Vladimir
Spokoiny
WIAS und HU Berlin
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06. November
Today
A Semismooth Newton Method for Obstacle-Type Quasivariational Inequalities
Abstract
Andrei
Yafaev
University College London
On the Andre-Pink-Zannier conjecture and its generalisations
Abstract.
This is a joint work with Rodolphe Richard (Manchester). The Andre-Pink-Zannier conjecture is a case of Zilber-Pink conjecture on unlikely intersections in Shimura varieties. We will present this conjecture and a strategy for proving it as well as its proof for Shimura varieties of abelian type. In the second talk we present a "hybrid conjecture" combining the recently proved Andre-Oort conjecture and Andre-Pink-Zannier. It is motivated by its analogy with Mordell-Lang for abelian varieties. We will explain this analogy as well as the proof of the hybrid conjecture for Shimura varieties of abelian type. (This is the second talk, the first one taking place on Tuesday at the Arithmetic Geometry Seminar).
Benjamin
Gess
TU Berlin
David
Hobson
U of Warwick
Anna
Zamojska-Dzienio
Warsaw University of Technology
Algebraic approach to barycentric coordinates
Abstract.
Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. They have been studied widely within the geometric literature, typically in response to the demands of numerical analysis and computer graphics. In this talk we bring an algebraic perspective to the problem, based on barycentric algebras. We present some recent results obtained together with A. Romanowska and J.D.H Smith.
07. November
Tomorrow
Alex
Black
David
Hobson
University of Warwick
Portfolio optimization under transaction costs with recursive preferences
Abstract.
The solution to the investment-consumption problem in a frictionless Black-Scholes market for an investor with additive CRRA preferences is to keep a constant fraction of wealth in the risky asset. But this requires continuous adjustment of the portfolio and as soon as transaction costs are added, any attempt to follow the frictionless strategy will lead to immediate bankruptcy. Instead as many authors have proposed the optimal solution is to keep the pair (cash, value of risky assets) in a no-transaction (NT) wedge. We return to this problem to see what we can say about: When is the problem well-posed? Where does the NT wedge lie? How do the results change if we use recursive preferences? We introduce the shadow fraction of wealth and show how we can make significant progress towards the solution by focussing on this quantity. Indeed many of the qualitative features of the solution can described by looking at a quadratic whose parameters depend on the parameters of the problem. This is joint work with Martin Herdegen and Alex Tse.
Johannes
Muhle-Karbe
Imperial College London
Concave Cross Impact
Abstract.
The price impact of large orders is well known to be a concave function of trade size. We discuss how to extend models consistent with this “square-root law” to multivariate settings with cross impact, where trading each asset also impacts the prices of the others. In this context, we derive consistency conditions that rule out price manipulation. These minimal conditions make risk-neutral trading problems tractable and also naturally lead to parsimonious specifications that can be calibrated to historical data. We illustrate this with a case study using proprietary CFM meta order data. (Joint work in progress with Natascha Hey and Iacopo Mastromatteo)
08. November
Fri W45
Vesna
Iršič Chenoweth
Burning game
12. November
Tue W46
Gernot
Akemann
Bielefeld Universität
Three universality classes in non-Hermitian random matrices
Abstract.
Non-Hermitian random matrices with complex eigenvalues have important applications, for example in open quantum systems in their chaotic regime. It has been conjectured that amongst all 38 symmetry classes of non-Hermitian random matrices only 3 different local bulk statistics exist. This conjecture has been based on numerically generated nearest-neighbour spacing distributions between complex eigenvalues so far. In this talk I will present first analytic evidence for this conjecture. It is based on expectation values of characteristic polynomials in the three simplest representatives for these statistics: the well-known Ginibre ensemble of complex normal matrices, complex symmetric and complex self-dual random matrices. After giving a basic introduction into the complex eigenvalue statistics of the Ginibre ensemble, I will present results for all three ensembles for finite matrix size N as well as in various large-N limits. These are expected to be universal, that is valid beyond ensembles with Gaussian distribution of matrix elements. This paper is based on joint work with Noah Aygün, Mario Kieburg and Patricia Päßler in arXiv/2410.21032
13. November
Wed W46
Alessandro
Verra
Università Roma Tre
Felix
Lotter
MPI-MiS Leipzig
Cyclic polytopes through the lens of iterated integrals
Abstract.
The volume of a cyclic polytope P can be obtained as a linear combination of iterated integrals along any convex piecewise linear path running through the edges of P. We explore the question what other functions on the set of cyclic (or more precisely, alternating) polytopes arise as iterated integrals in this way. In fact, we show that there are infinitely many such features which are algebraically independent. We obtain descriptive rings of functions on the set of alternating d-polytopes with n vertices, compatible with restrictions to subpolytopes.
14. November
Thu W46
Free boundary problems as limits of a bulk-surface model for receptor-ligand interactions on evolving domains
Abstract.
We derive various free boundary problems as reaction or singular limits of a coupled bulk-surface reaction-diffusion system on an evolving domain. These limiting free boundary problems may be formulated as Stefan-type problems on an evolving hypersurface. These results, which are new even in the setting where there is no domain evolution, are of particular relevance to an application in cell biology. In this talk, I will discuss the modelling, sketch the analysis, show some numerical simulations and finish with some open questions. Based on a joint work with Charlie Elliott, Chandrasekhar Venkataraman and Diogo Caetano.
Enrico
Bortoletto
and
Berenike
Masing
15. November
Fri W46
Ana Maria
Botero
U Bielefeld
and
José Ignacio
Burgos Gil
ICMAT
and
Jean-Benoît
Bost
U Paris XI
and
Maryna
Viazovska
EPFL
A Day of Arithmetic Geometry (on the occasion of the retirement of Jürg Kramer)
Abstract
19. November
Tue W47
Certified Reduced-Order Methods for Model Predictive Control of Time-Varying Evolution Processes
Abstract.
In this talk model predictive control (MPC) is utilized to stabilize a class of linear time-varying parabolic partial differential equations (PDEs). In our first example the control input is only finite-dimensional, i.e., it enters as a time-depending linear combination of finitely many indicator functions whose total supports cover only a small part of the spatial domain. In the second example the PDE involve switching coefficient functions. We discuss stabilizability and the application of reduced-order models to derive algorithms with closed-loop guarantees. <p>This is joint work with , and Benjamin Unger (Stuttgart).</p>
Guillaume
Baverez
Aix-Marseille Université
Uniqueness of Malliavin-Kontsevich-Suhov measures
Abstract.
About 20 years ago, Kontsevich & Suhov conjectured the existence and uniqueness of a family of measures on the set of Jordan curves, characterised by conformal invariance and another property called 'conformal restriction'. This conjecture was motivated by (seemingly unrelated) works of Schramm, Lawler & Werner on stochastic Loewner evolutions (SLE), and Malliavin, Airault & Thalmaier on 'unitarising measures'. The existence of this family was settled by works of Werner-Kemppainen and Zhan, using a loop version of SLE. The uniqueness was recently obtained in a joint work with Jego. I will start by reviewing the different notions involved before giving some ideas of our proof of uniqueness: in a nutshell, we construct a family of 'orthogonal polynomials' which completely characterise the measure. In the remaining time, I will discuss the broader context in which our construction fits, namely the conformal field theory associated with SLE.
Ya
Deng
Nancy
Euler Characteristic of Algebraic Varieties
Abstract.
This talk is based on joint works with Botong Wang. A conjecture by Chern-Hopf-Thurston states that an aspherical closed real n-manifold \(X\) satisfies \( (-1)^n\chi(X) \geq 0 \), where \( \chi(X) \) denotes the Euler characteristic of \(X\). I will focus on the case where \(X\) has the structure of a complex algebraic variety, which implies that \(X\) has large fundamental group. Inspired by this, in 1995, Kollár proposed the following conjecture: a complex projective manifold \(X\) satisfies \(\chi(K_X) \geq 0\) if it has generically large fundamental group. In this talk, I will outline the proofs of both conjectures under the assumption that \(\pi_1(X)\) is linear.
20. November
Wed W47
Bernhard
Stankewitz
Universität Potsdam
Julia
Komjathy
TU Delft
21. November
Thu W47
Eleonore
Bach
Yonatan
Shadmi
Imperial College London
27. November
Wed W48
Julien
Chhor
Toulouse School of Economics
29. November
Fri W48
Laura
Ciobanu
HWU
Undecidable problems in group theory
04. December
Wed W49
Fabian
Lehmann
Dirichlet Postdoc
Calabi-Yau 3-Folds with Boundary
Patrick
Cheridito
ETH Zurich
Günter
Last
KIT
05. December
Thu W49
Patrick
Cheridito
ETH Zürich
11. December
Wed W50
Sebastian
Bechtel
Université Paris-Saclay, France
12. December
Thu W50
Hana
Kourimska
Dante
Luber
Thesis defense
Abstract.
Thesis defense Dante Luber
13. December
Fri W50
Roman
Sauer
KIT
18. December
Wed W51
Computational Aspects of Quadratic Forms in Determining the Representation Type of Quiver Algebras
Zhen-Qing
Chen
U of Washington
Pascal
Maillard
CNRS
09. January
Thu W01
Roxana
Radulescu
10. January
Fri W01
Ilya
Chevyrev
U Edinburgh
Ilya
Cheyrev
U Edinburgh
15. January
Wed W02
21. January
Tue W03
Olivier
Marchal
Univ. St-Etienne
22. January
Wed W03
Jan-Frederik
Pietschmann
Universität Augsburg
29. January
Wed W04
Coherent Transport of Semiconductor Spin-Qubits: Modeling, Simulation and Optimal Control
Abstract
30. January
Thu W04
Stefan
Weber
Leibniz Universität Hannover
Robust Portfolio Selection Under Recovery Average Value at Risk
Abstract.
We study mean-risk optimal portfolio problems where risk is measured by Recovery Average Value at Risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical Average Value at Risk shows that portfolio selection under its recovery version allows financial institutions to better control the recovery of liabilities while still allowing for tractable computations. The talk is based on joint work with Cosimo Munari, Justin Plückebaum and Lutz Wilhelmy.
04. February
Tue W05
Raffaele
Vitolo
University of Salento
Bi-Hamiltonian geometry of WDVV equations: general results
Abstract.
It is known (work by Ferapontov and Mokhov) that a system of N-dimensional WDVV equations can be written as a pair of N-2 commuting quasilinear systems (first-order WDVV systems). In recent years, particular examples of such systems were shown to possess two compatible Hamiltonian operators, of the first and third order. It was also shown that all $3$-dimensional first-order WDVV systems possess such bi-Hamiltonian formalism. We prove that, for arbitrary N, if one first-order WDVV system has the above bi-Hamiltonian formalism, than all other commuting systems do. The proof needs some interesting results on the structure of the WDVV equations that will be discussed as well. (Joint work with S. Opanasenko).
12. February
Wed W06