Donnerstag, 1.12.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Donnerstag, 1.12.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Non-Levi branching rules and Littelmann paths
Freitag, 2.12.16, 10:15-11:15, Raum 404, Eckerstr. 1
Abstract: In recent work with Schumann we have proven a conjecture of\nNaito-Sagaki giving a branching rule for the decomposition of the\nrestriction of an irreducible\nrepresentation of the special linear Lie algebra to the symplectic Lie\nalgebra,\ntherein embedded as the fixed-point set of the involution obtained by\nthe folding of\nthe corresponding Dyinkin diagram. This conjecture had been open for\nover ten years,\nand provides a new approach to branching rules for non-Levi subalgebras\nin terms\nof Littelmann paths. In this talk I will introduce the path model,\nexplain the setting of the problem, our proof, and provide some\nexamples of other non-Levi branching situations.\n
Shape Analysis: Infinite-Dimensional Geometry, Statistics on Manifolds, and Applications
Freitag, 2.12.16, 12:00-13:00, Raum 404, Eckerstr. 1
Shape analysis aims at describing the variability of certain classes\nof geometric shapes in a statistical manner. This is of interest in\nmany diverse applications such as computational anatomy, computer\nvision, geology, optics, etc. I will give an overview of the theory,\nwhich involves infinite-dimensional differential geometry and\nstatistics on manifolds, and present some recent results in Riemannian\nshape analysis together with some biomedical applications.\n
The elastic trefoil is the twice covered circle (joint work with Heiko von der Mosel and Henryk Gerlach)
Montag, 5.12.16, 16:15-17:15, Raum 226, Hermann-Herder-Str. 10
Äquivarianter Bordismus
Montag, 5.12.16, 16:15-17:15, Raum 404, Eckerstr. 1
Für eine kompakte Lie Gruppe G ist der G-äquivarainter Bordismus ein Funktor, der jedem topologischen Raum mit stetiger G-Wirkung eine abelsche Gruppe zuordnet. Definiert wird der G-äquivariante Bordismus über eine Äquivalenzrelation auf kompakten glatten Mannigfaltigkeiten mit glatter G-Wirkung. Dadurch wird äquivarianter Bordismus zu einer Methode, die kompakte glatte Mannigfaltigkeiten mit glatter G-Wirkung klassifiziert. Da die Berechnung der äquivarainten Bordismenklassen schwierig ist, wird versucht diese mithilfe der Betrachtung von Fixpunkten auf den nicht-äquivarianten Fall zurückzuführen. In diesem Vortrag wird eine Einführung in die Theorie der äquivarianten Bordismen gegeben. Zusätzlich soll die Rolle von Fixpunkten aufgezeigt werden. Zum Schluss soll für G=Z2 gezeigt werden, wie sich die Berechnung der Z2 äquivarianten Bordismusgruppe auf den nicht-äquivarianten Fall reduziert.
Mixed adaptive finite element approximation of linear elliptic equations in nondivergence form with Cordes coefficients
Dienstag, 6.12.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
This talk discusses formulations of second-order elliptic partial\ndifferential equations in nondivergence form on convex domains\nas equivalent variational problems. These formulations enable\nthe use of standard finite element techniques for variational problems\nin subspaces of \(H^2\) as well as mixed finite element methods\nfrom the context of fluid computations.\nBesides the immediate quasi-optimal a priori error bounds,\nthe variational setting allows for a posteriori error control with\nexplicit constants and adaptive mesh-refinement. The convergence of an\nadaptive algorithm is proved. Numerical results on uniform and\nadaptive meshes are included.
Paare algebraisch abschlossener Körper sind äquational
Mittwoch, 7.12.16, 16:30-17:30, Raum 404, Eckerstr. 1
Analysis on Riemannian singular and noncompact spaces and Lie algebroids
Donnerstag, 8.12.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
After reviewing the definition of a Lie algebroid and a related\nSerre-Swan theorem, I will explain how Lie algebroids can be used to\nmodel simple singularities starting with conical and edge\nsingularities. Then I will explain how the structural algebroid, which\nplays the role of the tangent space, leads to a natural class of\nRiemannian metrics, called "compatible metrics." One of the main\nresults gives a connection between the structure of the Lie algebroid\nand the analysis of the geometric operators associated to a compatible\nmetric (Laplace, Dirac, ... ). This results expresses Fredholm\ncriteria in terms of operators invariant with respect to suitable\ngroups, which allows to use tools from harmonic analysis. These\nresults are part of joint works with B. Ammann, R. Lauter,\nB. Monthubert, and others
The Cremona group of the real and the complex plane
Freitag, 9.12.16, 10:15-11:15, Raum 404, Eckerstr. 1
Being the birational symmetry group of the simplest kind of variety, the Cremona groups are quite large, and, depending on the ground field, rather complicated. The classification of minimal surfaces over the complex numbers and over the real numbers is not the same, and from this some differences between the Cremona group of the plane over the complex numbers and over the real numbers arise. I would like to present some of them and motivate how they are related to the classification of minimal surfaces.
Starke Gauß'sche Approximation des Rasch-Mischungsmodells mit Anwendungen
Freitag, 9.12.16, 12:00-13:00, Raum 404, Eckerstr. 1
Das Rasch-Modell stellt ein berühmtes Modell aus der Psychometrie\ndar, das zur Auswertung von Umfragen verwendet wird, bei denen n Individuen m\nFragen beantworten müssen. Das Ergebnis lässt sich als binäre Matrix\nausdrücken, deren (j,k). Komponente genau dann gleich 1 ist, wenn die Antwort\ndes j. Individuums auf die k. Frage richtig ist. Im Rasch-Mischungsmodell\ngehen wir davon aus, dass die Individuen rein zufällig aus einer großen\nBevölkerungsgruppe ausgewählt wurden. Wir zeigen, dass das Rasch-\nMischungsmodell als statistisches Experiment asymptotisch äquivalent zu einem\nGauß'schen Beobachtungsmodell im Sinne von Le Cam ist, wenn n gegen\nunendlich strebt und m dabei in einer gewissen Ordnung in n wachsen darf. Als\neine erste Anwendung konstruieren wir ein gleichmäßiges asymptotisches\nKonfidenzellipsoid für die Schwierigkeitsparameter der Fragen. Dieser Vortrag\nbasiert auf einer gemeinsamen Arbeit mit Johanna Kappus und Friedrich Liese\n(beide Universität Rostock).
tba
Montag, 12.12.16, 16:15-17:15, Raum 404, Eckerstr. 1
Chaotic collisions of classical kinks
Dienstag, 13.12.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The collision of particle-like excitations known as kinks in integrable classical field theories in 1+1 dimensions is simple and well-understood — no matter what the initial velocities, the kinks pass through each other with unchanged velocities and a velocity-dependent phase shift. However when the theory is not integrable, the story is much more complicated, with nested sequences of “escape windows” which have an almost fractal-like structure. This talk will review how these windows can be understood in the perhaps the simplest nontrivial 1+1 dimensional field theory, called the phi^4 model, and then show how more elaborate generalisations are at work in the phi^6 model, and in the scattering of kinks against boundaries.
Active-Set-Strategien für Optimalen Transport
Dienstag, 13.12.16, 15:15-16:15, Raum 226, Hermann-Herder-Str. 10
Ein Ansatz zum Lösen von Transportproblemen ist die Approximation durch endlichdimensionale lineare Optimierungsprobleme. Diese können aber mit angemessenem Rechenaufwand nicht direkt gelöst werden.\n\nUnter gewissen Voraussetzungen sind die diskreten Lösungsmatrizen allerdings dünnbesetzt, sodass die Problemgröße durch ein Active-Set-Verfahren erheblich reduziert werden kann. \n\nIn meinem Vortrag stelle ich zwei solche Verfahren vor. Dabei wird einmal der Träger der optimalen Lösung durch die Lösung auf einem gröberen Gitter approximiert. Das zweite Verfahren verwendet die Optimalitätsbedingungen für lineare Programme, um den Träger zu approximieren.
Donnerstag, 15.12.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Relaxed highest weight representations from D-modules on the Kashiwara flag scheme
Freitag, 16.12.16, 10:15-11:15, Raum 404, Eckerstr. 1
The relaxed highest weight representations introduced by Feigin,\nSemikhatov and Tipunin are a special class of representations of the Lie\nalgebra affine sl2, which do not have a highest (or lowest) weight.\nWe formulate a generalization of this notion for an arbitrary affine\nKac-Moody algebra g. We then\nrealize induced g-modules of this type and their duals as global\nsections of twisted D-modules\non the Kashiwara flag scheme associated to g. The D-modules that appear\nin our construction\nare direct images from subschemes given by the intersection of finite\ndimensional Schubert cells with their translate by a simple reflection.\nBesides the twist, they depend on a complex number describing the monodromy\nof the local systems we construct on these intersections. These results\ndescribe for the first time explicit\nnon-highest weight g-modules as global sections on the Kashiwara flag\nscheme and extend several\nresults of Kashiwara-Tanisaki to the case of relaxed highest weight\nrepresentations. This is based on the preprint arxiv:1607.06342 [math.RT].\n\n
Statistical learning and patient trajectories in healthcare analytics
Freitag, 16.12.16, 12:00-13:00, Raum 404, Eckerstr. 1
Healthcare analytics helps improving the treatment quality for patients suffering\nfrom various illnesses. In this regard, one commonly collects patient-related infor-\nmation, often about their demography and prior illnesses, in order to predict the\noutcome of treatments. We demonstrate this by showing how patient charactistics\ncan forecast the severity of low back pain. In a next step, we follow an innovative\napproach and exploit the prognostic potential of patient trajectories. These stem\nfrom weekly surveys collected throughout a year. By employing a Markov model,\nwe can then gain a detailed understanding of how pain intensity evolves over time.\nThis immediately leads to our vision of helping patients with choosing tailored\ntreatments and the optimal timing thereof.
Gauged linear sigma model and hemisphere partition function
Montag, 19.12.16, 16:15-17:15, Raum 404, Eckerstr. 1
I will discuss how one can use a physical theory - the gauged linear sigma model - to study the Kahler moduli space of compact Calabi-Yau threefolds. In particular I will give the definition of the hemisphere partition function associated to objects in certain categories associated to the Calabi-Yau. I will present some results of an ongoing project with M. Romo and E. Scheidegger concerning the interpretation of the hemisphere partition function as a stability condition.
A-Motives
Dienstag, 20.12.16, 08:15-09:15, Raum 318, Eckerstr. 1
In the 1970's, motivated by the question how to generate and classify Galois extensions of function fields, Drinfeld introduced so-called Drinfeld-modules which were generalized by Anderson to A-modules and A-motives. First of all, we start with an introduction to these objects. Then we specify a way of constructing Galois extensions of function fields using A-motives and describe their Galois groups.
Multi-porosity elasticity: stability and uniqueness questions
Dienstag, 20.12.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We review development of models for linear elasticity with double or triple porosity. For example, in a double porosity material there are the usual macro pores, but also the skeleton may have cracks or fissures which are known as micro pores. Such materials have a multitude of applications in today's world, including to the controversial subject of hydraulic fracturing for gas ("fracking").\n\nWe look at the question of establishing a uniqueness theorem when the elastic coefficients are only symmetric and not required to be sign definite. The extension to stability under the same conditions is analysed. If time permits we shall also look at the extension of the linear theory to the fully nonlinear one and discuss aspects of nonlinear wave propagation.
Introduction to general varifolds
Dienstag, 20.12.16, 16:15-17:15, Raum 404, Eckerstr. 1
Cofinalities of Marczewski-like ideals
Mittwoch, 21.12.16, 16:30-17:30, Raum 404, Eckerstr. 1
Cofinalities of Marczewski-Like Ideals
Mittwoch, 21.12.16, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 22.12.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Noise in autoregulated gene expression
Freitag, 23.12.16, 12:00-13:00, Raum 404, Eckerstr. 1
Gene expression is the foundation of molecular biology. Genes can be active or deactive; active genes are transcribed into RNA; RNA is translated into functional protein. Since the chemical reaction network for these processes is linear, it can be solved explicitly. In contrast, we are dealing with genes regulating their own expression. A negative feedback arises when protein binds to the gene and (de-)activates it, leading to a positive (negative) feedback. Using the assumption of fast activation and deactivation of genes, we are interested in gene expression noise under feedback. Using an approach of Kang, Kurtz and Popovic, we can quantify the reduction of noise under negative feedback and the increase in noise under positive feedback. \n\n
Donnerstag, 29.12.16, 17:00-18:00, Hörsaal II, Albertstr. 23b