test
Wednesday, 1.5.13, 03:00-04:00, Raum 414, Eckerstr. 1
test
Thursday, 2.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Sunday, 5.5.13, 00:00-01:00, Hörsaal II, Albertstr. 23b
L^2 index theory for families
Monday, 6.5.13, 16:15-17:15, Raum 404, Eckerstr. 1
On the existence of a local pressure for general systems of incompressible viscous fluids
Tuesday, 7.5.13, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
In various models of incompressible viscous fluids one of the most challenging problem is the construction of a pressure function, which can be regarded as a Lagrangian multiplier of the system due to the restrain of divergence free condition of the velocity of the fluid. While for the well-known Navier-Stokes equations this problem can be solved by using the L^p theory for the Stokes operator for general fluid models the problem is unsolved. However, by introducing a new method of constructing a local pressure we are able to prove the existence of a weak solution to such systems, satisfying a new form of local energy identity involving the local pressure. This eventually\nwill lead new results of partial regularity of weak solutions to the equations of Non-Newtonian fluids.\n\n
Cusped Shell-like Structures
Tuesday, 7.5.13, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The talk is devoted to an updated exploratory survey of results concerning elastic\ncusped shells, plates, and beams and cusped prismatic shell-fluid interaction\nproblems. Mathematically, the corresponding problems lead to non-\nclassical, in general, boundary value and initial-boundary value problems for\ngoverning degenerate elliptic and hyperbolic systems in static and dynamical\ncases, respectively, with the corresponding mechanical (physical) interpretations.\nTwo principally different approaches of investigation are used:\n(1) to get results for 2D (two-dimensional) and 1D (one-dimensional) problems\nfrom results of the corresponding 3D (three-dimensional) problems and (2) to\ninvestigate directly governing degenerate and singular systems of 2D and 1D\nproblems. In both the cases, it is important to study the relationship of 2D and 1D\nproblems with 3D problems. On the one hand, it turned out that the second\napproach allows to investigate such 2D and 1D problems whose corresponding 3D\nproblems are not possible to study within the framework of the 3D model of the\ntheory of elasticity. On the other hand, the second approach is historically\napproved, since first the 1D and 2D models were created and only then the 3D\nmodel was constructed. Hence, the second approach gives a good chance for the\nfurther development (generalization) of the 3D model.
On the existence of a local pressure for general systems of incompressible viscous fluids
Tuesday, 7.5.13, 15:15-16:15, Raum 226, Hermann-Herder-Str. 10
In various models of incompressible viscous fluids one of the most challenging problem is the construction of a pressure function, which can be regarded as a Lagrangian multiplier of the system due to the restrain of divergence free condition of the velocity of the fluid. While for the well-known Navier-Stokes equations this problem can be solved by using the \(L^p\) theory for the Stokes operator for general fluid models the problem is unsolved. However, by introducing a new method of constructing a local pressure we are able to prove the existence of a weak solution to such systems, satisfying a new form of local energy identity involving the local pressure. This eventually will lead new results of partial regularity of weak solutions to the equations of Non-Newtonian fluids.
Hyperbolic Alexandrov-Fenchel quermassintegral inequalities
Tuesday, 7.5.13, 16:15-17:15, Raum 404, Eckerstr. 1
The pseudointersection number and the tower number
Wednesday, 8.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 9.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Quantum product for derived categories
Friday, 10.5.13, 10:00-11:00, Raum 404, Eckerstr. 1
Quantum cohomology ring of a smooth projective variety X is a certain deformation of its usual cohomology ring. This structure was introduced at the begging of 90's motivated by works of string theorists. Later on an analogue of the quantum product was defied in the K-theory. In this talk I will describe a way to define an analogue of the quantum product on the derived category of X.\n\n
Hasse-Weil L-function of elliptic curves over Q and beyond
Monday, 13.5.13, 16:15-17:15, Raum 404, Eckerstr. 1
Basic findings to Stokes eigenfunctions and notes on applications in rotating Hagen-Poiseuille flow in pipes
Tuesday, 14.5.13, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We give an overview on results, techniques, decomposition methods and constraints for the determination of eigenfunctions of the Stokes operator with homogeneous Dirichlet boundary conditions on the rigid part of the frontier of three-dimensional domains.\nWe explain wherefore the class of three-dimensional domains accessible for the specification of Stokes eigenfunctions is resticted on only five elements, namely at first the ball and the annulus - and secondary the infinite layer, the interior of a pipe and the interior of a double pipe \n(all equipped with periodic conditions).\nFurthermore, we illustrate the particular importance of explicitely known Stokes eigenfunctions emphasized by the fact, that one needs a good deal more information then - only the existence and completeness of such systems - in calculations and estimations. There we present the numerical\nstudy of rotating Hagen-Poiseuille flow as an example of applications also.
Analysis of a mean curvature flow action functional
Tuesday, 14.5.13, 16:15-17:15, Raum 404, Eckerstr. 1
Wednesday, 15.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
Unsound ordinals
Wednesday, 15.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
An ordinal zeta is unsound if there are subsets An (n in omega) of it such that as b ranges through the subsets of omega, uncountably many ordertypes are realised by\nthe sets $\bbigcup{n \bin b} An\(.\n\nWoodin in 1982 raised the question whether unsound ordinals\nordinals exist; the answer I found then (to be found in a paper\npublished in the Mathematical Proceedings of the Cambridge Philosophical Society volume 96 (1984) pages 391--411) is this:\n\n\nAssume DC. Then the following are equivalent:\n\ni) the ordinal \)\bomega1^{\bomega + 2}$ (ordinal exponentiation) is unsound\n\nii) there is an uncountable well-ordered set of reals\n\nThat implies that if omega1 is regular and the ordinal mentioned in i) is sound, then omega1 is strongly inaccessible in the constructible universe. Under DC, every\nordinal strictly less than the ordinal mentioned in i) is sound.\n\n\nThere are many open questions in this area: in particular, in\nSolovay's famous model where all sets of reals are Lebesgue measurable,\nis every ordinal sound ? The question may be delicate, as Kechris and Woodin have shown that if the Axiom of Determinacy is true then there\nis an unsound ordinal less than omega_2.\n\n
Thursday, 16.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Knightian Uncertainty in Economics and Finance
Friday, 17.5.13, 11:30-12:30, Raum 404, Eckerstr. 1
Thursday, 23.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Das Oberseminar Differentialgeometrie entfällt wegen der Antrittsvorlesung von Herrn Juniorprofessor Dr. Harald Ita um 17:15 im Großen HS des Physikalischen Institutes.
Monday, 27.5.13, 17:15-18:15, Hörsaal 2, Physik Hochhaus, Hermann-Herder-Straße 3
"Connected sum constructions in geometry and nonlinear analysis " (Frank Pacard's Note) Teil 1
Tuesday, 28.5.13, 16:15-17:15, Raum 404, Eckerstr. 1
Resurrecting Ramsey ultrafilters
Wednesday, 29.5.13, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 30.5.13, 17:00-18:00, Hörsaal II, Albertstr. 23b
Rational Motives over deeper bases
Friday, 31.5.13, 10:00-11:00, Raum 404, Eckerstr. 1
We begin with a brief introduction to motivic homotopy\ntheory and motives. Roughly, one notes that cohomology theories for schemes can be approached in close analogy to those for topological spaces: They factorize through a homotopy category, then through a stable homotopy category where they become representable by some object ("a spectrum"). If this object is a "ring spectrum", they\nfactor further through the category of modules over that ring spectrum - if one starts with motivic cohomology, the latter is the category of motives.\n\nFor a variety of reasons there have been proposed many alternative notions of scheme, e.g. to overcome the asymmetry between the "finite primes" and the "infinite primes" of a number field (\(\bmathbb{F}_1\)-geometry), to construct cohomology theories for spaces ("derived algebraic geometry") or to handle Frobenius lifts ("lambda\nalgebraic geometry"). In this talk we will present a way to construct motives for such alternative schemes: We construct a stable homotopy category and a K-theory spectrum therein, give a rational decomposition, pick a summand (the "alternative Beilinson spectrum") and pass to modules over it. The construction is compatible with base\nchange and admits a different description in terms of the positive rational motivic sphere.