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Mon, 19. May at 13:45
1.023 (BMS Room, ...
Teleman’s reconstruction theorem: adaptation for semi-simple F-CohFTs
Abstract. In his paper "The structure of 2D semi-simple field theories", Teleman showed that the Givental group acts transitively on semi-simple CohFTs, so that any semi-simple flat unit CohFT can be reconstructed from its cohomological 0-degree part by means of its associated Frobenius manifold. In "Semisimple flat F-manifolds in higher genus" Arsie, Buryak, Lorenzoni and Rossi found an adaptation of the Givental group and they showed that it can be used to produce a F-CohFT FΩ' from the cohomological 0-degree part of an original flat unit F-CohFT FΩ by means of the FΩ-associated Flat F-Manifold. I am going to adapt Teleman’s proof to show that FΩ and FΩ' actually coincide after taking the restriction to a partial compactification of the moduli space of Riemann Surfaces, namely to the union of those strata whose dual graphs are stable trees.
Tue, 20. May at 13:00
2.417
Tue, 20. May at 13:15
Room 3.006, Rudow...
Affine vs. Stein in rigid geometry
Abstract. What is the relation between coherent cohomology on a complex variety and that of the associated analytic space? The natural map between them is certainly not surjective for cardinality reasons. It is not even injective in general: this is a consequence of the existence of a nonaffine algebraic variety which is Stein. In a joint work with J. Poineau, we show that over non-Archimedean field the situation is, pun intended, far more rigid.
Tue, 20. May at 14:00
WIAS R411 HVP5-7 ...
Quantum circuit simulation with a localized dynamic time-dependent variational principle
Abstract. We introduce a novel tensor network simulation method for quantum circuits that addresses key limitations inherent in the widely used time-evolving block decimation algorithm (TEBD). TEBD suffers from truncation errors during many-body dynamics and, more critically, faces challenges in simulating long-range gates—requiring additional SWAP gate decompositions that further induce truncation errors and computational overhead. By representing quantum states in the matrix product state (MPS) format and evolving them via a locally adaptive time-dependent variational principle (TDVP), our approach rigorously projects the generator of each quantum gate onto the tangent space of the MPS manifold. This allows for dynamic adjustment of bond dimensions, accurately capturing entanglement growth while efficiently simulating long-range gates directly, without resorting to SWAP gates. Benchmarking against conventional TEBD simulations demonstrates that our local TDVP simulation scheme achieves improved numerical stability, lower bond dimensions with at least the fidelity of TEBD, paving the way for more reliable large-scale quantum circuit simulations.
Wed, 21. May at 10:00
HVP 11 a, R.313
Contextual dynamic pricing: Algorithms, optimality and local differential privacy constraints
Abstract. We study contextual dynamic pricing problems where a firm sells products to $T$ sequentially-arriving consumers, behaving according to an unknown demand model. The firm aims to minimize its regret over a clairvoyant that knows the model in advance. The demand follows a generalized linear model (GLM), allowing for stochastic feature vectors in $mathbb R^d$ encoding product and consumer information. We first show the optimal regret is of order $sqrtdT$, up to logarithmic factors, improving existing upper bounds by a $sqrtd$ factor. This optimal rate is materialized by two algorithms: an explore-then-commit (ETC) algorithm and a confidence bound-type algorithm. A key insight is an intrinsic connection between dynamic pricing and contextual multi-armed bandit problems with many arms with a careful discretization. We further extend our study to adversarial contexts and propose algorithms that are statistically and computationally more efficient than existing methods in the literature. We further study contextual dynamic pricing under local differential privacy (LDP) constraints. We propose a stochastic gradient descent-based ETC algorithm achieving regret upper bounds of order $dsqrtT/epsilon$, up to logarithmic factors, where $epsilon>0$ is the privacy parameter. The upper bounds with and without LDP constraints are matched by newly constructed minimax lower bounds, characterizing costs of privacy. Moreover, we extend our study to dynamic pricing under mixed privacy constraints, improving the privacy-utility tradeoff by leveraging public data. This is the first time such setting is studied in the dynamic pricing literature and our theoretical results seamlessly bridge dynamic pricing with and without LDP. Extensive numerical experiments and real data applications are conducted to illustrate the efficiency and practical value of our algorithms.
Wed, 21. May at 11:30
online
Scheduling on a Stochastic Number of Machines
Abstract
Wed, 21. May at 13:15
Room: 3.007 John ...
Prym maps of Galois coverings of genus 2 curves
Abstract. The Prym map is a map that associates to a covering of curves its (polarised) Prym variety. Classically, the Prym map has been studied for double coverings where Prym varieties are principally polarised. After a brief introduction, we will focus on a construction and properties of non-cyclic abelian coverings of genus 2 curves: Klein and \(\mathbb{Z}_3\times\mathbb{Z}_3\) coverings. We will show that the associated Prym maps are injective. This is a joint work with Anatoli Shatsila.
Wed, 21. May at 15:15
WIAS, Erhard-Schm...
Uncertainty quantification for a model for a magnetostrictive material involving a hysteresis operator
Wed, 21. May at 16:00
Wed, 21. May at 16:00
Wed, 21. May at 16:30
EN 058
Flat degenerations of flag supermanifolds for basic Lie superalgebras
Abstract. We are going to discuss a lift of the degeneration construction for embedded flag varieties via favourables modules to a supergeometric setting. Initially introduced by Feigin, Fourier and Littelmann, this methods relies on imposing properties of polytopes, such as normality, such that bases elements, parametrised by the lattice points of these polytopes, multiply in terms of an affine semigroup algebra up to higher terms. The most prominent example are the Feigin-Fourier-Littelmann polytopes for Lie algebras of type A and C. Kus and Fourier introduced bases similar to those given by the lattice points of the FFLV polytope for basic Lie superalgebras. We discuss how one can get a similar degeneration construction and what obstacles one faces. Finally, we also mention the recently introduced notion of Toric supervariety by Eric Jankowski and how it relates to this construction.
Thu, 22. May at 10:00
WIAS R411 HVP5-7 ...
Shape optimization with Lipschitz methods (joint work with Klaus Deckelnick (Magdeburg) and Philip Herbert (Sussex))
Abstract. We present a general shape optimisation 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 optimisation problems. To illustrate our approach we present a selection of PDE constrained shape optimisation problems and compare our findings to results from so far classical Hilbert space methods and recent p-approximations.
Thu, 22. May at 16:15
TU Berlin, Instit...
Optimal Control of Infinite-Dimensional Differential Systems with Randomness and Path-Dependence
Abstract. This talk is devoted to the stochastic optimal control problem of infinite-dimensional differential systems allowing for both path-dependence and measurable randomness. As opposed to the deterministic path-dependent cases studied by Bayraktar and Keller [J. Funct. Anal. 275 (2018) 2096–2161], the value function turns out to be a random field on the path space and it is characterized by a stochastic path-dependent Hamilton-Jacobi (SPHJ) equation. A notion of viscosity solution is proposed and the value function is proved to be the unique viscosity solution to the associated SPHJ equation.
Thu, 22. May at 17:15
TU Berlin, Instit...
Bounding adapted Wasserstein metrics
Abstract. The Wasserstein distance Wp is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years. The adapted Wasserstein distance AWp extends this theory to laws of discrete time stochastic processes in their natural filtrations, making it particularly well suited for analyzing time-dependent stochastic optimization problems. While the topological differences between AWp and Wp are well understood, their differences as metrics remain largely unexplored beyond the trivial bound Wp ≲ AWp. This paper closes this gap by providing upper bounds of AWp in terms of Wp through investigation of the smooth adapted Wasserstein distance. Our upper bounds are explicit and are given by a sum of Wp, Eder’s modulus of continuity and a term characterizing the tail behavior of measures. As a consequence, upper bounds on Wp automatically hold for AWp under mild regularity assumptions on the measures considered. A particular instance of our findings is the inequality AW1 ≤ C√W1 on the set of measures that have Lipschitz kernels. Our work also reveals how smoothing of measures affects the adapted weak topology. In fact, we find that the topology induced by the smooth adapted Wasserstein distance exhibits a non-trivial interpolation property, which we characterize explicitly: it lies in between the adapted weak topology and the weak topology, and the inclusion is governed by the decay of the smoothing parameter. This talk is based on joint work with Jose Blanchet, Martin Larsson and Jonghwa Park.
Fri, 23. May at 13:00
2.417
Numerical Solution of Interference Problems
Abstract. In our talk, we consider high-frequency acoustic transmission problems with jumping coefficients modelled by Helmholtz equations. The solution then is highly oscillatory and, in addition, may be localized in a very small vicinity of interfaces (whispering gallery modes). For the reliable numerical approximation a) the PDE is tranformed in a classical single trace integral equation on the interfaces and b) a spectral Galerkin boundary element method is employed for its solution. We show that the resulting integral equation is well posed and analyze the convergence of the boundary element method for the particular case of concentric circular interfaces. We prove a condition on the number of degrees of freedom for quasi-optimal convergence. Numerical experiments confirm the efficiency of our method and the sharpness of the theoretical estimates. This talk comprises joint work with B. Bensiali and S. Falletta.
Fri, 23. May at 14:15
TU (C 130)
Renormalization, fractal geometry and the Newhouse phenomenon
Tue, 27. May at 11:15
1.023 (BMS Room, ...
Batalin-Vilkovisky formalism, half-densities and Lagrangian relations
Abstract. Lagrangian relations model maps and more general correspondences between physical systems. In Batalin-Vilkovisky formalism, it is natural to generalize Lagrangian relations to distributional half-densities, as advocated by Ševera. We give a rigorous definition of linear distributional half-densities and describe their composition, thus constructing a linear version of a quantum odd symplectic category. As an application, we describe the computation of the BV effective action as a composition in this category. Based on [arXiv:2401.06110], joint with B. Jurčo and M. Zika.
Wed, 28. May at 10:00
HVP 11 a, R.313
Wed, 28. May at 14:00
ZIB, Room 2006 (S...
From Optimal Transport to Schrödinger Bridges: A Variational Perspective on Population Dynamics
Abstract. In this talk, I present a unified variational framework for modeling population dynamics from sparse, unaligned snapshots. I begin with the classical static Monge problem and its dynamic reformulation by Brenier-Benamou, showing how minimal-energy velocity fields connect two marginal distributions. Building on this foundation, I introduce a general Lagrangian cost to enable richer action modeling and add an entropy regularizer to capture diffusion effects. By leveraging the smoothness and convexity of the Lagrangian, I derive a dual formulation that reveals the coupled Hamilton-Jacobi-Bellman (HJB) - Fokker-Planck (FP) PDE system as an alternative perspective. Next, I survey four machine-learning methods—NLSB (Neural Lagrangian SB), DeepGSB (Deep Generalized SB), Action Matching, and GSB-Matching—and compare them in terms of convergence guarantees, supported cost functions, and computational scalability. I provide practical guidance on selecting and applying the right approach for real-world population-inference tasks.
Wed, 28. May at 15:15
WIAS, Erhard-Schm...
A variational approach to well-posedness and relaxation in viscoelastic phase separation
Wed, 28. May at 16:30
Rudower Chaussee ...
A lower bound on the normal radius of hypersurfaces with applications to bounded geometries with boundary
Abstract
Tue, 03. Jun at 11:15
1.023 (BMS Room, ...
Remodelling the Gauged Linear Sigma Model
Wed, 04. Jun at 10:00
HVP 11 a, R.313
Wed, 04. Jun at 11:30
online
On the Expressivity of Neural Networks
Abstract
Wed, 04. Jun at 12:00
ZIB, Room 2006 (S...
A Dynamical Systems Perspective on Measure Transport and Generative Modeling
Abstract. Generative modeling via measure transport can be effectively understood through the lens of dynamical systems that describe the evolution from a prior to the prescribed target measure. Specifically, this involves deterministic or stochastic evolutions described by ODEs or SDEs, respectively, that shall be learned in such a way that the respective process is distributed according to the target measure at terminal time. In this talk, we show that this principled framework naturally leads to underlying PDEs connected to the density evolution of the processes. On the computational side, those PDEs can then be approached via variational approaches, such as BSDEs or PINNs. Using the former, we can draw connections to optimal control theory and recover trajectory-based sampling methods, such as diffusion models or Schrödinger bridges - however, without relying on the concept of time reversal. PINNs, on the other hand, offer the appealing numerical property that no trajectories need to be simulated and no time discretization has to be considered, leading to efficient training and better mode coverage in the sampling task. We investigate different learning strategies (admitting either unique or infinitely many solutions) on multiple high-dimensional multimodal examples.
Wed, 04. Jun at 15:15
WIAS, Erhard-Schm...
Thu, 05. Jun at 13:00
Thu, 05. Jun at 16:15
TU Berlin, Instit...
Tue, 10. Jun at 13:15
Room 3.006, Rudow...
Wed, 11. Jun at 10:00
HVP 11 a, R.313
Wed, 11. Jun at 13:00
ZIB, Room 2006 (S...
Solving Optimal Experiment Design with Mixed-Integer Convex Methods
Abstract. We tackle the Optimal Experiment Design Problem, which consists of choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained about the system from the observations, leading to a convex integer optimization problem. We leverage Boscia.jl, a recent algorithmic framework, which is based on a non-linear branch-and-bound algorithm with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which is preserved by the method, unlike alternative methods relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of our proposed method, especially on large and challenging instances.
Wed, 11. Jun at 15:15
WIAS, Erhard-Schm...
Wed, 11. Jun at 16:30
EN 058
Entropy profiles and algebraic matroids
Abstract. Consider the uniform probability distribution on the solution set of a polynomial system with coefficients in a finite field k. When K ranges over the finite extensions of k, this defines a sequence of distributions and we are interested in their Shannon entropy profiles. Using results from the model theory of finite fields, we identify all convergent subsequences and compute their limits. The computability part relies on a difficult symbolic algorithm known as Galois stratification. In the special case that the polynomials define a k-irreducible algebraic variety, one of these limits turns out to be its algebraic matroid, which recovers a result previously obtained by F. Matúš.
Fri, 13. Jun at 14:15
HU
tba (Richard von Mises Lecture)
Wed, 18. Jun at 10:00
HVP 11 a, R.313
Wed, 18. Jun at 11:30
online
Brenier Generative Adversarial Neural Networks
Abstract
Wed, 18. Jun at 13:00
ZIB, Room 2006 (S...
Bounding geometric penalties in Riemannian optimization
Abstract. Riemannian optimization refers to the optimization of functions defined over Riemannian manifolds. Such problems arise when the constraints of Euclidean optimization problems can be viewed as Riemannian manifolds, such as the symmetric positive-definite cone, the sphere, or the set of orthogonal linear layers for a neural network. This Riemannian formulation enables us to leverage the geometric structure of such problems by viewing them as unconstrained problems on a manifold. The convergence rates of Riemannian optimization algorithms often rely on geometric quantities depending on the sectional curvature and the distance between iterates and an optimizer. Numerous previous works bound the latter only by assumption, resulting in incomplete analysis and unquantified rates. In this talk, I will discuss how to remove this limitation for multiple algorithms and as a result quantify their rates of convergence.
Wed, 18. Jun at 16:00
Wed, 18. Jun at 16:00
Wed, 18. Jun at 16:30
EN 058
Thu, 19. Jun at 13:00
Thu, 19. Jun at 13:15
Room 3.006, Rudow...
Thu, 19. Jun at 15:15
Rudower Chaussee ...
Thu, 19. Jun at 16:15
TU Berlin, Instit...
Option Exercise Games and the q Theory of Investment
Abstract. Firms shall be able to respond to their competitors’ strategies over time. Back and Paulsen (2009) thus advocate using closed-loop equilibria to analyze classic real-option exercise games but point out difficulties in defining closed-loop equilibria and characterizing the solution. We define closed-loop equilibria and derive a continuum of them in closed form. These equilibria feature either linear or nonlinear investment thresholds. In all closed-loop equilibria, firms invest faster than in the open-loop equilibrium of Grenadier (2002). We confirm Back and Paulsen (2009)’s conjecture that their closed-loop equilibrium (with a perfectly competitive outcome) is the one with the fastest investment and in all other closed-loop equilibria firms earn strictly positive profits. This work is jointly with Zhaoli Jiang and Neng Wang.
Tue, 24. Jun at 13:15
Room 3.006, Rudow...
Wed, 25. Jun at 10:00
HVP 11 a, R.313
Wed, 25. Jun at 13:15
Room: 3.007 John ...
Wed, 25. Jun at 15:15
rooms 405/406
Wed, 25. Jun at 16:30
EN 058
Fri, 27. Jun at 14:15
Urania
Wed, 02. Jul at 10:00
WIAS Erhard-Schmi...
Wed, 02. Jul at 11:30
online
Informing Opinion Dynamics Models with Online Social Network Data
Abstract
Wed, 02. Jul at 15:15
WIAS, Erhard-Schm...
Wed, 02. Jul at 16:00
Wed, 02. Jul at 16:00
Thu, 03. Jul at 15:15
Rudower Chaussee ...
Thu, 03. Jul at 16:15
TU Berlin, Instit...
Thu, 03. Jul at 16:15
TU Berlin, Instit...
Fri, 04. Jul at 14:15
TU (C 130)
Kovalevskaya Lecture
Sun, 06. Jul at 15:30
Rudower Chaussee ...
Positive sectional curvature and Ricci flow
Abstract
Wed, 09. Jul at 10:00
WIAS Erhard-Schmi...
Wed, 09. Jul at 15:15
WIAS, Erhard-Schm...
The three limits of the hydrostatic approximation
Abstract
Wed, 16. Jul at 10:00
WIAS Erhard-Schmi...
Wed, 16. Jul at 11:30
online
Data-Adaptive Discretization of Inverse Problems
Abstract
Wed, 16. Jul at 15:15
WIAS, Erhard-Schm...
Wed, 16. Jul at 16:00