Das Mathematische Kolloquium ist eine gemeinsame wissenschaftliche Veranstaltung des gesamten Mathematischen Instituts. Es steht allen Interessierten offen und richtet sich neben den Mitgliedern und Mitarbeitern des Instituts auch an die Studierenden. Das Kolloquium findet dreimal im Semester am Donnerstag um 15:00 s.t. im Hörsaal II, Albertstr. 23b statt. Danach (gegen 16:15) gibt es Kaffee und Kekse, zu dem der vortragende Gast und alle Besucher eingeladen sind.
Antrittsvorlesung "Konforme Feldtheorie und ihr Einsatz in der Geometrie"
Donnerstag, 2.6.16, 16:00-17:00, Hörsaal II, Albertstr. 23b
Antrittsvorlesung "Sonntagsmathematik: Einblicke in den Intuitionismus"
Donnerstag, 2.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Optimal liquidation under partial information and market impact
Donnerstag, 9.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Primitive Ideals of the enveloping algebra of the Lie algebra of trace free infinite matrices
Donnerstag, 16.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
If \(A\) is a commutative ring, its primitive ideals are just its maximal ideals, in other words, they form the maximal spectrum of \(A\). Describing the maximal spectrum goes back to the classics of algebra from the beginning of the 20th century. If \(U\) is a noncommutative ring, its primitive ideals are defined as the annihilators of simple \(U\)-modules. If \(U\) is an enveloping algebra of a finite-dimensional simple Lie algebra \(\bmathfrak{g}\) such as \(\bmathfrak{g}=\bmathrm{sl}(n,\bmathbb{C})\), then the primitive ideals of \(U\) are described by a celebrated theorem of Duflo and have been further studied by Borho, Joseph, and others. In this talk, I will describe the recent results of Alexey Petukhov and myself, providing a complete description of the primitive ideals of the universal enveloping algebra of the Lie algebra of finite matrices of unbounded size \(\bmathrm{sl}(\binfty)\). These results are somewhat surprising and yield an explicit solution to the problem. They are based on the pioneering work of A. Zhilinskii from 1990s.\n
Optimal cross-border mortgage decisions
Donnerstag, 23.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Abstract:\nIn this talk we study optimal cross-border mortgage decisions in a\ncross-border setting. In particular, we address the question how a\nhousehold should optimally split its mortgage portfolio in a\nfixed-rate-mortgage in the domestic currency and an\nadjustable-rate-mortgage denominated in a foreign currency. For this\npurpose, we employ a three-dimensional Gaussian affine model with\ncorrelated foreign and domestic interest rates which together determine\nthe time-varying drift of the exchange rate. We apply this model to a\ndataset consisting of Euro and Swiss LIBOR rates and the\nEUR-CHF-exchange rate. With the estimated parameters, we discuss whether\nit is optimal to take a fixed-rate mortgage in the domestic currency or\nan adjustable-rate-mortgage in the foreign currency or any affordable\ncombination of both.\n
Donnerstag, 30.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b