutations. In the proof, we make use of high-dimensional expansion phenomena and, extending results of Lubotzky, we construct new examples of cosystolic expanders over arbitrary finite abelian groups. This is joint with with Lukas Gohla.

**Location:** MPIM Lecture Hall

**Abstract:** I will talk about a complete proof of Mukai's Theorem describing K3 surfaces and prime Fano threefolds of genus g \in {7,8,9,10,12} as zero loci of global sections of equivariant vector bundles on Grassmannians, where the key role is played by Schubert divisors. This is a joint result with Arend Bayer and Emanuele Macri.

**Location:** Lipschitzsaal, Endenicher Allee 60

**Abstract:** Here is a motivating question, which is a special case of a more general problem: The moduli space of K3 surfaces in characteristic p is stratified by the height of the formal Brauer group, and the smallest stratum (the supersingular locus) is further stratified by the Artin invariant. If we give ourselves an explicit K3 surface, e.g. a quartic surface in P^3, how can we calculate in which stratum it lies? In my talk, I will explain what an F-zip is (I will not assume you already know this), and how this relates to the above problem. Under mild technical assumptions, we can associate an F-zip to every smooth projective variety in characteristic p, and such F-zips have been classified. I will explain some new techniques that allow us to calculate the F-zips of some accessible types of varieties, such as projective hypersurfaces.

**Location:** Lipschitzsaal, Endenicher Allee 60

**Location:** MPIM Seminar Room

**Location: **Raum 1.008 in MI

**Abstract: **An affine Lie algebra g is a central extension of the loop algebra of a complex simple Lie algebra, and a g-module is said to have (relative) level k if the canonical central element acts by the scalar k-h, where h is the dual Coxeter number. For all levels k that are not positive rational or zero, Kazhdan and Lusztig have defined a braided monoidal structure on a parabolic BGG category O of g-modules of level k. In this talk, I will explain the definition of a braided monoidal structure on the category O at positive rational levels, via a monoidal enhancement of Brundan and Stroppel's semi-inifnite Ringel duality.

This is based on joint work with Johannes Flake and Robert McRae.

**Location: **HIM lecture hall (Poppelsdorfer Allee 45, Bonn)

**Location:** Lipschitzsaal

**Location:** Endenicher Allee 60, Lipschitz hall

**Location: **Endenicher Allee 60, Lipschitz hall

**Location**: Max Planck Institute - Lecture Hall

**Abstract:**

Let X be a very general hypersurface of dimension 3 and degree d at least 6. Griffiths and Harris conjectured in 1985 that the degree of every curve on X is divisible by d. Substantial progress on this conjecture was made by Kollár in 1991 via degeneration arguments. However, the conjecture of Griffiths and Harris remained open in any degree d. In this talk, I will explain how to prove this conjecture (and its higher-dimensional analogues) for infinitely many degrees d.

**Location:** Lipschitzsaal

**Location: **Endenicher Allee 60, Lipschitz hall

**Location: **Max Planck Insitut - Hörsaal**Abstract:** we prove the Kuznetsov components of a series of hypersurface in projective space reconstruct the hypersurfaces. Our method allow us to work for hypersurfaces in weighted projective space, and obtain the reconstruction theorem of veronese double cone, which is a long-time open case. I will show how to construct the infinitesimal variation of Hodge structure from certain Kuznetsov components. Using classical generic Torelli theorem, this implies the Kuznetsov components reconstruct the algebraic variety generically. Joint with J. Rennemo and S.Z. Zhang.

### December 2024

**Location:** Lipschitzsaal

**Location:** Endenicher Allee 60, Lipschitz hall

**Location:** Endenicher Allee 60, Lipschitz Lecture Hall

**Abstract:** We present a general shape optimization framework based on the method of mappings in the Lipschitz topology. We propose and numerically analyse steepest descent and Newton-like minimisation algorithms for the numerical solution of the respective shape optimization problems. Our work is built upon previous work of the authors in (Deckelnick, Herbert, and Hinze, ESAIM: COCV 28 (2022)), where a Lipschitz framework for star-shaped domains is proposed. To illustrate our approach we present a selection of PDE constrained shape optimization problems and compare our findings to results from so far classical Hilbert space methods and recent p-approximations. This is joint work with Klaus Deckelnick from Magdeburg and Philip Herbert from Sussex.

**Location:** Lipschitzsaal

**Location: **Endenicher Allee 60, Lipschitz hall

**Abstract:** A moldable job is a job that can be executed on an arbitrary number of processors, and its processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing number of allotted processors. This talk addresses the problem of scheduling monotone moldable jobs to minimize the makespan. For certain compact input encodings, a polynomial algorithm has a running time polynomial in n and log m, where n is the number of jobs and m is the number of machines. We explore how monotony can counteract the complexity arising from compact encodings and present tight bounds on the approximability of the problem with compact encoding: it is NP-hard to solve optimally, but admits a PTAS. The main focus is on efficient approximation algorithms, including a (3/2+ϵ)-approximate algorithm with a running time polynomial in log m and 1/ϵ, and linear in the number n of jobs. This is joint work with Kilian Grage, Felix Land, and Felix Ohnesorge.**Location:** Seminarraum, 1st floor, Forschungsinstitut für Diskrete Mathematik/Arithmeum, Lennéstraße 2, 53113 Bonn

Location: Lipschitzsaal

**Location: **Endenicher Allee 60, Lipschitz hall

### January 2025

**Location:** Lipschitzsaal

**Location: **Endenicher Allee 60, Lipschitz hall

**Location:** Lipschitzsaal

**Location:** Endenicher Allee 60, Lipschitz hall

**Location: **Endenicher Allee 60, Lipschitz hall

**Location: **Endenicher Allee 60, Lipschitz hall

### February 2025

**Location: **Endenicher Allee 60, Lipschitz hall

### March 2025

### June 2025

**Location: **Lipschitz-Saal, Endenicher Allee 60, Bonn

Location: Endenicher Allee 60, Lipschitz hall