The Loewner equation for multiple slits
Wednesday, 8.4.15, 14:00-15:00, Raum 404, Eckerstr. 1
For which arbitrary set Γ ⊆ C can one measure the growth of Γ (via a differential equation)? One partial answer to this geometrical question can be provided by Loewner Theory.\n\n\nIf Γ ⊆ H admits a homeomorphism γ : [0,1] → Γ such that γ([0,1)) = Γ holds, then we call Γ a slit (in H). We will derive a Loewner equation for finitely many slits. By using [Roth und Schleißinger(2014)] one can now encode the grow of finitely many slits into a differential equation. Hereby we will extend results of [del Monaco und Gumenyuk(2013)]. Furthermore will discuss possible generalizations. \n\n\nLiteratur\n\n[del Monaco und Gumenyuk(2013)] del Monaco, A. und P. Gumenyuk (2013): Chordal Loewner Equation. eprint arxiv:1302.0898v2.\n\n[Roth und Schleißinger(2014)] Roth, O. und S. Schleißinger (2014): The Schramm-Loewner Equation for multiple slits. eprint arxiv:1311.0672v2.
Fundamentals
Tuesday, 14.4.15, 13:30-14:30, Hörsaal II, Albertstr. 23b
Entropy at work
Tuesday, 14.4.15, 15:15-16:15, Hörsaal II, Albertstr. 23b
Classification of invariant measures
Tuesday, 14.4.15, 16:30-17:30, Hörsaal II, Albertstr. 23b
On the Natural Appearance of Continuous Negative Definite Functions in the Analysis of Stochastic Processes
Thursday, 23.4.15, 17:00-18:00, Hörsaal II, Albertstr. 23b
Continuous negative definite functions in the sense of Schoenberg appear\nin various parts of modern mathematics. One example is\npotential theory on locally compact Abelian groups. In the theory of\nstochastic processes it is well known that with each Lévy process one\nassociates a function of this class and that this relationship is in a\ncertain sense 1:1. In this talk, we analyze other occasions where\ncontinuous negative definite functions show up, namely in the context of\nFeller processes as well as homogeneous diffusions with jumps. We give\nan overview on the applications or theses functions in analyzing path\nand distributional properties of the processes under consideration.\n\nBibliography:\n\n[1] Behme, A. and Schnurr, A. (2014+): A Criterion for Invariant\nMeasures of Itô Processes Based on the Symbol. To appear in Bernoulli.\n\n[2] Schnurr, A. (2013): Generalization of the Blumenthal-Getoor Index to\nthe Class of Homogeneous Diffusions with Jumps and Some Applications.\nBernoulli 19(5A) (2013), 2010-2032.\n
Towards a motivic spectral sequence for hermitian K-theory
Friday, 24.4.15, 10:15-11:15, Raum 404, Eckerstr. 1
The motivic spectral sequence can be seen as an analogue of the Atiyah-Hirzebruch spectral sequence in (complex) topological K-theory. Postulated by Quillen and Beilinson around 1980, it was finally shown to exist by a number of related results of Voevodsky, Grayson and Suslin in the 90s and early 2000s.\n\nBut the story doesn’t end here: For hermitian K-theory, often said to correspond to real topological K-theory, things are far from clear. In my talk I will present results from my dissertation that generalise Grayson’s ideas on this topic.\n\nI will begin with the basics and revise a certain construction of algebraic and hermitian K-theory. I will then explain conceptionally how spectral sequences can arise from a filtration of the K-theory space.\n\nFinally I will show how Grayson uses tuples of commuting elements of the general linear group to construct his tower and how their role is taken by orthogonal, symplectic, symmetric and antisymmetric matrices in the hermitian realm.
Variation of GIT quotients and derived categories
Monday, 27.4.15, 10:00-11:00, Hörsaal II, Albertstr. 23b
Metric measure spaces with lower Ricci curvature bounds - An introduction
Monday, 27.4.15, 16:15-17:15, Raum 404, Eckerstr. 1
Variation of GIT quotients and derived categories
Tuesday, 28.4.15, 12:00-13:00, Hörsaal II, Albertstr. 23b
Variation of GIT quotients and derived categories
Wednesday, 29.4.15, 10:00-11:00, Hörsaal II, Albertstr. 23b
Partielle Ordnungen mit beschraenkten Antiketten
Wednesday, 29.4.15, 16:30-17:30, Raum 404, Eckerstr. 1
Pierre Simon hat kuerzlich bewiesen, dass eine unendliche\npartielle Ordnung mit beschraenkten Antiketten eine unendliche lineare Ordnung interpretiert.\n
Variation of GIT quotients and derived categories
Thursday, 30.4.15, 10:00-11:00, Hörsaal II, Albertstr. 23b
Thursday, 30.4.15, 17:00-18:00, Hörsaal II, Albertstr. 23b