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 17:00 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.
Thursday, 21.4.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
From the impossibility of computing algebraically the position of a planet at prescribed time (Newton) to the general structure of period relations (Ayoub)
Thursday, 28.4.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
\nAbstract: In lemma XXVIII of his Principia (1687), Newton asserts the\nimpossibility of computing algebraically the area of a section of a\nfixed oval in terms of the position of the line which cuts it. While the\nvalidity of both the statement and its proof have been vigorously\ndebated during three centuries, this has launched a vast reflection\nabout the transcendence of volumes of algebraic solids (as functions of\ndefining parameters), and more generally about the nature of the\nalgebraic relations relating such volumes. A general structure theorem,\nas simple to state as difficult to prove, has finally been found by J.\nAyoub (2015).\nIn this talk, we will review Newton’s lemma and its marvelous proof,\nstate the transcendence problem and explain Ayoub’s result.\n
Thursday, 5.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 12.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 19.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 26.5.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Antrittsvorlesung "Konforme Feldtheorie und ihr Einsatz in der Geometrie"
Thursday, 2.6.16, 16:00-17:00, Hörsaal II, Albertstr. 23b
Antrittsvorlesung "Sonntagsmathematik: Einblicke in den Intuitionismus"
Thursday, 2.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Optimal liquidation under partial information and market impact
Thursday, 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
Thursday, 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
Thursday, 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
Thursday, 30.6.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Vorstellungsvortrag: Descent
Thursday, 7.7.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
The notion of descent is ubiquitous in mathematics. An object satisfies descent\nwhenever its nature is determined by local conditions, for instance:\n\n1. (sheaf condition) A function on a topological space can be given locally on an open\ncovering. The local functions can be glued to a global function if they agree on\noverlaps.\n\n2. (descent) A vector bundle on a topological space can - by definition - be given\nlocally on an open covering. The local bundles are glued to a global one by means of\nglueing data on overlaps that satisfy a compatibility condition on "overlaps of\noverlaps".\nThis comes in many flavors such as descent for modules over rings, families of\nvarieties, etc.\n\n3. (cohomological descent) Any type of cohomology of a topological space or\nalgebraic variety can be recovered (in a certain sense) from the cohomology of an\nopen cover. The "glueing data" in this case is much more complicated and carries the\nessential information.\nWe will explain in this talk how all these instances of descent (and many more) are\nunified by adopting a higher-categorical point of view, the examples above becoming\ndescent for set-like objects, 1-category like objects, or infinity-categorical objects. As\nmodel for "infinity-categorical" questions of descent, we present the theory of fibered\nderivators, the topic of the habilitation thesis of the speaker. Our main motivation has\nbeen descent for Grothendieck six-functor formalisms (encoding Serre duality,\nVerdier duality, etc.).
The mathematics behind LIGO Experiment's first ever detection of gravitational waves
Thursday, 14.7.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
On 11 February 2016 the LIGO and Vigo Collaborations announced\nthe detection of gravitational waves. These gravitational waves were produced\nabout 1.3 billion years ago from the inspiral and merger of a pair of black holes\nof 29 and 36 solar masses into a single one of 62 solar masses. The difference\nin their masses was transformed in gravitational radiation, which propagated\nthrough the spacetime as gravitational waves, to reach the Earth on 14\nSeptember 2015. These observations demonstrate the existence of binary\nstellar-mass black hole systems. They also provide the first direct detection of\ngravitational waves and the first observation of a binary black hole merger.\n\nIn this talk I will present the mathematics behind this recent detection of\ngravitational waves, whose existence was predicted by Einstein in 1916, one\nyear after he formulated his equation for General Relativity.\n\nDownload the invitation as PDF.