Departement Mathematik

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Zurich graduate colloquium

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Frühjahrssemester 2021

Datum / Zeit Referent:in Titel Ort
20. April 2021
16:15-18:30 		Dr. Maria Yakerson
ETH Zürich
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Zurich Graduate Colloquium

Titel What is... an infinity-category?
Referent:in, Affiliation Dr. Maria Yakerson, ETH Zürich
Datum, Zeit 20. April 2021, 16:15-18:30
Ort Onlline Seminar
Abstract In different areas of mathematics it is convenient to work with categories, i.e., with sets of objects (possibly united by some property) and morphisms between them. However, when it comes to objects of topological nature, we often would like to consider the higher structure of morphisms between morphisms. For examples, higher structures are relevant when we work with topological spaces, continuous maps and homotopies, or with smooth manifolds, their cobordisms and diffeomorphisms between them. A generalization of a category that allows to encode the data of (infinitely many) higher morphisms is the notion of an infinity-category. In this talk, I will give a definition of an infinity-category and explain some of the main ideas behind this concept, as well as provide various examples.
What is... an infinity-category?read_more
Onlline Seminar
27. April 2021
16:15-18:30 		Francesco Fournier Facio
ETHZ
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Zurich Graduate Colloquium

Titel What is... group stability?
Referent:in, Affiliation Francesco Fournier Facio, ETHZ
Datum, Zeit 27. April 2021, 16:15-18:30
Ort Onlline Seminar
Abstract Consider the following algorithmic question: given two permutations of degree n, find an algorithm that checks whether they commute. It is easy to find a linear-time algorithm that does this, but when n is very large, this may take too long. So let us ask instead: is there a constant-time algorithm that accepts commuting permutations, and rejects permutations which are far from any pair of commuting ones, with high probability? ,This problem belongs to the realm of property-testing, a very active field of research in computer science. But surprisingly, the first answer comes from group theory. Starting from this problem, we will introduce the notion of stability in permutations of a group, which was introduced in 2014 by Arzhantseva and Paunescu. We will compare this with other more classical stability problems, and see that it has connections to many different fields of mathematics. ,Time permitting, we will explain why the framework of stability provides a promising strategy in the quest for a non-sofic group.
What is... group stability?read_more
Onlline Seminar
11. Mai 2021
16:15-18:30 		Simran Tinani
Universität Zürich
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Zurich Graduate Colloquium

Titel What is... a k-normal element?
Referent:in, Affiliation Simran Tinani, Universität Zürich
Datum, Zeit 11. Mai 2021, 16:15-18:30
Ort Onlline Seminar
Abstract Normal bases in finite fields constitute a vast topic of large theoretical and practical interest. Recently, \(k\)-normal elements were introduced as a natural extension of normal elements. The questions of the existence and cardinalities of \(k\)-normal elements comprise an active research avenue, and in full generality remain open problems. In this talk I will first give a description of normal elements, some key results on them, and their significance. I will then define \(k\)-normal elements and provide some results on their existence and numbers, along with brief outlines of the methods employed in the proofs. In particular, a general lower bound for the number of k-normal elements, assuming that they exist, will be formulated. Further, a new existence condition for \(k\)-normal elements using the general factorization of the polynomial \(x^m-1\) into cyclotomic polynomials, will be derived. Finally, an existence condition will be stated for normal elements in a finite field with a non-maximal but high multiplicative order in the group of units. This final result is seen to be closely related to the well-known Primitive Normal Basis Theorem, and is also proven using the same techniques.
What is... a k-normal element?read_more
Onlline Seminar
18. Mai 2021
16:15-18:30 		Patricia Dietzsch
ETHZ
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Zurich Graduate Colloquium

Titel What is... homological mirror symmetry?
Referent:in, Affiliation Patricia Dietzsch, ETHZ
Datum, Zeit 18. Mai 2021, 16:15-18:30
Ort Onlline Seminar
Abstract The phenomenon of mirror symmetry was first observed in the 1980's by physicists who realised that distinct manifolds can be used to construct equivalent models in string theory. The mathematical framework to explain these observations has been formulated by Kontsevich in 1994. His Homological Mirror Symmetry (HMS) conjecture predicts a close connection between the symplectic geometry of a Calabi-Yau manifold and the algebraic geometry of "its mirror-dual" complex algebraic manifold. In this talk, I'd like to share an informal view on the subject, trying to explain what the conjecture is about, without assuming any knowledge in symplectic or algebraic geometry. We will then focus on the specific case of elliptic curves, for which the HMS conjecture has been proved by Polishchuk and Zaslow in 1998. We follow closely Andrew Port's introductory paper from 2015.
What is... homological mirror symmetry?read_more
Onlline Seminar
25. Mai 2021
16:15-18:30 		Matthis Lehmkühler
ETHZ
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Zurich Graduate Colloquium

Titel What is... the Brownian loop soup?
Referent:in, Affiliation Matthis Lehmkühler, ETHZ
Datum, Zeit 25. Mai 2021, 16:15-18:30
Ort Onlline Seminar
What is... the Brownian loop soup?
Onlline Seminar
1. Juni 2021
16:15-18:30 		Marco Caporaletti
Universität Zürich
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Zurich Graduate Colloquium

Titel What is... Bose-Einstein condensation?
Referent:in, Affiliation Marco Caporaletti, Universität Zürich
Datum, Zeit 1. Juni 2021, 16:15-18:30
Ort Onlline Seminar
Abstract In the 1920s Bose and Einstein predicted that certain quantum many-particle systems at sufficiently low temperature exhibit what is now called Bose-Einstein condensation (BEC). In this phenomenon, a macroscopic fraction of the particles behaves collectively as one, with important consequences on the Physics of the system. Since its first experimental observation in 1995, much effort has been devoted in the Mathematical Physics community to the challenging problem of obtaining a rigorous proof of BEC for reasonable classes of systems. In this talk I will introduce the mathematical description of such systems and give an overview of (un)known results.
What is... Bose-Einstein condensation?read_more
Onlline Seminar

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