Departement Mathematik

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Zurich graduate colloquium

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Frühjahrssemester 2019

Datum / Zeit Referent:in Titel Ort
19. Februar 2019
17:15-18:30 		Élise Delphine Le Mélédo
Universität Zürich
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Zurich Graduate Colloquium

Titel What are... numerical schemes for conservation laws?
Referent:in, Affiliation Élise Delphine Le Mélédo, Universität Zürich
Datum, Zeit 19. Februar 2019, 17:15-18:30
Ort KO2 F 150
Abstract Lot of natural phenomenon can be modelled and investigated through the so-called problems of conservation laws, where the time-space dynamics preserves quantities such motion, energy and mass. ,Their analytical solution (if any) is most of the time unknown. Therefore, we have to apply numerical methods that are paying attention to the physical quantities preserved through the dynamic. Another main challenge for constructing those methods is coming from the theory where discontinuities are developing within the solution. Thus, weak solutions are required and paying a special attention to the conservation laws is primordial.,If this concern traces back to the 20's, the numerical solvers commonly used nowadays in applications are still lacking efficiency, preferring stability to high performance. We focus on improving existing high order schemes by involving theoretical results in their construction and design new ones by combining general techniques with the known properties of those problems.
What are... numerical schemes for conservation laws?read_more
KO2 F 150
26. Februar 2019
17:15-18:30 		Stephan Artmann
ETHZ
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Zurich Graduate Colloquium

Titel What is... total unimodularity?
Referent:in, Affiliation Stephan Artmann, ETHZ
Datum, Zeit 26. Februar 2019, 17:15-18:30
Ort KO2 F 150
Abstract A matrix is called totally unimodular (TU) if every square submatrix has determinant 0, +1, or -1. In this talk, we will first take a quick glance at how this relates to integer linear optimization. Then, we consider the beautiful TU-decomposition theorem by Seymour, which shows that a TU matrix can be decomposed into `base blocks' of TU matrices of a very special kind.
What is... total unimodularity?read_more
KO2 F 150
5. März 2019
17:15-18:30 		Johannes Alt
University of Geneva
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Zurich Graduate Colloquium

Titel What is... a random matrix?
Referent:in, Affiliation Johannes Alt, University of Geneva
Datum, Zeit 5. März 2019, 17:15-18:30
Ort KO2 F 150
Abstract Random matrices were introduced in the first half of the 20th century by Wishart and Wigner for applications in statistics and quantum physics, respectively. As of today, many other applications of random matrices, in physics, biology and engineering, as well as many connections to other branches of mathematics have been discovered. ,In this talk, we give an introduction to certain aspects of the mathematical theory of random matrices. Moreover, we present some recent results on the eigenvalue density of large Hermitian random matrices with correlated entries and general expectation. Typically, their eigenvalue density becomes deterministic when the matrix size goes to infinity and this limit is determined by the Matrix Dyson equation. Under general conditions on the correlations and expectation, the limiting eigenvalue density is real analytic apart from finitely many square root edges and cubic root cusps. Close to a square root edge the fluctuation of the eigenvalues is governed by the famous Tracy-Widom distribution that only depends on the basic symmetry type of the random matrix. This is joint work with László Erdos, Torben Krüger and Dominik Schröder.
What is... a random matrix?read_more
KO2 F 150
26. März 2019
17:15-18:30 		Jacopo Borga
Universität Zürich
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Zurich Graduate Colloquium

Titel What is... a permuton?
Referent:in, Affiliation Jacopo Borga, Universität Zürich
Datum, Zeit 26. März 2019, 17:15-18:30
Ort KO2 F 150
Abstract How does a large random permutation behave? We will try to answer this question for different classical models of random permutations, such as uniform permutations, pattern-avoiding permutations, Mallows permutations and many others. An appropriate framework to describe the asymptotic behaviour of these pemutations is to use a quite recent notion of scaling limits for permutations, called permutons. We will investigate some first interesting examples of these objects, like the Brownian separable permuton.,Permutons lead to some nice connections between probability theory and combinatorics, and during the talk, we will investigate some of them. ,In the last part, we will also present a new and complementary recent local limit approach for the study of large random permutations introduced by the speaker. Indeed, permutons are appropriate to describe the "global shape" of permutations but not the "finer details". These are on the contrary encoded by local limits.
What is... a permuton?read_more
KO2 F 150
9. April 2019
17:15-18:30 		Nicola Capacci
Universität Zürich
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Zurich Graduate Colloquium

Titel What is... a factorization algebra?
Referent:in, Affiliation Nicola Capacci, Universität Zürich
Datum, Zeit 9. April 2019, 17:15-18:30
Ort KO2 F 150
Abstract Factorization Algebras, simply put, gives a way to assign algebraic data over a topological space, in a way that is analogous to that of a cosheaf. It arises from the need to describe the local-to-global relations of observables in Quantum Field Theory, but at the same time it is broadly connected to various ares of Mathematics from the theory of Operads to Algebraic Topology. In this short lecture I will motivate the definition of a Factorization Algebra from the physical point of view, outlining its other applications and its connection to "Higher Structues".
What is... a factorization algebra?read_more
KO2 F 150
16. April 2019
17:15-18:30 		Carlos De la Cruz Mengual
ETHZ
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Zurich Graduate Colloquium

Titel What is... bounded cohomology?
Referent:in, Affiliation Carlos De la Cruz Mengual, ETHZ
Datum, Zeit 16. April 2019, 17:15-18:30
Ort KO2 F 150
Abstract If in the usual definition of singular cohomology we require cochains to be bounded, we get a different, very rich invariant called bounded cohomology. In the setting of manifolds, bounded cohomology gives us an insight on the kind of Riemannian metrics that they can carry. On the other hand, a corresponding notion of bounded cohomology for groups has found many applications in the realms of geometric group theory and rigidity theory. In this talk, I'll present some of the features of this theory and motivations to consider it.
What is... bounded cohomology?read_more
KO2 F 150
7. Mai 2019
17:15-18:30 		Simone Steinbrüchel
Universität Zürich
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Zurich Graduate Colloquium

Titel What is... Plateau's problem?
Referent:in, Affiliation Simone Steinbrüchel, Universität Zürich
Datum, Zeit 7. Mai 2019, 17:15-18:30
Ort KO2 F 150
Abstract In the 19th century, the problem of finding the surface of least area among those spanning a given boundary is called Plateau's problem. In this talk, we will present various ways how to tackle the problem and then focus on the methods of Geometric Measure Theory in order to discuss existence and some properties of minimal surfaces.
What is... Plateau's problem?read_more
KO2 F 150
21. Mai 2019
17:15-18:30 		Alessandro Neri
Universität Zürich
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Zurich Graduate Colloquium

Titel What is... the MDS conjecture?
Referent:in, Affiliation Alessandro Neri, Universität Zürich
Datum, Zeit 21. Mai 2019, 17:15-18:30
Ort KO2 F 150
Abstract The MDS conjecture dates back to 1955, and was proposed by Segre. It takes its name from tha family of Maximum Distance Separable codes, used in algebraic coding theory for communication in presence of noise. These codes are of high interest since they have the greatest error correction and detection capabilities. Moreover, they have equivalent descriptions in the language of projective geometry, vector spaces and matrix theory. Many of the most important results on the MDS conjecture obtained so far are due to these connections. ,The aim of the talk is to answer the following questions: what is the theory of error correcting codes? What is a linear code? What are the links between coding theory, projective geometry, vector spaces and matrix theory? What is the MDS conjecture? Finally, some recent results on this conjecture are presented.
What is... the MDS conjecture?read_more
KO2 F 150

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