Vlad
Robu
K3 Surfaces
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27. June
Today
30. June
Mon W26
Antonello
Pesce
U Bologna
Heat kernel estimates for Brownian SDEs with low regularity coefficients and unbounded drift
Adrian
Martini
TU Berlin
Energy Solutions to a Multiplicative Noise Ornstein–Uhlenbeck SDE with Singular Drift
01. July
Tue W26
Johannes
Storn
Uni Leipzig
A Quasi-Optimal Space-Time FEM With Local Mesh Refinements For Parabolic Problems
Abstract.
Abstract: We present a space-time finite element method for the heat equation that computes quasi-optimal approximations with respect to natural norms while incorporating local mesh refinements in space-time. The discretized problem is solved with a conjugate gradient method with a (nearly) optimal preconditioner. This is joint work with Lars Diening and Rob Stevenson.
02. July
Wed W26
Merle
Munko
Otto-von-Guericke University Magdeburg
Multiple Tests for Mean Functions of Functional Data
Abstract.
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs for comparing different groups or inferring factor effects. We propose a new class of testing procedures for arbitrary linear hypotheses in general factorial designs with functional data. Our methods allow global as well as multiple inference of both univariate and multivariate mean functions without assuming particular error distributions or homoscedasticity. That is, we allow for different structures of the covariance functions between groups. We analyse the (joint) asymptotic behaviour of suitable test statistics and propose a resampling approach to approximate the limit distributions. The resulting global and multiple testing procedures are asymptotically valid under weak conditions and applicable in general functional MANOVA settings. We evaluate their small-sample performance in extensive simulations and finally illustrate their applicability by analysing a data set.
Frank
Konietschke
Charité Berlin
Jonas
Köppl
WIAS Berlin
Two edges suffice: the planar lattice two-neighbor graph percolates
Abstract.
The $k$-neighbor graph is a directed percolation model on the hypercubic lattice $\mathbb{Z}^d$ in which each vertex independently picks exactly $k$ of its $2d$ nearest neighbors at random, and we open directed edges towards those. We prove that the $2$-neighbor graph percolates on $\mathbb{Z}^2$, i.e., that the origin is connected to infinity with positive probability. The proof rests on duality, an exploration algorithm, a comparison to i.i.d. bond percolation under constraints as well as enhancement arguments. As a byproduct, we show that i.i.d. bond percolation with forbidden local patterns has a strictly larger percolation threshold than $1/2$. Additionally, our main result provides further evidence that, in low dimensions, less variability is beneficial for percolation.
Lara
Théallier
HU Berlin
Benjamin
Gess
TU Berlin and MPI Leipzig
From large deviations around porous media, to PDEs with irregular coefficients, to gradient flow structures
Abstract
Fabio
Toninelli
TU Vienna
Mathieu
Laurière
NYU Shanghai
Amanda
Hirschi
U Sorbonne
Global Kuranishi charts in symplectic Gromov-Witten theory, part 2
Abstract
03. July
Thu W26
Gerard
BargallĂł i GĂłmez
HU Berlin
Dynamics and disc filling methods
Abstract.
First, we give a gentle introduction to contact geometry through the exploration of dynamical questions leading to the Weinstein conjecture (now Taubes' theorem). The true goal of the talk is to explain how holomorphic curve theory can help study dynamical questions, in this case the existence of closed orbits. After an introduction to basic features of holomorphic curves (closed, with boundary and with punctures) we use them to explain Hofer's proof of the Weinstein conjecture for 3-manifolds that are overtwisted or have π_2.
Stefan
Sauter
Uni ZĂĽrich
Joscha
Gedicke
Uni Bonn
Oliver
Sander
Technische Universität Dresden
Finsler geodesics and finite-strain plasticity
Abstract.
The theory of energetic rate-independent systems is an elegant way to describe nonlinear systems in mechanics and other fields. One particular advantage is that it yields a natural time discretization that consists of a sequence of minimization problems. Unfortunately, in many interesting cases the objective functional is only given implicitly as the solution of a second minimization problem for a curve length in the state space. Therefore, its evaluation and obtaining derivatives can be very costly. Instead, we present a transformation based on the Finsler exponential map that turns the second minimization problem into an initial-value-problem for a second-order ODE. Solutions of this can be found much cheaper numerically, or may even be available in closed form. We show examples of this construction, and how to use it to obtain fast and robust Proximal Newton solvers for finite-strain elastoplasticity.
Mathieu
Lauriere
NYU Shanghai
Sören
Christensen
Christian-Albrechts-Universität zu Kiel
04. July
Fri W26
Silvia
De Toffoli
IUSS Pavia
Kovalevskaya Lecture
06. July
Sun W26
08. July
Tue W27
Julia
Schaeffer
HU Berlin
Subrabalan
Murugesan
Heriot-Watt University
09. July
Wed W27
Vincent
Rivoirard
Université Dauphine, Paris
Johannes
Bäumler
UCLA
Daniel
Matthes
TU MĂĽnchen
A mediocre two-component variant of the famous result on equilibration in scalar Fokker-Planck equations
Abstract
Antoine
Deza
McMaster University
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).
10. July
Thu W27
Thierry
Gallay
Grenoble Alpes University, France
Sadok
Kallel
11. July
Fri W27
Andrea
Walther
HU Berlin
On optimality conditions for nonsmooth functions
14. July
Mon W28
Joachim
Naumann
15. July
Tue W28
Rob
Klabbers
HU Berlin
16. July
Wed W28
Claudia
Strauch
Universität Heidelberg
Alice
Marveggio
Hausdorff Center for Mathematics Universität Bonn
Frank
Seifried
U Trier
17. July
Thu W28
Jayden
Wang