Freitag, 2.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
Rational curves and asymptotic base locus of some divisors
Freitag, 9.1.09, 11:15-12:15, Raum 403, Eckerstr. 1
I will present two joint works with Gianluca Pacienza and also Sébastien Boucksom for one of them.\n\nThe geometry of the rational curves on a variety is a fundamental tool for the classification of complex projective varieties.\nRecently, two notions of base locus attached to divisors/complex line bundles have been discovered and studied by Nakayama, Boucksom, Nakamaye and others.\nOne of them, the non-nef locus, is as suggest his name, empty if and only if the divisor (or the first chern of the line bundle) is nef. That is, it has non-negative instersection on every curve in the variety. We will show how this base loci are related to the geometry of rational\ncurves on a variety. Namely, I will give a survey of the proof of the two following statements:\nIf X is a projective variety with nef anticanonical bundle (dual of the canonical bundle) then every non-nef base locus of a divisor is uniruled. It is a generalization of a result of Takayama who proved this result in the case of varieties with (numerically) trivial anticanonical bundle.\n\nIf X is big then X is rationnally connected modulo the non-nef locus of -KX : two points of X are connected by a chain of curves which are either rational or in the non-nef locus of -KX . This a generalization of the well-known result of the rational connectedness of Fano varieties. The proof uses technics introduced by Zhang and\nHacon-McKernan for the proof of the rational connectedness of weak log Fano varieties and the proof of the Shokurov conjecture.
Rationale Kurven auf algebraischen Varietäten
Freitag, 9.1.09, 16:30-17:30, Hörsaal II, Albertstr. 23b
On some applications of bi-invariant metrics on solvmanifolds
Montag, 12.1.09, 16:15-17:15, Raum 404, Eckerstr. 1
Theory and Numerics for the Navier-Stokes-Korteweg Equations and the Associated Sharp Interface Model
Dienstag, 13.1.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Del Pezzo surfaces, unprojections, and Calabi threefolds
Freitag, 16.1.09, 11:15-12:15, Raum 403, Eckerstr. 1
A geometric transition between two Calabi-Yau threefolds is the composition of a degeneration a contraction and a smoothing. In my talk I would like to describe geometric transitions for which the contraction is an unprojection contracting a del Pezzo surface to a point. I shall show how using such constructions one can obtain new families of well described Calabi-Yau threefolds.
Billiards und p-adische Differentialgleichungen
Freitag, 16.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
Kompetenzen und Leitideen im Mathematikunterricht der Oberstufe
Dienstag, 20.1.09, 19:30-20:30, Hörsaal II, Albertstr. 23b
Explicit Beilinson-Bernstein theorem for arithmetic D-modules
Freitag, 23.1.09, 11:15-12:15, Raum 403, Eckerstr. 1
In the years 80's, Beilinson-Bernstein and Brylinski-Kashiwara proved that there is an equivalence of categories between the D-modules on the flag variety of a semi-simple algebraic group over the field of complex numbers and modules over the Lie algebra of the group, with some condition on the action of the center of the envelopping algebra. This result lead to important results in the theory of Lie Algebra representation. We will explain here an arithmetic version of this equivalence of category by considering flag varieties in car. p>0 and arithmetic D-modules of Berthelot attached to these varieties.
A monolithic FEM solver for fluid structure interaction in ALE formulation
Freitag, 23.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
A monolithic algorithm to solve the problem of time dependent interaction\nbetween an incompressible, possibly non-Newtonian, viscous fluid and an\nelastic\nsolid is investigated. The continuous formulation of the problem and its\ndiscretization is done in a monolithic way, treating the problem as\none continuum and discretized by the finite elements method. The\nresulting nonlinear algebraic system of equations is solved\nby an approximate Newton method with coupled geometric multigrid\nlinear solver for solving the linear subproblems. We discuss\npossible efficient strategies of setting up the resulting system and\nits solution.\n
Aubry-Mather-Theorie fuer Lorentzmannigfaltigkeiten
Montag, 26.1.09, 16:15-17:15, Raum 404, Eckerstr. 1
A Local Discontinuous Galerkin Discretization for Shallow Incompressible Flows with Free Surface
Dienstag, 27.1.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Mittwoch, 28.1.09, 09:15-10:15, Raum 404, Eckerstr. 1
Freitag, 30.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b