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Wed, 18. Jun at 10:00
HVP 11 a, R.313, ...
Adaptive Estimation under Differential Privacy Constraints
Abstract. Estimation guarantees in nonparametric models typically depend on underlying function classes (or hyperparameters) that are seldom known in practice. Adaptive estimators provide simultaneous near-optimal performance across multiple such function classes. In this talk, I will discuss recent work with co-authors Tony Cai and Abhinav Chakraborty, in which we study adaptation under differential privacy constraints. Differential privacy fundamentally limits the information that can be revealed about each individual datum by each data holder. We develop a general theory for adaptation under differential privacy in the context of estimating linear functionals of a density. Our framework characterizes the difficulty of private adaptation problems through a specific 'between-class modulus of continuity' that exactly describes the optimal achievable performance for private estimators that must adapt across two or more function classes. Our theory reveals and quantifies the extent to which adaptation between specific function classes suffers as a consequence of imposing differential privacy constraints.
Wed, 18. Jun at 11:00
MA 875
Packing plane graphs in random geometric graphs
Abstract. The study of graph packings has a long history whose systematic study began with the landmark result of Wilson. In his paper from 1975 he proved the existence of graph packings on complete digraphs under certain divisibility conditions. Packing problems on other graphs besides complete graphs are also widely studied, yet many open questions remain. We will study packings in random r-geometric graphs. That is, intersection graphs of disks with radius r chosen randomly from the unit square. The main result is that we can pack non-crossing cycles of arbitrary length into a random r-geometric graph covering almost all edges. The proof uses tessellations and their symmetry.
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 16:00
Wed, 18. Jun at 16:15
Arnimallee 3
Palettes determine uniform Turán density
Abstract. We study Turán problems for hypergraphs with an additional uniformity condition on the edge distribution. This kind of Turán problems was introduced by Erdős and Sós in the 1980s but it took more than 30 years until the first non-trivial exact results were obtained. Central to the study of the uniform Turán density of hypergraphs are palette constructions, which were implicitly introduced by Rödl in the 1980s. We prove that palette constructions always yield tight lower bounds, unconditionally confirming present empirical evidence. This results in new and simpler approaches to determining uniform turán densities, which completely bypass the use of the hypergraph regularity method.
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
Polytope indecomposability and new rays of the submodular cone
Abstract. A polytope is called indecomposable if it cannot be expressed (non-trivially) as a Minkowski sum of other polytopes. It is hard to certify the indecomposability of a polytope, and several criteria with increasing strength have been developed since the concept was introduced by Gale in 1954. I'll present a new approach to certifying polytope indecomposability via the (extended) graph of edge dependencies that encompasses most of the previous techniques. The main motivation for this is to provide new family of indecomposable deformed permutahedra that are not matroid polytopes. The problem of characterizing the extreme rays of the submodular cone, that is, indecomposable deformed permutahedra, goes back to Edmonds in 1970, and is wide open. This is joint work with Germain Poullot.
Thu, 19. Jun at 15:15
online
A tailored, matrix free interior point method for fast optimization on gas networks
Thu, 19. Jun at 15:15
Room 3.006, Rudow...
Boundedness theorems for abelian fibrations
Abstract. I will report on forthcoming work, joint with Filipazzi, Greer, Mauri, and Svaldi, on boundedness results for abelian fibrations. We will discuss a proof that irreducible Calabi-Yau varieties admitting an abelian fibration are birationally bounded in a fixed dimension; and that Lagrangian fibrations of symplectic varieties, in a fixed dimension, are analytically bounded. Conditional on the generalized semiampleness/hyperkahler SYZ conjecture, this bounds the number of deformation classes of hyperkahler varieties in a fixed dimension, with second Betti number at least 5.
Thu, 19. Jun at 16:15
TU Berlin, Instit...
Semi-static variance-optimal hedging with self-exciting jumps
Abstract. In this talk, we study a quadratic hedging problem in an affine Heston model with self-exiting jumps of Hawkes type. The hedging problem is set up for a variance swap and the strategies we consider are of semi-static type, that is, they consist of a dynamic part, based on the stock and continuously re-balanced, and of a static part, that is buy-and-hold positions in a given basket of European options. Semi-static strategies have the advantage that they reduce the hedging error in comparison to purely dynamic strategies. The model we present is new and combines features of continuous stochastic volatility models and of models with self-exciting jumps in the affine framework. Our results are based on Fourier methods and therefore the affine structure plays a central role for the set-up of the semi-static variance optimal strategy. In particular, we study the Laplace transform of our model and obtain semi-explicit expressions for the hedging strategy. This is a joint work with Giorgia Callegaro, Beatrice Ongarato and Carlo Sgarrra.
Thu, 19. Jun at 16:15
Free University B...
Mathematical billiards
Abstract. Mathematical billiards provide a concrete context in which to study phenomena that arise across dynamics as well as connections to number theory, geometry and applications. Many questions remain open, even the existence of periodic orbits.
Thu, 19. Jun at 17:15
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
Mon, 23. Jun at 14:00
SR 115, Arnimallee 3
Energy Solutions to a Multiplicative Noise Ornstein–Uhlenbeck SDE with Singular Drift
Tue, 24. Jun at 11:15
1.023 (BMS Room, ...
Tue, 24. Jun at 13:15
Humboldt-Universi...
Tue, 24. Jun at 15:15
Room 3.006, Rudow...
l-adic completion of motivic sheaves
Abstract. Rigidity theorems imply that l-adic sheaves are motivic in nature, so that l-adic realization of Voevodsky's motivic sheaves simply amounts to l-adic completion. We will explain the structural properties of this process, with positive and negative results: the analogy between rings of integers and smooth curves breaks here, since motivic sheaves behave quite differently in equal characteristics and in mixed characteristics. This yields new cohomology theories that measure the lack of functoriality of integral models in situations of good reduction. We will also discuss a conjectural property of l-adic completion of Weil-étale sheaves over Witt vectors of a finite field that is interesting in its own right: it can be shown to be a consequence of the Tate conjecture combined with a conjecture of Beilinson, and it has spectacular consequences, namely independence of l of suitable derived categories of l-adic sheaves of geometric origin over varieties over a finite field.
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 13:15
Humboldt-Universi...
Implementation of the LSFEM for Indefinite Second Order PDE
Wed, 25. Jun at 15:15
rooms 405/406
Brief notes about Earth's atmosphere energy budget, entropy, climate, and CO2 emissions
Abstract
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
Abstract
Mon, 30. Jun at 14:00
SR 115, Arnimallee 3
Heat kernel estimates for Brownian SDEs with low regularity coefficients and unbounded drift
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 13:15
Humboldt-Universi...
Wed, 02. Jul at 10:00
HVP 11 a, R.313, ...
Wed, 02. Jul at 11:30
Weierstrass Lectu...
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.
Wed, 02. Jul at 11:30
online
Informing Opinion Dynamics Models with Online Social Network Data
Abstract
Wed, 02. Jul at 13:15
Humboldt-Universi...
Wed, 02. Jul at 15:15
WIAS, Erhard-Schm...
Wed, 02. Jul at 16:00
Wed, 02. Jul at 16:00
Wed, 02. Jul at 16:30
Rudower Chaussee ...
Thu, 03. Jul at 14:15
Humboldt-Universi...
Thu, 03. Jul at 14:15
Humboldt-Universi...
Thu, 03. Jul at 15:15
Rudower Chaussee ...
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.
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
Tue, 08. Jul at 13:15
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 11:30
Weierstrass Lectu...
Wed, 09. Jul at 14:00
WIAS, Erhard-Schm...
The three limits of the hydrostatic approximation
Abstract
Wed, 09. Jul at 15:30
WIAS, Erhard-Schm...
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).
Thu, 10. Jul at 10:00
WIAS, Erhard-Schm...
Thu, 10. Jul at 13:00
Fri, 11. Jul at 14:15
FU (T9)
On optimality conditions for nonsmooth functions
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
Thu, 17. Jul at 15:00