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Veranstaltungen

Datum Gastredner Thema Ort
16.06.2021
14:00
Dozentinnen und Dozenten
Fakultät für Mathematik, TU Dortmund
Vorstellung der Arbeitsgruppen und der Wahlpflichtbereiche Mathematik, Technomathematik, Wirtschaftsmathematik [WWW]
Informationen über die Wahlpflichtbereiche im Bachelor- und Masterstudium Mathematik, Technomathematik, Wirtschaftsmathematik Vorstellung von Themen und Vorlesungen im Wintersemester 2021/2022 und in nachfolgenden Semestern
Fakultät für Mathematik (digital)
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
22.06.2021
14:00 Uhr
Sasha Sodin
Queen Mary, University of London
TBA [WWW] virtuell
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
22.06.2021
15:00 Uhr
Alexander Pushnitski
King's College London
Spectral properties of Hardy kernel matrices

Zusammenfassung


A function of two variables and is called a Hardy kernel, if it is homogeneous of degree minus one: . Hardy kernels are usually associated with integral operators on the positive semi-axis. Because of the homogeneity of the kernel, such operators are easily diagonalisable by the Mellin transform, and so the spectral theory of this class of operators is very simple. In the talk, I will discuss spectral properties of matrices , obtained by restrictions of Hardy kernels onto integers. Of course, after restricting to integers, the homogeneity property ``disappears`` and it is no longer clear how to diagonalise such matrices. Nevertheless, it turns out that some progress can be made in their spectral analysis. I will state some general theorems and consider in detail some examples.
[Abstract]
[WWW]
virtuell
24.06.2021
17 bis 21 Uhr
Studienfachberatung, Zentrale Studienberatung und andere
Fakultät für Mathematik, TU Dortmund
Nacht der Beratung (Langer Abend der Studienberatung) [WWW] TU Dortmund (digital)
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
29.06.2021
14:00 Uhr
Christopher Strothmann
TU Dortmund
Dependence beyond correlation [WWW] virtuell
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
29.06.2021
15:00 Uhr
Wolfgang Trutschnig
Paris Lodron University of Salzburg
Stochastic aspects of copulas [WWW] virtuell
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
13.07.2021
14:00 Uhr
Norbert Peyerimhoff
Durham University
Bakry-Emery curvature, Buser inequality and eigenvalue ratios for graphs or The unreasonable effectiveness of the heat equation

Zusammenfassung


A challenging mathematical problem is to introduce meaningful curvature notions on discrete spaces like graphs (which do not have any smooth structure). An analytic Ricci type curvature, based on Bochner's identity involving a Laplacian (or more generally the generator of a Markov semigroup) and going back to Bakry and Emery in 1985, was initially studied in the context of graphs by Elworthy, Schmuckenschlaeger, Lin/Yau and others. The first aim of this talk is to motivate and to introduce this curvature notion. We will then present a graph theoretical version of Buser's inequality. Buser's inequality links non-negative Ricci curvature, a fundamental isoperimetric constant named after Jeff Cheeger, and the first positive eigenvalue of the Laplace operator. Buser provided back in 1982 two proofs of his inequality (both of them geometric in flavour - one was using Geometric Measure Theory and the Heintze-Karcher inequality while the other was more elementary). An alternative analytical proof in the graph setting and based on the heat semigroup was later given by Klartag/Kosma/Ralli/Tetali in 2016. They utilized a heat semigroup reformulation of Bakry-Emery curvature and their proof is analogous to a corresponding analytical proof by Ledoux in 2004 in the manifold case. This is one of the many instances when the seemingly innocent heat equation is of central importance in completely different and new contexts. If everything goes according to plan, I will finish the talk with an optimal ratio estimate between higher eigenvalues and the first Laplace eigenvalue by combining an improved Cheeger inequality for graphs due to Kwok/Lau/Lee/Oveis Gharan/Trevisan (2013) with the above mentioned Buser inequality. This talk is a review of joint work with Shiping Liu (USTC, Hefei, China).
[Abstract]
[WWW]
virtuell
Oberseminar Analysis, Mathematische Physik, Dynamische Systeme
13.07.2021
15:00 Uhr
Denis Borisov
Institute of Mathematics UFRC RAS
Resolvents of elliptic operators on quantum graphs with small edges: holomorphy and Taylor series

Zusammenfassung


In the talk we discuss an arbitrary metric graph, to which we glue a graph with edges of lengths proportional to a small parameter . On such graph, we consider a general self-adjoint second order differential operator with varying coefficients subject to general vertex conditions; all coefficients in differential expression and vertex conditions are supposed to be holomorphic in . We introduce a special operator on a special graph obtained by rescaling the aforementioned small edges and assume that it has no embedded eigenvalues at the threshold of its essential spectrum. Under such assumption, we show that that certain parts of the resolvent of the original operator are holomorphic in and we show how to find effectively all coefficients in their Taylor series. This allows us to represent the resolvent of by an uniformly converging Taylor-like series and its partial sums can be used for approximating the resolvent up to an arbitrary power of . In particular, the zero-order approximation reproduces recent convergence results by G. Berkolaiko, Yu. Latushkin, S. Sukhtaiev and by C. Cacciapuoti, but we additionally show that next-to-leading terms in -expansions of the coefficients in the differential expression and vertex conditions can contribute to the limiting operator producing the Robin part at the vertices, to which small edges are incident.
[Abstract]
[WWW]
virtuell
14.07.2021
17:00 Uhr

Mitgliederversammlung des Vereins der Freunde der Fakultät für Mathematik [WWW]
Auch die 18. Mitgliederversammlung findet in digitaler Form statt.
digital (Zoom)
23.07.2021

Ende der Vorlesungszeit im Sommersemester 2021 [WWW] TU Dortmund
06.09.2021
8 Uhr

Fakultät für Mathematik, TU Dortmund
Beginn der Vorkurse Mathematik (06.-24. September 2021) [WWW] TU Dortmund
04.10.2021
tba
Fachschaften Mathematik und Wirtschaftsmathematik
Fakultät für Mathematik, TU Dortmund
Beginn der Orientierungsphasen Mathematik und Wirtschaftsmathematik [WWW]
In der Woche vor dem Beginn der Lehrveranstaltungen finden die Orientierungsphasen statt, zu denen die neuen Studierenden der Fakultät für Mathematik herzlich eingeladen sind.
TU Dortmund
11.10.2021

Beginn der Vorlesungszeit im Wintersemester 2021/2022 [WWW] TU Dortmund
Im Rahmen des Mathematischen Kolloquiums
22.11.2021
nachmittags

Fakultät für Mathematik, TU Dortmund
Mathematisches Kolloquium
Am 22.11. planen wir ein mathematisches Kolloquium und hoffen ganz stark auf Präsenz ...
Mathematikgebäude (geplant: Hörsaal E28 oder E29)
04.02.2022

Ende der Vorlesungszeit im Wintersemester 2021/2022 [WWW] TU Dortmund