Georgi
Mitsov
HU Berlin
Inf-sup constants for interface problems
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14. April
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Willem
van Zuijlen
WIAS Berlin
Anderson Hamiltonians with correlated Gaussian potentials
Abstract.
Anderson Hamiltonians, which are random Schrödinger operators, model the evolution of electrons or quantum states in a disordered system. Philip Warren Anderson (1958) showed that if there is too much disorder in the system, instead of seeing a diffusive behaviour for the electron, they get trapped. A similar localisation effect takes place in the parabolic Anderson model, which is the parabolic problem or Cauchy problem related to the Anderson Hamiltonian. The spectral properties of the Hamiltonian determine this localisation behaviour. Many such models have been studied, but often with a potential field that is i.i.d. We study these Hamiltonians with a correlated Gaussian potential and consider its eigenvalue order statistics. <br>This is joint work with Giuseppe Cannizzaro and Cyril Labbé.
Pierluigi
Colli
Università Pavia, Italy
Well-posedness and optimal velocity control of a Brinkman--Cahn--Hilliard system with curvature effects
Abstract
16. April
Thu W15
José Antonio
Carrillo
University of Oxford, United Kingdom
Primal dual methods for Wasserstein gradient flows
Abstract
17. April
Fri W15
Alexandra
Carpentier
U Potsdam
Statistical and computational challenges in unsupervised learning: focus on ranking
20. April
Mon W16
Immanuel
Zachhuber
Elliptic operators with distributional coefficients
21. April
Tue W16
Pierrick
Bousseau
Oxford University
Boomerangs, elliptic curves and del Pezzo surfaces
Abstract.
We study boomerangs in the derived category of an elliptic curve C. These are filtrations of the zero object whose factors are polystable objects with strictly increasing phase. The numerical invariants of a boomerang are given by the Chern characters of the direct summands of these factors, which together determine a lattice polygon. When this polygon is a T-polygon, we show that the moduli space of boomerangs with a fixed collection of polystable factors is the complement of an anti-canonical embedding of C in a del Pezzo surface Z. The proof uses exceptional collections on Z, and the result has applications to the theory of q-Painlevé equations. This is joint work in progress with Tom Bridgeland and Luca Giovenzana.
Nathan
Arnaud
HU Berlin
Corentin
Bodart
Oxford
Subgroup membership and formal languages
Abstract.
The intersection of Geometric Group Theory and Formal Language Theory has been fruitful in the last 50 years. I'll start by recalling some of the key results in the area, such as the Muller-Schupp theorem on groups with context-free Word Problem and Lehnert's conjecture on groups with co-context-free Word Problem. In joint work with André Carvalho and Carl-Fredrik Nyberg-Brodda, we have been looking at similar languages related to another decision problem in groups: Subgroup Membership. I'll explain the toolbox we have been developing, apply it to examples and non-examples, and highlight some open problems along the way.
Malte
Kampschulte
Charles University Prague, CZ
Variational methods for problems with inertia and their limits
Abstract
22. April
Wed W16
Eddie
Aamari
École Normale Supérieure, Paris
and
Arthur
Stéphanovich
ENSAE-CREST, Paris
Regularity of the score and convergence rates of generative diffusion models
Abstract.
We show that diffusion-based generative models adapt to the smoothness of the target distribution: the score function inherits the target’s regularity. Leveraging this adaptivity, we obtain a concise proof that diffusion models achieve minimax-optimal rates for density estimation.
27. April
Mon W17
Willem
van Zuijlen
Discrete Anderson Hamiltonians with correlated Gaussian potentials
28. April
Tue W17
Demian
Goos
HU Berlin
Analysis of the mathematical content of recently discovered letters from Dedekind to Cantor
Abstract.
The correspondence between Georg Cantor and Richard Dedekind plays a pivotal role in the understanding of the emergence of set theory. It is in this exchange that the foundational concepts and key results have been developed. Until recently, only Cantor's letters in Dedekind's Nachlass were available for research. However, in the past months Dedekind's side of the correspondence has been discovered. In this seminar the main mathematical results of Dedekind's letters will be analyzed. Particular attention will be paid to the letters from November 30 and December 26, both 1873. This analysis will then open the room for a discussion concerning the authorship of Cantor's seminal 1874 paper that kicked off set theory, as the letters reveal that a part of the paper were, in fact, results obtained by Dedekind.
Simon
Andre
Paris
29. April
Wed W17
Nicola
Gnecco
Imperial College London
Extremes of Structural Causal Models
Abstract.
The behaviour of extreme observations is well-understood for time series or spatial data, but little is known if the data generating process is a structural causal model (SCM). We study the behavior of extremes in this model class, both for the observational distribution and under extremal interventions. We show that under suitable regularity conditions on the structure functions, the extremal behavior is described by a multivariate Pareto distribution, which can be represented as a new SCM on an extremal graph. Importantly, the latter is a sub-graph of the graph in the original SCM, which means that causal links can disappear in the tails. We further introduce a directed version of extremal graphical models and show that an extremal SCM satisfies the corresponding Markov properties. Based on a new test of extremal conditional independence, we propose two algorithms for learning the extremal causal structure from data. The first is an extremal version of the PC-algorithm, and the second is a pruning algorithm that removes edges from the original graph to consistently recover the extremal graph. The methods are illustrated on river data with known causal ground truth.
Elena
Magnanini
WIAS Berlin
Stefanie
Schindler
WIAS
Time-asymptotic self-similarity of the damped Euler equations in parabolic scaling variables
Abstract
Laura
Ciobanu
TU Berlin
05. May
Tue W18
Damien
Simon
Sorbonne Universite
Operadic structure of spatial Markov processes
Abstract.
The study of Markov chains intertwins probability theory and classical linear algebra, as a consequence of the 1D Markov property. When considering two-dimensional models of statistical mechanics, a spontaneous reflex is often to split the 2D geometry into a 1+1 geometry through the transfer matrix and reuse 1D result. In the present talk, we will consider the 2D Markov property of such models on its own and see how it invites to replace classical linear algebra by a more general operadic structure. In particular, we will focus on how new practical computations and equations emerge from this new formalism. We illustrate them on discrete-lattice Gaussian models.
Karl
Kunisch
Karl-Franzens-Universität Graz
A machine learning based approximation of semi-concave functions with applications to optimal control
Abstract.
Semiconcave functions are of vital importance for many variational problems, including optimal feedback control, game theory, and optimal transport. To investigate this class of functions we leverage the fact that semiconcave functions can be represented as the infimum of a countable family of C^2 functions. This infimum is expressed in a form that allows approximation by finitely many functions, which, combined with smoothing operations, remains semiconcave. Moreover, the gradients of the elements in the expansion of the approximating functions form a probability distribution, a property of particular interest for the value function in optimal control. We conclude by proposing a benchmark problem for a nonlinear optimal control problem, depending on a parameter which allows to vary the value function between being C^1 regular and semiconcave. This is joint work with D. Vasquez-Varas, Univ. Santiago, Chile
06. May
Wed W18
Vladimir
Spokoiny
WIAS Berlin
07. May
Thu W18
Benjamin
Massat
Université de Toulouse
Idris
Karoubi
Sorbonne Université, Paris
08. May
Fri W18
12. May
Tue W19
Burkhard
Eden
The off-shell one and two-loop box recovered from intersection theory
Abstract.
We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one- and two-loop box graphs in exactly four-dimensional configuration space. Closing the integration contours for the MB parameters we transform these into double sums. Polygamma functions in the MB representation of the double box and the occurrence of higher poles are taken into account by parametric differentiation. Summing over any one of the counters results into a p+1Fp that we replace by its Euler integral representation. The process can be repeated a second time and results in a two- or four-parameter Euler integral, respectively. We use intersection theory to derive Pfaffian systems of equations on related sets of master integrals and solve for the box and double box integrals reproducing the known expressions. Finally, we use a trick to re-derive the double box from a two-parameter Euler integral. This second computation requires only very little computing resources.
13. May
Wed W19
Holger
Dette
RUB
Multiple change point detection in functional data with applications to biomechanical fatigue data
Abstract.
Injuries to the lower extremity joints are often debilitating, particularly for professional athletes. Understanding the onset of stressful conditions on these joints is therefore important in order to ensure prevention of injuries as well as individualised training for enhanced athletic performance. We study the biomechanical joint angles from the hip, knee and ankle for runners who are experiencing fatigue. The data is cyclic in nature and densely collected by body worn sensors, which makes it ideal to work with in the functional data analysis (FDA) framework. We develop a new method for multiple change point detection for functional data, which improves the state of the art with respect to at least two novel aspects. First, the curves are compared with respect to their maximum absolute deviation, which leads to a better interpretation of local changes in the functional data compared to classical $L^2$-approaches. Secondly, as slight aberrations are to be often expected in a human movement data, our method will not detect arbitrarily small changes but hunts for relevant changes, where maximum absolute deviation between the curves exceeds a specified threshold, say $\Delta > 0$. We recover multiple changes in a long functional time series of biomechanical knee angle data, which are larger than the desired threshold $\Delta$, allowing us to identify changes purely due to fatigue. In this work, we analyse data from both controlled indoor as well as from an uncontrolled outdoor (marathon) setting.
Martin
Heida
WIAS
20. May
Wed W20
Johannes
Schmidt-Hieber
Twente
Riccarda
Rossi
University of Brescia, Italy
Johannes
Rau
Universidad de los Andes
21. May
Thu W20
Paolo
Pigato
University of Rome
John
Armstrong
King's College London
22. May
Fri W20
26. May
Tue W21
Nikolai
Kuchumov
Abo Akademi
27. May
Wed W21
Alexander
Meister
Rostock
Ester
Mariucci
Université de Versailles Saint Quentin, Paris Saclay
David
Dereudre
University of Lille
Tomáš
Roubíček
Charles University Prague and Inst. of Thermomechanics, Czech Acad. Sci.
29. May
Fri W21
Angela
Gibney
U Penn
Kovalevskaya Colloquium
02. June
Tue W22
Nikolai
Kuchumov
Abo Akademi
Limit shapes and harmonic tricks
Abstract.
The talk will be on the tangent plane method — a novel method for analysys of limit shapes of the dimer model. It will consist of three parts. In the first part, we will briefly introduce the dimer model and the necessary concepts including the associated variational problem. The second part will focus on the underlying geometry using harmonic parametrization. In the third part, we will consider two specific examples of limit shape parametrized by a modular parameter: the Aztec diamond with a hole, and a hexagon with a hexagonal hole. The talk is based on arXiv/2603.21255
04. June
Thu W22
Jim
Gatheral
CUNY
Jonathan
Tam
University of Oxford
09. June
Tue W23
Lasse
Merkens
HU Berlin
10. June
Wed W23
Michael
Sørensen
University of Copenhagen
16. June
Tue W24
Bertrand
Eynard
IPhT CEA Saclay
17. June
Wed W24
Anna
Calissano
University College London
23. June
Tue W25
Anna
Hartkopf
FU Berlin, MIP.labor
24. June
Wed W25
Bertrand
Even
LMO, Orsay
26. June
Fri W25
Emanuel
Milman
Technion
01. July
Wed W26
Tobias
Rossmann
University of Galway
07. July
Tue W27
Alexander
Alexandrov
IBS Pohang
08. July
Wed W27
Gilles
Blanchard
Université Paris Saclay
Romanos
Malikiosis
Aristotle University of Thessaloniki
10. July
Fri W27
Silvia
de Toffoli
IUSS Pavia
14. July
Tue W28
Alexander
Alexandrov
IBS Pohang
Sara
Daneri
GSSI L'Aquila, Italy
15. July
Wed W28
Christina
Lienstromberg
Universität Stuttgart
16. July
Thu W28
Xiang
Yu
The Hong Kong Polytechnic University
Chiara
Rossato
ETH Zurich
17. December
Thu W50
Lars
Kastner
TU Berlin
Drawing algebraic curves in OSCAR