1st Steklov eigenvalue of embedded minimal surfaces w/ free boundary 1 (by Fraser and Schoen)
Dienstag, 3.7.12, 16:15-17:15, Raum 404, Eckerstr. 1
Commuting with L.-C. Kappe
Donnerstag, 5.7.12, 17:15-18:15, Hörsaal II, Albertstr. 23b
Wissenschaftliches Kolloquium anlässlich des 50-jährigen\nPromotionsjubiläums von Frau Prof. Dr. Luise-Charlotte Kappe mit einem Festvortrag von Prof. Martin L. Newell, National University of Ireland, Galway\nThema: "Commuting with L.-C. Kappe".\n
Totalkrümmung immersierter Laminationen mit transversalem Maß
Montag, 9.7.12, 16:15-17:15, Raum 404, Eckerstr. 1
1st Steklov eigenvalue of embedded minimal surfaces w/ free boundary 2 (by Fraser and Schoen)
Dienstag, 10.7.12, 16:15-17:15, Raum 404, Eckerstr. 1
The Lasso and interaction models
Mittwoch, 11.7.12, 11:15-12:15, Hörsaal Virologie, Hermann-Herder-Straße 11
Dieser Vortrag findet im Rahmen des "Mini-symposium on Statistical approaches for integrating high-dimensional molecular data from different sources" statt.\n\n\nAbstract:\n\nThe Lasso is a popular tool for high-dimensional model building. First I will review recent computational advances that enable the Lasso to be applied to large datasets. Then I will describe very recent work on fitting interaction models. Statisticians commonly demand that an interaction only be included in a model if both variables are marginally important. We study the problem of identifying hierarchical two-way interaction models from the viewpoint of the Lasso (i.e., L1-penalized regression). We show that by adding a set of convex constraints to the Lasso problem, we can produce sparse interaction models that honor the hierarchy restriction. In contrast to stepwise procedures that are most commonly used for building interaction models, our formulation is convex, and its solution is completely characterized by a set of optimality conditions. This makes it easier to study as a statistical estimator. We argue that restricting to hierarchical interactions can be advantageous both statistically and computationally. We study its properties, give examples and present an efficient computational algorithm.\n\nThis is based on the PhD thesis work of my student Jacob Bien and is also joint with Jonathan Taylor.
Finite-time singularities in Mean Curvature Flow and Ricci flow
Mittwoch, 11.7.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
In this talk, we will study finite-time singularities of two\ngeometric flows. I will start with the Mean Curvature Flow\nfor which I will draw a lot of pictures and recall (without proofs) some of the most important results about the singularity formation. \n\nI will then show how these results should be translated to corresponding statements for finite-time Ricci flow singularities. Some of these statements have recently been proved in joint work with various collaborators, some of them are work in progress and others are completely open conjectures.\n\n
Donnerstag, 12.7.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Die infinitesimal-äquivariante Eta-Invariante
Montag, 16.7.12, 16:15-17:15, Raum 404, Eckerstr. 1
Point-singularities of Willmore Surfaces [new and augmented version]
Dienstag, 17.7.12, 16:15-17:15, Raum 404, Eckerstr. 1
We consider a branched Willmore surface immersed in \(\bR^{m\bge3}\) with square-integrable second fundamental form. We develop around each branch point local asymptotics for the immersion, its first, and its second derivatives. These expansions are given in terms of a first residue" (constant vector in $\bR^m$) and in terms ofsecond residues" (integer-valued). These residues are computed as circulation integrals around each branch point. We then deduce explicit point removability conditions in terms of the residues, ensuring that the (branched) immersion is smooth across its branch points. Do residues pass through the weak limit? We'll see...\n[Talk based on a joint-work with Tristan Rivière]
On the ordered conjecture
Mittwoch, 18.7.12, 16:30-17:30, Raum 404, Eckerstr. 1
Eine Martingalmethode zur Lösung optimaler Stoppspiele
Donnerstag, 19.7.12, 10:15-11:15, Raum 232, Eckerstr. 1
Donnerstag, 19.7.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Cotangent Complex of Moduli Spaces and Symplectic Structures
Freitag, 20.7.12, 10:00-11:00, Raum 404, Eckerstr. 1
A remarkable theorem of Mukai is the existence of symplectic structures on the smooth moduli spaces of semistable sheaves on K3 surfaces, which identifies the cotangent bundle of a moduli space with its dual. In this talk I will describe the cotangent complex of a possibly singular moduli space, viewed as an Artin stack, and show that it shares a similar duality property as in the case of a smooth moduli space.
Khintchine-Pollaczek formula for random walks whose steps have one geometric tail
Freitag, 20.7.12, 11:15-12:15, Raum 404, Eckerstr. 1
We derive a Khinchine-Pollaczek formula for random walks whose steps have a geometric left tail. The construction rests on the memory-less property of the geometric distribution. An example from a tandem queue modeling dynamic instability for microtubules is given.
Eta-Formen für Familien mit integrabler horizontaler Distribution
Montag, 23.7.12, 16:15-17:15, Raum 404, Eckerstr. 1
Global analysis of the generalised Helfrich flow of curves immersed in IR^n
Mittwoch, 25.7.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
The Helfrich energy is a measure of the elastic bending energy of a manifold, and for surfaces has been in the mind of researchers in one form or another since Poisson's treatise on elasticity in 1812. In 1973 Helfrich used the theory of elastic lipid bilayers to motivate the specific form of the functional which is common today. In its full generality, the functional incorporates an ambient "spontaneous curvature". The presence of even a trivial (constant) spontaneous curvature has historically resisted analysis. In this talk we consider the gradient flow of the functional defined on an immersed curve, with arbitrary codimension. We shall prove that under mild assumptions on the spontaneous curvature the flow exists for all time for initial data with arbitrarily high energy, subconverging to a critical point of a limiting functional. Asymptotic analysis is made particularly difficult by the presence of the spontaneous curvature: we shall present explicit examples where the flow exists for all time but does not converge. Nevertheless (time permitting), following an idea of Ben Andrews, we shall present three conditions under which it is possible to obtain full convergence of the flow. One of these conditions includes the case of the Willmore flow, strengthening a well-known result of Dziuk, Kuwert, and Schaetzle.
About a de Rham complex describing intersection space cohomology in a non-isolated singularity case
Mittwoch, 25.7.12, 16:15-17:15, Hörsaal Weismann-Haus Albertst. 21
For manifolds Poincaré duality is one of the most important properties\nof singular (co)homology theory. However proceeding to singular\nspaces, in general ordinary singular (co)homology does not satisfy \nPoincaré duality no more. But there are several generalized \n(co)homology theories\nfor pseudomanifolds that satisfy Poincaré duality. One of those\ntheories is M. Banagl's (co)homology theory of Intersection Spaces.\nIn [Ban11] M. Banagl derived an alternate description of Intersection\nSpace cohomology of a stratified pseudomanifold X, in cases where one\nhas a singular stratum with flat link bundle endowed with a Riemannian\nmetric such that the structure group of the bundle is contained in the\nisometries of the link. For that purpose he makes use of a certain\nsubcomplex of the complex of differential forms on M, the non-singular\npart of X. In the isolated-singularity case the existence of an\nisomorphism between the two descriptions was shown.\nWe want to generalize this De Rham isomorphism to the non-isolated \nsingularity case where we have a trivial link bundle. We therefore \nmake use of the Künneth-theorem.\n
Explorative Data Analysis for Prediction? Ecological Statistics between Anything Goes and the Statistical Cutting Edge
Freitag, 27.7.12, 11:15-12:15, Raum 404, Eckerstr. 1
Ecological data are a mess: environmental states are difficult to measure, extremely variable, governed by processes at various spatial and temporal scales and describing highly adaptive systems. Ecologists are rarely trained well enough in statistics to even recognise the problems they are facing. At the same time, environmental questions are high on the political agenda and ecologists desire to support policy with their knowledge. A typical example is the attempt to predict the ``whereabouts'' of species under climate change. Large data bases are currently being filled with geographical locations of where species currently are, analysed statistically and the predicted to climate change scenarios. In this talk I will present some statistical challenges that our discipline is facing and the strategies it has developed. Specifically, I will touch on spatial autocorrelation, multicollinearity and typical modelling approaches. I would like to dwell a bit on prediction uncertainty and on the unrelatedness of two fundamental developments in the trade, Bayesian statistics (focussing on embracing detection probabilities) and machine learning (focussing on flexible relationships between predictors and the response). In the end I hope to have given the audience an overview of the many challenges ecological statistics are stubbornly trying to address.
Feynman Graph Techniques in Mathematical Physics
Freitag, 27.7.12, 14:15-15:15, Raum 404, Eckerstr. 1
Ubiquitous in the heuristics and computations of quantum field theory, Feynman graph expansions are notorious for their mathematical problems, often being first termwise ill-defined and then (after renormalization) divergent series, but they have over the years been developed into a technique that lends itself to mathematical proofs. This talk is to provide an overview of some ideas and results, in particular about the emergence of diffusion in long-time quantum dynamics and about equilibrium states of quantum many-body systems.