Gauge Theory on G2-manifolds
Wednesday, 1.2.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
G2-manifolds are a special kind of Ricci-flat 7-manifolds. On a G2-manifold one can study a special class of Yang-Mills connections, called G2-instantons. The theory of G2-instantons is governed by an index zero supercritical elliptic equation.\n\nConjecturally, to each bundle over a G2-manifold one can associate a "G2 Casson invariant" obtained by "counting" the moduli space of G2-instantons. Such an invariant could prove to be very useful in understanding the landscape of G2-manifolds. Unfortunately, there are quite a large number of technical problems in the theory of G2-instantons. I will briefly discuss one of the major issues having to do with non-compactness phenomena.\n\n An important class of G2-manifolds are those arising from Joyce's generalised Kummer construction. I will briefly review this construction, and explain a program to study G2-instantons on these G2-manifolds. In particular, I will give an existence result obtained via a gluing method as well as a partial compactness theorem. Time permitting, I will describe a remaining analytic problem whose solution would make the "G2 Casson invariant" rigorous and, in fact, computable on certain bundles over generalised Kummer constructions.\n
Burning cars in a parking lot
Thursday, 2.2.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
The Family Index Theorem and the Eta-Form
Monday, 6.2.12, 16:15-17:15, Raum 404, Eckerstr. 1
We'll give an overview of the index theorem in different situations and then we'll concentrate on families of closed manifolds. We are interested in the eta-form and its convergence at infinity and zero.\nOur presentation will be based on "Heat Kernels and Dirac Operators" by Berline, Getzler and Vergne.
Existenz schwacher Lösungen stationärer Bewegungen von Fluiden mit scherspannungsabhängiger Viskosität im unbeschränkten Gebiet
Tuesday, 7.2.12, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Volume and area renormalizations for Conformally compact Einstein metrics III
Tuesday, 7.2.12, 16:15-17:15, Raum 127, Eckerstr. 1
Determiniertheit und Forcing
Wednesday, 8.2.12, 16:30-17:30, Raum 404, Eckerstr. 1
t.b.a.
Thursday, 9.2.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Invarianten arithmetischer Gruppen
Friday, 10.2.12, 10:00-11:00, Raum 404, Eckerstr. 1
Kozykel für charakteristische Klassen
Monday, 13.2.12, 16:15-17:15, Raum 404, Eckerstr. 1
In meinem Vortrag konstruiere ich nach Brylinski-Mc Laughlin Kozykeldarstellungen für charakteristische Klassen in der glatten Deligne-Kohomologie.
Volume and area renormalizations for Conformally compact Einstein metrics IV
Tuesday, 14.2.12, 16:15-17:15, Raum 127, Eckerstr. 1
Zur "Charakter bildenden Kraft" der Mathematik
Tuesday, 14.2.12, 19:30-20:30, Hörsaal II, Albertstr. 23b
Eine der Konstanten mathematischer Selbstbeschreibung, die sich nahezu ungebrochen von der\nFrühen Neuzeit bis in die Gegenwart fortschreibt, ist die Vorstellung, dass die intensive\nBeschäftigung mit der Mathematik den Charakter präge. Dieser Überzeugung sind schon die\nMathematiker Joachim Jungius (1587-1657) und Erhart Weigel (1625–1699), die beide über die\nTugenden des Mathematikers räsonieren. Auch Georg Kerschensteiner (1854-1932) meint, der\nMathematikunterricht solle "im Dienste der Charakterbildung" stehen und neben den\nKenntnissen "moralische, ästhetische und gewisse intellektuelle Erziehungswerte" vermitteln. Und\nnoch Georg Hamel (1877-1954) betont die „besondere Beziehung“, die zwischen dem Erwerb\nmathematischen Wissens und der Ausbildung einer spezifischen "Geisteshaltung" bestehe.\nWelche Wirkung das Mathematische allerdings genau auf den Charakter hat oder haben soll,\nist alles andere als unumstritten. In der Frühen Neuzeit erwartet man sich vor allem ein\ngelassenes, unparteiisches und irenisches Gemüt, Im 19. und 20. Jahrhundert treten hingegen\nverstärkt aktivische Charakteristika in den Vordergrund. Ich werde am Beispiel von einer Reihe von\nFundstücken die Auffassungen zur "formalen Fernwirkung" der mathematischen Unterweisung auf\ndie "seelische Entwicklung" (Heinz George) nachzeichnen und aus historischer Perspektive zu\nklären versuchen, wie sinnvoll die Rede von der "Charakter bildenden Kraft" der Mathematik\neigentlich ist.
Lagrangian mean curvature flow and Gauss maps
Wednesday, 15.2.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
In the first part of the talk we will give an overview\nof the Lagrangian mean curvature flow. In the second part we develop a connection between the Gauss maps of certain hypersurfaces and the Lagrangian mean curvature flow of their Gauss maps into Grassmannians and present some convergence results in the two-positive case.\n\n
The two-cardinal transfer problem: the singular case
Wednesday, 15.2.12, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 16.2.12, 17:00-18:00, Hörsaal II, Albertstr. 23b
Koszul-Dualität
Friday, 17.2.12, 10:00-11:00, Raum 404, Eckerstr. 1
Optimal Stopping of Markov Chains, Gittins Index and Related Optimization Problems
Friday, 17.2.12, 11:15-12:15, Raum 404, Eckerstr. 1
In this talk I will discuss the problem of Optimal Stopping (OS) of Markov Chains (MCs), the methods for its solution, the classical and the generalized Gittins indices and related problems: the Katehakis-Veinott Restart Problem and the Whittle family of Retirement Problems. The celebrated Gittins index, its generalizations and related techniques play an important role in applied probability models, resource allocation problems, optimal portfolio management problems as well as other problems of financial mathematics. It is well known that a connection exists between the Ratio (cycle) maximization problem, the Katehakis-Veinott (KV) Restart Problem and the Whittle family of Retirement Problems, and that their key characteristics, the classical Gittins index, the KV index, and the Whittle index are equal in a classical setting. These indices were generalized by the author (Statistics and Probability Letters, 2008) in such a way that it is possible to use the so called State Elimination algorithm, developed earlier to solve the OS of MCs problem to calculate this common index. One of the goals of this talk is to demonstrate also that the equality of these indices is a special case of a similar equality for three simple abstract optimization problems. A more general - continue, quit, restart problem will be also discussed.
Regularity for Fractional Harmonic Maps in the critical dimension
Wednesday, 22.2.12, 16:15-17:15, Hörsaal II, Albertstr. 23b
The theory of fractional harmonic maps can be seen as an extension of Riviere's celebrated result for critical points of conformally invariant variational functionals in two dimensions.\nI will present some arguments necessary for the regularity results, as well as applications of these arguments for related energies.\n