Test
Thursday, 1.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
An isomorphism of > motivic Galois groups
Friday, 2.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Strong convergence with rates for discretizations of SPDEs with non-Lipschitz drift
Tuesday, 6.5.14, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10
I discuss the convergence analysis for space-time discretizations of three nonlinear SPDEs: the stochastic Navier-Stokes equation, the stochastic Allen-Cahn equation, and the stochastic mean curvature flow of planar curves of graphs.\n\nDepending on the drift operator, optimal rates with respect to strong convergence are valid for errors on large subsets, or on the whole sample set.
The area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain
Tuesday, 6.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
tba
Wednesday, 7.5.14, 16:00-17:00, Raum 404, Eckerstr. 1
Thursday, 8.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Non-Commutative Polynomial Optimization
Friday, 9.5.14, 14:00-15:00, Hörsaal I, Physik Hochhaus, Hermann-Herder Straße 3
In this talk, I consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed; and the associated polynomial inequalities, as semidefinite positivity constraints. To solve these problems, I introduce a complete hierarchy of semidefinite programming relaxations. This hierarchy, that can be understood as the non-commutative analogue of the Lasserre-Parrilo method for polynomial minimization, gives the user the power to make rigorous claims about the possible expectation values of infinite dimensional operators satisfying a number of polynomial identities. I will review several applications that noncommutative polynomial optimization has found in physics and quantum information theory since the conception of our hierarchy, as well as some interesting extensions of the original method. Finally, I will list some of the current challenges of this young field.
String-Topology
Monday, 12.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Local solutions to a free boundary problem for the Willmore functional
Tuesday, 13.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
The generalized Lipman-Zariski problem
Thursday, 15.5.14, 10:15-11:15, Raum 403, Eckerstr. 1
We study a generalized version of the Lipman-Zariski conjecture: let (x in X) be an n-dimensional singularity such that for some integer 1 <= p <= n - 1, the sheaf Omega_X^[p] of reflexive differential p-forms is free. Does this imply that (x in X) is smooth? We give an example showing that the answer is no even for p = 2 and X a terminal threefold. However, we prove that if p = n - 1, then there are only finitely many log canonical counterexamples in each dimension, and all of these are isolated and terminal.\nOn the other hand, if (x in X) is a hypersurface singularity with singular locus of codimension at least three, we give an affirmative answer to the above question for any 1 <= p <= n - 1.
Compatible discrete operator schemes for elliptic problems on polyhedral meshes
Thursday, 15.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Compatible discrete operator schemes aim at preserving basic\nproperties of the continuous problem at the discrete level. We analyze a\nclass of such schemes for a model elliptic problem. The cornerstone in\nthe design of the scheme is the discrete Hodge operator linking discrete\ngradient and fluxes. We present the two abstract properties to be\nsatisfied by this operator to achieve convergence. Then, we focus on the\ndesign of this operator using the concept of local gradient\nreconstruction. We highlight connections to various schemes developed in the literature.\n Finally, we present numerical examples.
Symmetries of the Hesse pencil with applications
Friday, 16.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
The Hesse normal form t(x^3+y^3+z^3)+uxyz=0 allows an efficient implementation of the arithmetic on an elliptic curve and immediately exhibits the 9 inflection points in characteristic different from 3.\nFurthermore Artebani and Dolgachev have shown that the group of projective transformations leaving the Hesse pencil invariant can be realized as a group of automorphisms on a singular K3 surface (i.e. one with Picard number 20 in characteristic 0). I intend to demonstrate the\nconstruction of one such surface.
How superadditive can a risk measure be?
Friday, 16.5.14, 11:30-12:30, Raum 404, Eckerstr. 1
Der Satz von Poincare-Hopf für Laminationen
Monday, 19.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Analysis on QAC manifolds
Tuesday, 20.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk I will present a program for doing analysis on QAC spaces. These are geometries that generalize the AC (asymptotically conical) manifolds.
Tuesday, 20.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
test
Free amalgamation and automorphism groups
Wednesday, 21.5.14, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 22.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Minkowski decompositions
Friday, 23.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Developing Prediction Models and Visualization Tools for Predictive Toxicology
Friday, 23.5.14, 11:30-12:30, Raum 404, Eckerstr. 1
Smoothing theory on homology spheres and its application on Algebraic K-theory
Monday, 26.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Willmore Fläche I
Tuesday, 27.5.14, 16:15-17:15, Raum 404, Eckerstr. 1
Thursday, 29.5.14, 17:00-18:00, Hörsaal II, Albertstr. 23b
Tilting Theory via Stable Homotopy Theory
Friday, 30.5.14, 10:15-11:15, Raum 404, Eckerstr. 1
Tilting theory is a derived version of Morita theory.\nIn the context of quivers Q and Q' and a field k, this ammounts to looking for conditions which guarantee that the derived categories of the path algebras D(kQ) and D(kQ') are equivalent as triangulated categories.\n\nIn this project (which is j/w Jan Stovicek) we take a different approach to tilting theory and show that some aspects of it are formal consequences of stability. Slightly more precisely, we show that certain tilting\nequivalences can be lifted to the context of arbitrary stable derivators. Plugging in specific examples this tells us that refined versions of these tilting results are also valid over arbitrary ground rings, for quasi-coherent modules on a scheme, in the differential-graded context, and also in the spectral context.
The Renormalisation Group via Statistical Inference
Friday, 30.5.14, 14:00-15:00, Hörsaal I, Physik Hochhaus, Hermann-Herder Straße 3
In physics one attempts to infer the rules governing a system given only\nthe results of imperfect measurements. Hence, microscopic theories may\nbe effectively indistinguishable experimentally. We develop an\noperationally motivated procedure to identify the corresponding\nequivalence classes of theories. Here it is argued that the\nrenormalisation group arises from the inherent ambiguities in\nconstructing the classes: one encounters flow parameters as, e.g., a\nregulator, a scale, or a measure of precision, which specify\nrepresentatives of the equivalence classes. This provides a unifying framework and identifies the role played by information in renormalisation. Our methods also provide a way to extend\nrenormalisation techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the distinctions between various type of RG.