Weakly coupled systems of conservation laws on moving surfaces
Dienstag, 2.5.17, 15:00-16:00, Raum 226, Hermann-Herder-Str. 10
Social welfare relation and irregular sets
Mittwoch, 3.5.17, 16:30-17:30, Raum 404, Eckerstr. 1
Zame and Lauwers recently showed connections between set theory\nand theoretical economics. In particular they showed that the existence of\nsocial welfare relations satisfying intergenerational equity imply the\nexistence of non-constructible objects, such as non-Ramsey and non-measurable\nsets. In this talk I prove some connection also with another popular\nregularity property, i.e., the Baire property, and if there is any time left\nI propose to use Shelah's amalgamation in order to show that the two above\nimplications does not reverse.
Donnerstag, 4.5.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Zeta regularized determinant and Functorial QFT
Montag, 8.5.17, 16:15-17:15, Raum 404, Eckerstr. 1
An attempt to axiomatize locality of path integrals leads to the notion of functorial quantum field theory (usually known as Atiyah-Segal field theory). In this talk, we will review this notion and briefly indicate how it predicts the gluing relation for the zeta regularized determinant of Laplacian. We will also discuss how to construct a functorial quantum field theory for the scalar field theory. Time permitting, we will outline a construction of functorial quantum field theory arising from two dimensional perturbative quantum scalar field theories.
test
Mittwoch, 10.5.17, 00:00-01:00, test
What can be expressed in first-order logic with bounded quantifier rank and why do we want to know that?
Mittwoch, 10.5.17, 16:30-17:30, Raum 404, Eckerstr. 1
Quotients of the unit ball by unipotent discrete groups
Freitag, 12.5.17, 10:15-11:15, Raum 404, Eckerstr. 1
We study actions of unipotent discrete groups on the unit ball in C^n and give a criterion which permits to decide when the associated quotient manifold is Stein.
Statistical methodology for comparing curves
Freitag, 12.5.17, 12:00-13:00, Raum 404, Eckerstr. 1
An important problem in drug development is to establish the similarity between two dose response curves (bridging studies). We propose new statistical methodology improving the current state of the art in at least two directions. On the one hand efficient designs are constructed minimizing the width of the confidence band for the difference between the regression functions, which is currently used for a test of similarity. The use of the new designs yields a reduction of the width of the confidence band by more than 50 percent and consequently to a substantially more powerful test. On the other hand – and more importantly – we propose new and substantially more powerful tests for the hypothesis of ”similarity”. In particular, we develop some non-standard parametric bootstrap procedure and prove its consistency. We also explain some not so well known results about classical goodness of fit tests (such as Kolmogorov-Smirnov-tests) under fixed alternatives.\n\n\n\n
Spin geometry II
Montag, 15.5.17, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk, we explain how to use Kirby calculus and characteristic sublinks to examine the spinnability of 4-dimensional cobordisms. We will illustrate this approach with some concrete examples.
Spin structures on 3- and 4-manifolds
Montag, 15.5.17, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk, we explain how to use Kirby calculus and characteristic sublinks to describe spin structures on 3-manifolds and the obstruction to extending a given spin structure on the boundary of a 4-dimensional cobordism. We will illustrate this approach with some concrete examples.
Ultrametric spaces, isometry, and isometry groups
Mittwoch, 17.5.17, 16:30-17:30, Raum 404, Eckerstr. 1
Gao and Kechris proposed in 2003 two somewhat related problems\nconcerning ultrametric spaces, namely:\n\n1) Determine the complexity of the isometry relation on locally compact\nPolish ultrametric spaces.\n\n2) Characterize the Polish groups that are isomorphic (as topological\ngroups) to the isometry group of some Polish ultrametric space.\n\nWe will present a construction strictly relating ultrametric spaces and a\nspecial kind of trees which helps in tackling these two problems. This\ntechnique applies to both separable and non-separable complete ultrametric\nspaces, and allows us to e.g. show that they are unclassifyiable up to\nisometry even when considering only discrete spaces. (Joint work with R.\nCamerlo and A. Marcone.)\n
Norm resolvent concergence of operators in varying spaces and applications
Donnerstag, 18.5.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
In many problems one is interested in the convergence of Laplacians on\nspaces, that change not only metrically, but also topologically.\nAn example is given by the (Neumann) Laplacian on a small neighbourhood\nof an embedded graph, or by Laplacians on manifolds with small obstacles\nremoved.\n\nWe will discuss a generalised norm resolvent convergence, that allows\nthe operators to act in varying spaces, and which still has the usual\nconsequences of norm resolvent convergence, such as convergence of the\nspectra.
Klt varieties with trivial canonical class - holonomy, differential forms, and fundamental groups
Montag, 22.5.17, 16:15-17:15, Raum 404, Eckerstr. 1
We investigate the holonomy group of singular Kähler-Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the\nnumber of connected components, a Bochner principle for holomorphic tensors,\nand a connection between irreducibility of holonomy representations and stability\nof the tangent sheaf are established. As a consequence, we show that up to finite\nquasi-étale covers, varieties with strongly stable tangent sheaf are either Calabi-Yau (CY) or irreducible holomorphic symplectic (IHS). Finally, finiteness properties of fundamental groups of CY and IHS varieties are established.
Dissertationsthema
Dienstag, 23.5.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
An extension problem for Riemannian metrics
Dienstag, 23.5.17, 16:15-17:15, Raum 404, Eckerstr. 1
The problem of extending a given metric on a finite three\ndimensional domain to one which is asymptotically flat and which satisfies the constraint equations of general relativity was proposed by Robert Bartnik. He proposed that the minimal mass of such an extension would be a measure of the quasi-local mass of the domain and this is called the Bartnik mass. In this talk we will describe this problem and recent results on it including a comparison of the Bartnik mass to other quasi-local mass notions.
Neeman-Forcing
Mittwoch, 24.5.17, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 25.5.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Volumes of open surfaces
Freitag, 26.5.17, 10:15-11:15, Raum 404, Eckerstr. 1
A volume of an open surface measures the rate of growth for\nthe number ofpluricanonical sections with simple poles at infinity. By Alexeev and Mori, there exists an absolute minimum for the set of positive volumes, with an explicit -- but unrealistically small -- bound. I will explain a related conjecture due to Kollár and some existing examples. Then I will explain a new candidate for the surface of the smallest volume, found in a joint work with Wenfei Liu.
Homotopy Theory for Connective Spaces
Montag, 29.5.17, 16:15-17:15, Raum 404, Eckerstr. 1
Connective spaces are a generalization of both graphs and topological spaces.\nThey carry a structure that is somewhat weaker than a topology, yet strong\nenough to support a sort of "algebraic topology". We shall look at their\nproperties, define suitable morphisms and introduce a homotopy theory.\nIn the end we will see a theorem that allows us to directly compare the\nhomotopy groups of manifolds and graphs.\n\n
An extension problem for Riemannian metrics
Dienstag, 30.5.17, 16:00-17:00, Raum 404, Eckerstr. 1
The problem of extending a given metric on a\nfinite three dimensional domain to one which is\nasymptotically flat and which satisfies the constraint\nequations of general relativity was proposed by Robert\nBartnik. He proposed that the minimal mass of such an\nextension would be a measure of the quasi-local mass of the\ndomain and this is called the Bartnik mass. In this talk we\nwill describe this problem and recent results on it\nincluding a comparison of the Bartnik mass to other\nquasi-local mass notions.\n
Minkowski's formula, Reilly's formula and Alexandrov's theorem
Dienstag, 30.5.17, 16:00-17:00, Raum 404, Eckerstr. 1
In this talk, I first review the method of Reilly and Ros on reproving Alexandrov’s theorem about the rigidity of embedded CMC (constant mean curvature) hypersurfaces in Euclidean space by simply using two integral formulae —Minkowski's formula and Reilly's formula. Then I will introduce our recent result on new Reilly type formula and Minkowski type formula as well as their applications on Alexandrov type theorem in two different settings: (i) the ambient spaces in a sub-static warped product spaces and\n(ii) hypersurfaces with free boundary in unit ball in space forms.\nThis is a report of joint works with Junfang Li, and separately with Guofang Wang.
Minkowski's formula, Reilly's formula and Alexandrov's theorem
Dienstag, 30.5.17, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk, I first review the method of Reilly and Ros on reproving Alexandrov’s theorem about the rigidity of embedded CMC (constant mean curvature) hypersurfaces in Euclidean space by simply using two integral formulae —Minkowski's formula and Reilly's formula. Then I will introduce our recent result on new Reilly type formula and Minkowski type formula as well as their applications on Alexandrov type theorem in two different settings: (i) the ambient spaces in a sub-static warped product spaces and\n(ii) hypersurfaces with free boundary in unit ball in space forms.\nThis is a report of joint works with Junfang Li, and separately with Guofang Wang.