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Arbeitsgruppe Funktionalanalysis

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 2.041

Adresse
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe


samira.junge@kit.edu, natascha.katz@kit.edu




Übungsscheine für Analysis I, II, III (Mathematik, Lehramt Mathematik, Physik, Informatik)
Übungsscheine für HM I, II (Informatik)

zusätzlich: studienbegleitende Klausuren zu den Vorlesungen der Dozenten der Arbeitsgruppe.

Öffnungszeiten:
9:00 - 11:00

Tel.: 0721 608 43727

Fax.: 0721 608 67650

Forschungsseminar (Dauerveranstaltung)



Vorträge im Wintersemester 2018/2019

Die Vorträge finden, sofern nicht anders angekündigt, jeweils von 14:00-15:30 Uhr in Raum 2.066 im Kollegiengebäude Mathematik (20.30) statt.


29.01.2019Fabian Hornung (Karlsruhe)Neural Network Approximation for high dimensional Kolmogorov PDE.
First we introduce some basic concepts in the theory of artificial neural networks (ANNs) and present how Kolmogorov PDEs can be reformulated as a minimization problem using techniques from stochastic analysis. This can serve as foundation of deep learning algorithms to numerically solve these PDEs.
In the second part of the talk, we sketch a proof that artificial neural networks approximate the PDE-solution without curse of dimensionality, i.e. that the number of parameters of the approximating ANN is bounded by a polynomial in the dimension of the problem and the reciprocal of the accuracy.
The talk is based on joint work with Philipp Grohs, Arnulf Jentzen, and Philippe von Wurstemberger.

Der Vortrag findet um 15:45 in Raum 3.060 statt.
12.03.2019Boris Baeumer (Dunedin)Boundary conditions for Levy processes on bounded domains and their governing PDEs.
Levy processes are jump processes governed by non-local operators on \mathbb{R}^d and are used to model dispersive systems where the occasional large dispersal event (many standard deviations) is driving the system. In modelling, boundaries appear naturally and in 1D we answer the question of what type of boundary condition for the non-local operator corresponds to what type of boundary behaviour of the process by using numerical approximation schemes.

Der Vortrag findet von 14:00 bis 15:00 in Raum 2.066 statt.
12.03.2019Petru Cioica-Licht (Essen)SPDEs on domains with corner singularities.
Although there exists an almost fully-fledged L_p-theory for (semi-)linear second order stochastic partial differential equations (SPDEs, for short) on smooth domains, very little is known about the regularity of these equations on non-smooth domains with corner singularities. As it is already known from the deterministic theory, corner singularities may have a negative effect on the regularity of the solution. For stochastic equations, this effect comes on top of the already known incompatibility of noise and boundary condition. In this talk I will show how a system of mixed weights consisting of appropriate powers of the distance to the vertexes and of the distance to the boundary may be used in order to deal with both sources of singularity and their interplay.

Der Vortrag findet von 15:00 bis 16:00 in Raum 2.066 statt.




Ältere Vortragstitel finden Sie im Vortragsarchiv des Forschungsseminars.