Pseudo-finite dimensions, after Hrushovski and Wagner
Mittwoch, 1.6.16, 16:30-17:30, Raum 404, Eckerstr. 1
Antrittsvorlesung "Konforme Feldtheorie und ihr Einsatz in der Geometrie"
Donnerstag, 2.6.16, 16:00-17:00, Hörsaal II, Albertstr. 23b
Donnerstag, 2.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
wurd verschoben
Antrittsvorlesung "Sonntagsmathematik: Einblicke in den Intuitionismus"
Donnerstag, 2.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Capital allocation for dynamic risk measures
Freitag, 3.6.16, 12:00-13:00, Raum 125, Eckerstr. 1
apital allocations have been studied in conjunction with static risk measures in various\npapers. The dynamic case has been studied only in a discrete-time setting. We address the\nproblem of allocating risk capital to subportfolios in a continuous-time dynamic context.\nFor this purpose we introduce a classical differentiability result for backward stochastic\nVolterra integral equations and apply this result to derive continuous-time dynamic capital\nallocations. Moreover, we study a dynamic capital allocation principle that is based on\nbackward stochastic differential equations and derive the dynamic gradient allocation for\nthe dynamic entropic risk measure. As a consequence we finally provide a representation result for\ndynamic risk measures that is based on the full allocation property of the Aumann-Shapley\nallocation, which is also new in the static case.\n
Sharp estimates for the principal eigenvalue of p-operators
Dienstag, 7.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
Given a strongly elliptic operator L = div(A∇u) in divergence form, defined on a compact Riemannian manifold (possibly with strictly convex boundary), which satisfies BE(0, N ) we define a non-linear p−operator L p and use the intrinsic Γ 2 - calculus to prove the sharp estimate λ ≥ (p−1)π p p /D p for the principal eigenvalue of L p , where D denotes the diameter of M . Equality holds if and only if dim(M ) = 1 and L = ∆ g up to rescaling. We also derive the lower bound π 2 /D 2 +a/2 for the real part of the principal eigenvalue of non-symmetric operators L = div(A∇u) + B(u) satisfying BE(a, ∞).
Die Formel von Erimbetov-Shelah
Mittwoch, 8.6.16, 16:30-17:30, Raum 404, Eckerstr. 1
Optimal liquidation under partial information and market impact
Donnerstag, 9.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
New Concepts for Reliable Assessment of Statistical Methods
Freitag, 10.6.16, 12:00-13:00, Raum 404, Eckerstr. 1
In Bioinformatics and Systems Biology, a huge variety of computational tools and statistical approaches have been developed. However, many computational methods are not well-tested in application settings and their applicability is often seriously delimited. Therefore, selecting an optimal analysis strategy of often difficult in applications and missing guidelines hamper the transfer of theoretical approaches to experimental research.\nIn this talk, new concepts for assessing statistical algorithms will be introduced and illustrated. The suggested methodology enables less biased, more reliable and valid comparisons of competing approaches than currently performed in the literature. The presented concepts can be applied to establish optimized analysis pipelines and for developing general decision guidelines for the selection of appropriate analysis methods. Thereby, the presented methodology constitutes a promising perspective for transferring computational approaches to basic research in academia and to industrial applications like drug development.
Ricci curvature of non-symmetric diffusion operators
Montag, 13.6.16, 16:15-17:15, Raum 414, Eckerstr. 1
On the full space-time discretization of the generalized Stokes system: the Dirichlet case
Dienstag, 14.6.16, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
Primitive Ideals of the enveloping algebra of the Lie algebra of trace free infinite matrices
Donnerstag, 16.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
If \(A\) is a commutative ring, its primitive ideals are just its maximal ideals, in other words, they form the maximal spectrum of \(A\). Describing the maximal spectrum goes back to the classics of algebra from the beginning of the 20th century. If \(U\) is a noncommutative ring, its primitive ideals are defined as the annihilators of simple \(U\)-modules. If \(U\) is an enveloping algebra of a finite-dimensional simple Lie algebra \(\bmathfrak{g}\) such as \(\bmathfrak{g}=\bmathrm{sl}(n,\bmathbb{C})\), then the primitive ideals of \(U\) are described by a celebrated theorem of Duflo and have been further studied by Borho, Joseph, and others. In this talk, I will describe the recent results of Alexey Petukhov and myself, providing a complete description of the primitive ideals of the universal enveloping algebra of the Lie algebra of finite matrices of unbounded size \(\bmathrm{sl}(\binfty)\). These results are somewhat surprising and yield an explicit solution to the problem. They are based on the pioneering work of A. Zhilinskii from 1990s.\n
Complex multiplication and K3 surfaces over finite fields
Freitag, 17.6.16, 10:15-11:15, Raum 404, Eckerstr. 1
The zeta function of a K3 surface over a finite field satisfies a number of obvious (archimedean and l-adic) constraints and a number of less obvious (p-adic) constraints. We consider the converse question, in the style of Honda-Tate: given a rational function Z satisfying all these constraints, does there exist a K3 surface whose zeta-function equals Z?
Integral curvature and area of domains in surfaces
Montag, 20.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 21.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
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Mittwoch, 22.6.16, 16:30-17:30, Raum 404, Eckerstr. 1
Optimal cross-border mortgage decisions
Donnerstag, 23.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract:\nIn this talk we study optimal cross-border mortgage decisions in a\ncross-border setting. In particular, we address the question how a\nhousehold should optimally split its mortgage portfolio in a\nfixed-rate-mortgage in the domestic currency and an\nadjustable-rate-mortgage denominated in a foreign currency. For this\npurpose, we employ a three-dimensional Gaussian affine model with\ncorrelated foreign and domestic interest rates which together determine\nthe time-varying drift of the exchange rate. We apply this model to a\ndataset consisting of Euro and Swiss LIBOR rates and the\nEUR-CHF-exchange rate. With the estimated parameters, we discuss whether\nit is optimal to take a fixed-rate mortgage in the domestic currency or\nan adjustable-rate-mortgage in the foreign currency or any affordable\ncombination of both.\n
Formulas for special values of zeta-functions of schemes over Spec Z.
Freitag, 24.6.16, 10:15-11:15, Raum 404, Eckerstr. 1
A short trip through the tree of life: from Ebola over Diphtheria and Tuberculosis to Penguins
Freitag, 24.6.16, 12:00-13:00, Raum 404, Eckerstr. 1
Genetic sequencing data contain a fingerprint of past evolutionary and population dynamic processes. Phylogenetic methods infer evolutionary relationships — the phylogenetic tree — between individuals based on their genetic sequences. Phylodynamics aims to understand the population dynamic processes — such as epidemiological or macroevolutionary processes — giving rise to the phylogenetic tree. I will present the mathematical and computational aspects of our recently developed phylodynamic tools. Then I will discuss epidemiological applications, focussing on the recent Ebola outbreak in West Africa and a potential emergence of Diphtheria in African refugee camps. Second, I will focus on a macroevolutionary application, shedding light on the radiation of penguins.\n\n
Positive energy representations of gauge groups
Freitag, 24.6.16, 14:00-15:00, Hörsaal II, Albertstr. 23b
E families of exceptional groups: from Painlevé analysis to invariant theory and supergravity models
Freitag, 24.6.16, 15:45-16:45, Hörsaal II, Albertstr. 23b
Lorentzian Kac-Moody algebras with 2-reflective Weyl groups
Freitag, 24.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Minimal Geodesics on a K3
Montag, 27.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
I will give an introduction to my PhD thesis topic. My emphasis will be on explaining the problem by stating known resutls of interest to a broader audience of differential geometers. Most of the talk should be understandable without a detailed knowledge of K3 surfaces.
Numerical approximation of a phase-field model for multicomponent incompressible flow
Dienstag, 28.6.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Min-Max theory and the Willmore conjecture, Fernando C. Marques, André Neves
Dienstag, 28.6.16, 16:15-17:15, Raum 404, Eckerstr. 1
Full-splitting Miller trees and infinitely often equal reals
Mittwoch, 29.6.16, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 30.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b