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Frühjahrssemester 2025

Datum / Zeit Referent:in Titel Ort
20. März 2025
14:15-15:15 		Dr. Léo Mathis
Goethe University Frankfurt, DE
Details

DACO Seminar

Titel Non centered Gaussian determinants with Gaussian zonoids
Referent:in, Affiliation Dr. Léo Mathis, Goethe University Frankfurt, DE
Datum, Zeit 20. März 2025, 14:15-15:15
Ort HG G 19.1
Abstract A Theorem of Vitale, Molchanov and Wespi, states that the expected absolute determinant of a random matrix with independent columns is equal to the mixed volume of some convex bodies called zonoids. In the case where the columns of the matrix are centered Gaussian, the corresponding zonoids are ellipsoids and this was studied by Kabluchko and Zaporozhets. The case of non centered Gaussian vectors, however, remains relatively unstudied. The convex bodies we obtain in this case, which I call Gaussian zonoids, are not ellipsoids. In this talk, I will show you what a Gaussian zonoid looks like and how one can approximate it with an ellipsoid. At the level of random determinants, this allows to approximate expectation of non centered Gaussian determinants with centered ones. If time allows, I will show how this applies to Gaussian random fields. Namely, I will show how one can give a quantitative estimate of the concentration of a small Gaussian perturbation of a hypersurface.
Non centered Gaussian determinants with Gaussian zonoidsread_more
HG G 19.1
27. März 2025
14:15-15:15 		Prof. Dr. Irene Waldspurger
CEREMADE (Université Paris-Dauphine)
Details

DACO Seminar

Titel Correctness guarantees for the Burer-Monteiro heuristic on MaxCut-type problems
Referent:in, Affiliation Prof. Dr. Irene Waldspurger, CEREMADE (Université Paris-Dauphine)
Datum, Zeit 27. März 2025, 14:15-15:15
Ort HG G 19.1
Abstract Since numerically solving high-dimensional semidefinite programs is challenging, solvers should exploit the structure of the problem at hand, when it allows for speedups. In this talk, we will consider the setting where we have the a priori information that the solution is of low rank (for instance, rank 1). A standard way to exploit this information is through the Burer-Monteiro factorization: we represent the unknown matrix as a product of "thin" matrices (i.e. with few columns); then, we optimize the factors instead of the whole square matrix. This technique reduces the dimensionality of the problem, allowing for important computational savings. However, it makes the problem non-convex, thereby possibly introducing non-optimal critical points which can cause the solver to fail. With Faniriana Rakoto Endor, we have considered the specific category of so-called "MaxCut-type" semidefinite problems. We have exhibited a simple property which guarantees that the resulting non-convex problem has no non-optimal critical point, and hence ensures the success of the algorithm.
Correctness guarantees for the Burer-Monteiro heuristic on MaxCut-type problemsread_more
HG G 19.1
* 22. Mai 2025
15:15-16:15 		Jiaheng Chen
University of Chicago, US
Details

DACO Seminar

Titel Sharp concentration of simple random tensors
Referent:in, Affiliation Jiaheng Chen, University of Chicago, US
Datum, Zeit 22. Mai 2025, 15:15-16:15
Ort Zoom
Abstract Tensors are fundamental objects in mathematics, physics, statistics, and computer science, and they play an important role in a wide range of applied sciences and engineering disciplines. In this talk, we will focus on concentration inequalities for simple random tensors. We establish sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of our analysis, we use generic chaining techniques to obtain a sharp high-probability upper bound on the suprema of multi-product empirical processes. In so doing, we generalize classical results for quadratic and product empirical processes to higher-order settings.
Sharp concentration of simple random tensorsread_more
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