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Tue, 10. Jun at 11:15
1.023 (BMS Room, ...
From knots to quivers via exponential networks
Abstract. I will present our proposal for a mirror derivation of the quiver description of open topological strings known as the knots-quivers correspondence, based on enumerative invariants of augmentation curves encoded by exponential networks. Quivers are obtained by studying M2 branes wrapping holomorphic disks with Lagrangian boundary conditions on an M5 brane, through their identification with a distinguished sector of BPS kinky vortices in the 3d-3d dual QFT. Our proposal suggests that holomorphic disks with Lagrangian boundary conditions are mirror to calibrated 1-chains on the associated augmentation curve, whose intersections encode the linking of boundaries. This is based on works arXiv:2407.08445, arXiv:2412.14901 with Pietro Longhi.
Tue, 10. Jun at 15:00
Rudower Chaussee ...
Bifurcations typical for piecewise smooth maps and related bifurcation structures
Tue, 10. Jun at 15:15
Room 3.006, Rudow...
Wed, 11. Jun at 10:00
HVP 11 a, R.313, ...
Data assimilation with the 2D Navier-Stokes equations: Optimal Gaussian asymptotics for the posterior measure
Abstract. A functional Bernstein von Mises theorem is proved for posterior measures arising in a data assimilation problem with the two-dimensional Navier-Stokes equation where a Gaussian process prior is assigned to the initial condition of the system. The posterior measure, which provides the update in the space of all trajectories arising from a discrete sample of the dynamics, is shown to be approximated by a Gaussian random function arising from the solution to a linear parabolic PDE with Gaussian initial condition. The approximation holds in the strong sense of the supremum norm on the regression functions, showing that predicting future states of Navier-Stokes systems admits root(N)-consistent estimators even for commonly used nonparametric models. Consequences to credible bands and uncertainty quantification are discussed, and a functional minimax theorem is derived that describes the Cramer-Rao lower bound for estimating the state of the non-linear system, which is attained by the data assimilation algorithm.
Wed, 11. Jun at 11:30
Weierstrass Lectu...
Wed, 11. Jun at 11:30
Weierstrass Lectu...
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...
Derivatives of rate-independent evolutions
Abstract
Wed, 11. Jun at 16:00
A6, SR031
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
On the Bernstein-von Mises theorem
Abstract
Tue, 17. Jun at 13:00
Humboldt-Universi...
Weighted Aleksandrov Estimates
Abstract. We present a stronger version of the classical Aleksandrov estimate for the Monge–Amp`ere operator. Instead of the Monge–Amp`ere measure of the whole domain, a weight function is integrated with respect to the Monge–Amp`ere measure and this weight function decays to the boundary – roughly speaking with a certain power of the distance to the boundary. The inequality implies a stronger Aleksandrov–Bakelman–Pucci principle for uniformly elliptic equations and an extension of the theorem about existence of solutions of the Dirichlet problem of the Monge–Amp`ere equation. Additionally, there is a generalization for the k-Hessian measure. The results expand those in ”Weighted Aleksandrov estimates: PDE and stochastic versions” by N.V. Krylov.
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
Humboldt-Universi...
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
Fundamental polytopes and the Wasserstein arrangement.
Abstract. We can associate a polytope to a metric on a finite set of points, the so-called fundamental polytope. The question of classifying metric spaces by the combinatorial properties of their fundamental polytopes has been posed by Vershik (2015). It has been studied for special types of metrics (generic, tree-like) in recent years. This talk gives an introduction to the basic concepts and an overview of other classifications and their compatibility. A hyperplane arrangement dividing the metric cone respecting the combinatorial type of the polytope is introduced and analysed. This is joint work with Emanuele Delucchi and Lukas KĂĽhne.
Thu, 19. Jun at 13:00
Thu, 19. Jun at 15:15
Rudower Chaussee ...
Thu, 19. Jun at 15:15
Room 3.006, Rudow...
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 closedloop 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.
Mon, 23. Jun at 14:00
SR 115, Arnimallee 3
Heat kernel estimates for Brownian SDEs with low regularity coefficients and unbounded drift
Tue, 24. Jun at 11:15
1.023 (BMS Room, ...
Tue, 24. Jun at 13:00
Humboldt-Universi...
Tue, 24. Jun at 15:15
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, WIAS
Wed, 25. Jun at 16:30
EN 058
Fusion rings from lattice points
Abstract. Fusion rings are abstract versions of Grothendieck rings of certain tensor categories, i.e., categories that are endowed with a bifunctor called tensor product. The prototypical example is the category of finite-dimensional representations of a finite group. The corresponding fusion ring is a finite rank free algebra over the integers whose base elements correspond to isomorphism classes of irreducible representations and whose relations are defined by the decomposition of the tensor product of two irreducibles into a direct sum of irreducibles. Another source is conformal field theory, which is undoubtedly a driving force in the theory of fusion rings. The computation of fusion rings amounts to finding their multiplication matrices for given basic data. The multiplication matrices must satisfy linear equations that result from the Frobenius-Perron theorem. Therefore they are given by lattice points in polytopes of extremely high dimension, often > 200. The computation is only possible since the points must additionally satisfy quadratic equations that represent the associativity of the algebra. Normaliz contains an interface for fusion rings and is an efficient solver for them. Part of the results so far are reported in the paper "Classification of modular data of integral modular fusion categories up to rank 13" with Max A. Alekseyev, Sébastien Palcoux and Fedor V. Petrov (arXiv:2302.14345).
Fri, 27. Jun at 14:15
Urania
Finite simple groups and K3-like varieties
Mon, 30. Jun at 14:00
SR 115, Arnimallee 3
Energy Solutions to a Multiplicative Noise Ornstein–Uhlenbeck SDE with Singular Drift
Tue, 01. Jul at 11:15
1.023 (BMS Room, ...
Tue, 01. Jul at 13:00
Humboldt-Universi...
Wed, 02. Jul at 10:00
HVP 11 a, R.313, ...
Wed, 02. Jul at 11:30
Weierstrass Lectu...
Wed, 02. Jul at 11:30
online
Informing Opinion Dynamics Models with Online Social Network Data
Abstract
Wed, 02. Jul at 13:00
Humboldt-Universi...
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 17:15
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
Tue, 08. Jul at 13:00
Humboldt-Universi...
Tue, 08. Jul at 14:00
1.023 (BMS Room, ...
Wed, 09. Jul at 10:00
HVP 11 a, R.313, ...
Wed, 09. Jul at 15:15
WIAS, Erhard-Schm...
The three limits of the hydrostatic approximation
Abstract
Wed, 09. Jul at 16:30
EN 058
Is the squared inverse of the distance between kissing polytopes always an integer?
Abstract. A lattice $(d,k)$-polytope is the convex hull of a set of points in dimension $d$ whose coordinates are integers ranging from $0$ to $k$. We investigate the smallest possible distance between two disjoint lattice $(d,k)$-polytopes. A pair of such polytopes are called kissing polytopes. This question arises in various contexts where the minimal distance between such polytopes appears in complexity bounds for optimization algorithms. We provide nearly matching lower and upper bounds for this distance and propose an algebraic model. Our formulation yields explicit formulas in dimensions $2$ and $3$, and allows for the computation of previously intractable values. We also discuss related results, such as the Alon–Vu bounds for flat simplices — that is, the minimum distance between a vertex of a lattice $(d,1)$-simplex and the affine space spanned by the remaining vertices. Finally, we observe that all the known squared distances between kissing polytopes are inverses of integers, and we ask whether this observation holds in general. Based on joint-work with Shmuel Onn (Technion), Sebastian Pokutta (Zuse Institute Berlin and TU Berlin), and Lionel Pournin (Université Paris 13).
Tue, 15. Jul at 11:15
1.023 (BMS Room, ...
Wed, 16. Jul at 10:00
HVP 11 a, R.313, ...
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