Institutskolloquium Wintersemester 2018/19

Das Institutskolloquium findet während der Vorlesungszeit an jedem Donnerstag um 17:15 Uhr im Raum 05-432 (Hilbertraum) statt. Ab 16:45 Uhr gibt es Kaffee und Kuchen.

Programm

18.10.2018 17 Uhr c.t. NN
Titel

25.10.2018 17 Uhr c.t. Prof. Dr. Daniel Grieser (Carl von Ossietzky Universitaet Oldenburg)
Dreiecke aus der Sicht von Elementargeometrie, Spektraltheorie und singulärer Analysis

08.11.2018 17 Uhr c.t. NN
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15.11.2018 17 Uhr c.t. NN
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22.11.2018 17 Uhr c.t. Prof. Dr. Georg Stadler (Courant Institute New York, USA)
Simulation and Parameter Inference in Non-Newtonian Fluids

29.11.2018 17 Uhr c.t. Prof. Dr. Günter Last (KIT Karlsruhe)
Hyperuniform stable matchings of point processes

06.12.2018 17 Uhr c.t. Dr. Noémie Combe (MPIM Bonn)
Geometric invariants of the configuration space of d marked points on the complex plane

13.12.2018 17 Uhr c.t. NN
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20.12.2018 17 Uhr c.t. reserviert
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10.01.2019 17 Uhr c.t. Prof. Dr. Markus Bachmayr - Antrittsvorlesung in der "Alten Mensa"
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17.01.2019 17 Uhr c.t. NN
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24.01.2019 17 Uhr c.t. NN
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31.01.2019 Festkolloquium aus Anlass des 60. Geburtstags von Herrn Prof. Dr. Duco van Straten
Prof. David Mond (University of Warwick):
Fitting ideals and multiple points of mappings: questions and conjecture
Prof. Klaus Altmann (FU Berlin)
Three kinds of differences among polytopes and their toric interpretation
Prof. Philipp Candelas (University of Oxford)
Prof. Xenia de la Ossa (University of Oxford)

07.02.2019 17 Uhr c.t. Prof. Laszlo Szekelyhidi (Universität Leipzig)
Titel

14.02.2019 17 Uhr c.t. Prof. Dr. Thomas Sonar (TU Braunschweig)
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Abstracts:

25.10.2018: Dreiecke aus der Sicht von Elementargeometrie, Spektraltheorie und singulärer Analysis
Gibt es im 21. Jahrhundert noch etwas Neues über Dreiecke zu entdecken? Ja!

Ich werde drei Resultate vorstellen: Das erste betrifft eine Frage, die man in der Schule stellen könnte, deren Antwort aber Mittel der höheren Analysis benötigt. Das zweite verwendet das erste und beantwortet die Frage ‚Kann man die Form eines Dreiecks hören?‘. Mathematisch geht es hier um die Spektraltheorie des Laplace-Operators. Das dritte Resultat betrifft die Asymptotik der Lösungen einer partiellen Differentialgleichung auf ‚dünnen‘ Dreiecken. Es gibt eine neue Perspektive auf das zweite Resultat, und sein Beweis nutzt moderne geometrische Methoden der singulären Analysis.

22.11.2018: Simulation and Parameter Inference in Non-Newtonian Fluids
I will present examples involving non-Newtonian fluids, with a particular focus on flows in Earth's mantle. These problems are computationally challenging due to the nonlinearity of their constitutive relations and, as a result, solution features on very different scales. Despite the use of modern numerical methods (high-order discretizations, adaptive mesh refinement), the resulting discrete problems can have hundreds of millions of unknowns and thus require specialized solvers and preconditioners. These challenges are only compounded if one aims to infer parameters from observational data in an inverse problems. I will present efforts towards systematic parameter estimation for instantaneous mantle flow problems, which required to study and robustify methods for the underlying non-Newtonian fluid dynamics problems.

29.11.2018: Hyperuniform stable matchings of point processes
Stable matchings were introduced in a seminal paper by Gale and Shapley (1962) and play an important role in economics. Following closely Holroyd, Pemantle, Peres and Schramm (2009), we first discuss a few basic properties of stable matchings between two discrete point sets (resp. point processes) in IRd, where the points prefer to be close to each other. For comparison we also discuss a stable transport from Lebesgue measure to a Poisson process, introduced in a seminal paper by Holroyd and Peres (2005). In the second part of the talk we consider a stable matching τ between the d-dimensional lattice and a stationary Poisson process (or a determinantal point process) with intensity α > 1. The matched points from Ψ form a stationary and ergodic (under lattice shifts) point process Ψτ with intensity 1. This thinning of Ψ has many remarkable properties. For α close to 1 the point process Ψ very much resembles a Poisson process, while for α → ∞ it approaches the lattice. Moreover, Ψτ is hyperuniform, that is, the variance of the number of points in an increasing window grows much slower than the volume. Furthermore, the point process Ψτ is number rigid, that is the number of points in a bounded set is almost surely determined by the points in the complement of that set. These properties are in sharp contrast to a Poisson process. Still the pair correlation of Ψτ decays exponentially fast.
The talk is based on recent joint work with M. Klatt (Princeton) and D. Yogeshwaran (Bangalore).

06.12.2018: Geometric invariants of the configuration space of d marked points on the complex plane
A configuration space is a mathematical object related to state spaces in Physics. The most well known configuration space is the space Confd of d marked points on a Riemann surface, for example on the complex plane. Those configuration spaces are not homotopy invariant.
In the 1970s, Arnold and Fuchs calculated the cohomology groups of these spaces by using a given cellular decomposition. Although these spaces have been considered extensively in a given framwork, a different approach brings out new insight on the structure of Confd.
We stratify this space, using its natural relation to the space of complex, monic, degree d polynomials. A stratum Aσ is a set of polynomials indexed by a bi-colored chord diagram σ (a superposition under constraints of two chord diagrams of different colors). These graphs are the isotopy classes of images of P(-1)(IR ∪ ιIR). A study of incidence relations between the strata gives a very detailed geometric description of this configuration space and a classification of polynomials in terms of graphs: each graph tells precisely the placement of roots, critical points, and critical values of the polynomials.
We show that:
1) this stratification is invariant under a finite Coxeter group, which defines new (geometric) invariants of Confd.
2) this decomposition forms a good cover in the sense of Cech (the strata are contractible, multiple intersections are contractible).
As an application of these results, one may calculate explicitly the cohomology groups of braids.

31.01.2019:
Prof. Mond: Fitting ideals and multiple points of mappings: questions and conjecture
Returning to an old topic with a new approach and increased computing power has yielded some new partial results and new conjectures. The talk surveys earlier work of mine and Pellikaan, Duco van Straten and Theo de Jong, and Kleiman and Ulrich, before describing recent progress and questions.
Prof. Altmann: Three kinds of differences among polytopes and their toric interpretation
For two polytopes P,Q in a finite-dimensional vector space M we can introduce three different notions of differences:
1) the formal difference P-Q for turning the semigroup of polytopes (under Minkowski addition) into a group,
2) the set (P:Q) consisting of all elements m of M such that m+Q is contained in P, and
3) the set theoretic difference P\Q.
The goal of the talk is to explain the meaning of these constructions within toric geometry where the polytopes P and Q represent certain invertible sheaves.

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Vorschau: Sommersemester 2019

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