Free fermions and tau-functions
Montag, 3.12.12, 16:15-17:15, Raum 404, Eckerstr. 1
The formalism of free fermions \nused for construction of tau-functions of classical \nintegrable hierarchies is reviewed.\nWe give a derivation of \ngroup-like properties of the normally ordered exponents, \ntransformations between different normal orderings,\nthe bilinear identity and the generalized Wick's\ntheorem. We also consider various examples of tau-functions\nand give their fermionic realization.
Modeling and simulation of fluid-structure interaction in haemodynamics
Dienstag, 4.12.12, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We consider the fluid-structure interaction problem arising in\nhaemodynamic applications where the blood interacts with the arterial\nwall. Blood dynamics is described by the Navier-Stokes equations for\nNewtonian fluids, conveniently rewritten in Arbitrary Lagrangian\nEulerian (ALE) formulation to account for the deformation of the fluid\ndomain boundary; arterial dynamics is described by non-linear\nfinite elasticity equations.\n\nWe consider partitioned algorithms based on Robin interface conditions\nto solve numerically the fluid-structure interaction problem. At each\ntime step the non-linear or linearized fluid and structure subproblems\nare solved iteratively until convergence and linear combinations of\nvelocities and normal stresses (Robin interface conditions) are\nexchanged at the common interface. In particular, we discuss suitable\nchoices of the coefficients in the Robin conditions based on reduced\nmodels and show how the optimized Robin conditions greatly reduce the\neffect of added mass on the convergence of the iterative algorithm.\n\nWe present finally some simulations of blood flow in carotid\nbifurcations reconstructed from MRI data, from patients having\natherosclerotic plaques, before and after the plaque removal.\n\nReferences\n\n[1] S. Badia, F. Nobile, and C. Vergara (2008). Fluid-structure\npartitioned procedures based on Robin transmission\nconditions. J. Comp. Phy 227, 7027–7051.\n\n[3] P. Causin, J. Gerbeau, and F. Nobile (2005). Added-mass effect in\nthe design of partitioned algorithms for fluid-structure\nproblems. Comput. Methods Appl. Mech. Engrg 194(42-44), 4506– 4527.\n\n[4] F. Nobile, M. Pozzoli, C. Vergara, Exact and inexact partitioned\nalgorithms for fluid-structure interaction problems with finite\nelasticity in haemodynamics, MOX Report 37/2012, submitted.
Symplectic tools for studying quantum entanglement
Dienstag, 4.12.12, 15:45-16:45, Hörsaal 1, Physik Hochhaus, Hermann-Herder-Straße 3
A description for non-specialists of the mathematical tools which have been recently implemented in the development of measuring devices for degrees of quantum entanglement will be given. These methods involve symmetry considerations in representation theoretic settings. The talk will conclude\nwith a survey of recent results.\n
Confined structures of least bending energy
Mittwoch, 5.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
We analyze a constrained minimization problem for the Willmore energy. For a given parameter a>0 we consider smooth embeddings of the sphere into the unit ball with surface area \(a\). In this class we minimize the Willmore energy and investigate the dependence of the minimal energy value on the parameter a. (This is joint work with Stefan Müller, Bonn.)\n\n
Confined structures of least bending energy
Mittwoch, 5.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
We analyze a constrained minimization problem for the Willmore energy. For a given parameter a>0 we consider smooth embeddings of the sphere into the unit ball with surface area \(a\). In this class we minimize the Willmore energy and investigate the dependence of the minimal energy value on the parameter a. (This is joint work with Stefan Müller, Bonn.)\n
Wadge-like reducibilities on arbitrary (quasi-)Polish spaces
Mittwoch, 5.12.12, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 6.12.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Homology stability for special linear group and scissors congruence groups.
Freitag, 7.12.12, 10:00-11:00, Raum 404, Eckerstr. 1
The Scissors Congruence group - or pre-Bloch group - P(F),\nof a field F is a group presented by generators and relations which derive from the five-term functional equation of the dilogarithm.\n\nThe Bloch group is a subgroup of P(F) which, by a result of Suslin, is naturally a quotient of the indecomposable K3 of F, and this in turn is a quotient of the group H3(SL(2,F),Z). Up to some possible 2-torsion, the kernel of the map H3(SL(2,F),Z) to K3^ind(F) coincides with the kernel of the stabilization map from H3(SL(2,F),Z) to H3(SL(3,F),Z). We will describe how, for fields with valuations, lower bounds - and even exact computations - of this latter kernel can be expressed as direct sums of pre-Bloch groups of residue fields.
Montag, 10.12.12, 16:00-17:00, Raum 404, Eckerstr. 1
First order deformations in heterotic compactifications
Montag, 10.12.12, 16:00-17:00, Raum 404, Eckerstr. 1
Many beautiful geometric structures, such as Calabi-Yau (CY) manifolds and their moduli spaces, arise naturally in the context of string theory. In heterotic string theory a generalization of CY geometry is given by holomorphic vector bundles over CY spaces. This talk is concerned with more general heterotic geometries: vector bundles over complex but typically non-Kaehler manifolds. I will review this geometric structure and its origin in string theory and then focus on a characterization of the first order deformation space of these geometries.\n\n
Local results for Ricci flow on regions with curvature bounded from below
Dienstag, 11.12.12, 16:15-17:15, Raum 414, Eckerstr. 1
Donnerstag, 13.12.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
L2-dbar-cohomology of singular complex spaces
Freitag, 14.12.12, 10:00-11:00, Raum 404, Eckerstr. 1
We will explain how one can use a resolution of singularities to understand the L2-Dolbeault-cohomology of a singular Hermitian complex space \(X\)\n(in the sense of finding a smooth model for the cohomology). The central tool is an L2-resolution for the Grauert-Riemenschneider canonical sheaf of \(X\).\nWe obtain particularly nice results if X is a Gorenstein space with canonical singularities, including an L2-representation of the cohomology of the structure sheaf.\nTo attack the more general case, we introduce a new kind of canonical sheaf, namely the canonical sheaf of square-integrable holomorphic\ntop-degree-forms with some (Dirichlet) boundary condition at the singular set of X. An L2-resolution for this sheaf allows to describe the L2-cohomology of arbitrary isolated singularities.
Geometric flows and special holonomy
Montag, 17.12.12, 16:15-17:15, Raum 404, Eckerstr. 1
Metrics with holonomy contained in G_2 on a 7-manifold are \ninduced by so-called positive 3-forms which are torsionfree, i.e. satisfy a \ncertain nonlinear 1st order PDE. I will discuss a parabolic flow on \npositive 3-forms whose stationary points are precisely given by the\ntorsionfree ones. This is joint work with F. Witt.\nIf time permits I will describe a generalization to a spinorial setting \n(joint with B. Ammann and F. Witt).
Witten's proof of positive mass theorem
Dienstag, 18.12.12, 16:15-17:15, Raum 404, Eckerstr. 1
I'll give a talk on Witten's proof of the positive mass theorem using spinors.
Cardinal Invariants and the P-Ideal Dichotomy
Mittwoch, 19.12.12, 16:30-17:30, Raum 404, Eckerstr. 1
Nichtstandardanalysis --- eine Anwendung auf interagierende Teilchensysteme
Donnerstag, 20.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
Nichtstandardanalysis --- eine Anwendung auf interagierende Teilchensysteme, Filter und Semifilter
Donnerstag, 20.12.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
Filter und Semifilter
Donnerstag, 20.12.12, 17:15-18:15, Hörsaal II, Albertstr. 23b
Pulling back differential forms
Freitag, 21.12.12, 10:00-11:00, Ort noch nicht bekannt
Donnerstag, 27.12.12, 17:00-18:00, Hörsaal II, Albertstr. 23b