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.
18.10.2018 17 Uhr c.t. NN
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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 im Konferenzsaal des Helmholtz-Instituts Mainz (Staudingerweg 18, 55128 Mainz)
Numerische Methoden für hochdimensionale und stochastische Probleme
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)
Periods, zeta-functions and N=2 supersymmetric black holes
07.02.2019 17 Uhr c.t. Prof. Laszlo Szekelyhidi (Universität Leipzig)
Stirring the turbulence problem
14.02.2019 17 Uhr c.t. Prof. Dr. Thomas Sonar (TU Braunschweig)
Geschichte der Indivisibeln
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.
Prof. Philip Candelas: Periods, zeta-functions and N=2 supersymmetric black holes
The previous title is what happens when you try to decide between alternatives as you write. I would like to give "Periods, zeta-functions and what N=2 supersymmetric black holes are made of” but we do not yet have an answer to the last part and it is reckless to count on this coming together in the next three weeks.
07.02.2019:Stirring the turbulence problem
The interest in turbulent flows goes back many centuries. In the 20th century innumerable applications from aeronautics to atmospheric and oceanic circulation have been the major driving force for progress, and based on scaling predictions of Kolmogorov in 1941 (K41) and to Onsager’s 1949 criterion for anomalous energy dissipation we have had the beginnings of a theoretical understanding. However, from experiments and numerical simulations in the last forty years, it is now clear that simple K41 scale invariance is broken, and turbulent flows have so far been modelled mostly using ad hoc probabilistic models. In this lecture I will describe recent important advances in the mathematical ab initio understanding of turbulence which are rapidly leading to a paradigm shift.
14.02.19: Geschichte der Indivisibeln
Von Archimedes bis Leibniz wurde der Kalkül der Indivisibeln sehr erfolgreich eingesetzt, wenn es um die Berechnung von Flächen und Volumina ging. Im Vortrag forschen wir nach den Anfängen dieses Kalküls in der vorsokratischen Philosophie und verfolgen seine Entwicklungen von Archimedes und Aristoteles über das lateinische Mittelalter hin zur Renaissance und enden schließlich bei John Wallis, der den Übergang von den Indivisibeln zu den Infinitesimalen in ganz natürlicher Weise vollzogen hat.
Vorschau: Sommersemester 2019
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