Classifying 8-dimensional E-manifolds
Montag, 3.6.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
A manifold M is called an E-manifold if it has homology only\nin even dimensions, ie. H{2k+1}(M;Z) = 0 for all k. Examples include\ncomplex projective spaces and complete intersections. We consider\n8-dimensional simply-connected E-manifolds. Those that have Betti\nnumbers b2 = r and b4 = 0, and fixed second Stiefel-Whitney class\nw2 = w form a group \btheta(r;w), which acts on the set of E-manifolds\nwith b2 = r and w2 = w. The classification of E-manifolds based on\nthis action consists of 3 steps: computing \btheta(r;w), classifying\nthe set of orbits and finding the stabilizers. In this talk I will\npresent results in each of these steps, as well as an application, the\nproof of a special case of Sullivan's conjecture about complete\nintersections.\n
Vektorgeometrie mediengestützt entdecken
Dienstag, 4.6.19, 19:30-20:30, Hörsaal II, Albertstr. 23b
In diesem Vortrag stellen Schülerinnen und Schüler der Gewerblich Hauswirtschaftlichen Schulen Emmendingen eine Unterrichtseinheit zur Vektorgeometrie in der Sekundarstufe II der beruflichen Gymnasien vor. Die Teilnehmer werden eingeladen, anhand von Holzmodellen, Geogebra-Applets, und digital verfügbaren Arbeitsblättern Realisierungsmöglichkeiten eines digital gestützten Mathematikunterrichts exemplarisch zu erproben. Dazu werden einige Tablets zur Verfügung gestellt, die Teilnehmer können aber auch eigene Geräte mitbringen. \nBei der anschließenden Einordnung des Beispiels in den didaktischen Kontext der Unterrichtseinheit werden darüber hinaus Diagnoseaufgaben, Möglichkeiten der Instruktion und der Organisation des Unterrichtssettings diskutiert. \n
Donnerstag, 6.6.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
Arithmetic of Curves
Donnerstag, 6.6.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
In 1922, while studying rational solutions to polynomial equations\n \nf(x,y)=0\n\nin two variables, Mordell had the astounding idea that the structure of the problem might be intimately related to the geometry and topology of the complex solution set. This became known as the Mordell conjecture, stating that the equation has only finitely many rational solutions when the genus is at least two.\n\nThis was proved by Faltings in 1983 in a landmark result that developed an astounding array of techniques in arithmetic geometry and led to great advances in numerous areas of number theory and algebraic geometry. This talk will give an eclectic survey of this history and discuss the harder problem of finding all rational solutions to such equations, often called the effective Mordell conjecture.\n\n
Tame topology and algebraic geometry
Freitag, 7.6.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
In the 80's Grothendieck argued that general topology, which was developed for the needs of analysis, should be replaced by a "tame topology" if one wants to study the topological properties of natural geometric forms. Such a tame topology was developed by model theorists under the name "o-minimal structures". In this talk I will review the notion of o-minimal structure, and some of its applications to complex algebraic geometry, in particular for studying periods of algebraic varieties.\n\n
G2 manifolds with isolated conical singularities and asymptotically conical G2 manifolds
Montag, 17.6.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Motives
Freitag, 21.6.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
I am going to give an informal survey of the different theories of motives and how they relate.
Cardinal Preserving Forcing of Closed Unbounded Sets into Stationary Sets
Montag, 24.6.19, 14:15-15:15, Raum 404, Ernst-Zermelo-Str. 1
This is the presentation of Daniel Kurz's master's thesis:\n\nWe select a result from U.Abraham's and S.Shelah's 1983 paper "Forcing\nClosed Unbounded Sets" (J.Symb.Log. Vol.48 No.3) and show how a set \(S\n\bsubseteq \bkappa\) that is a special kind of stationary ("fat") in\n\(\bkappa\) in terms of the groundmodel acquires a closed unbounded subset\nin a generic extension while cardinals \(\bleq \bkappa\) (and in some cases\nof \(\bkappa\) even all cardinals) are preserved. Here, in terms of the\ngroundmodel \(\bkappa\) is a cardinal such that either \(\bkappa = \bmu^+\),\n\(\bmu = \bmu^{< \bmu}\) an infinite cardinal, or \(\bkappa\) is strongly\ninaccessible.\n\n
The parametrix construction in the b-calculus: a case study
Montag, 24.6.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
In this talk I will review the parametrix construction in the b-calculus by describing in detail a concrete example, the construction of the resolvent for the Laplacian on functions for an asymptotically Euclidean manifold.\nI will mostly follow the two papers Resolvent at Low Energy and Riesz Transform for Schrödinger Operators on Asymptotically Conic Manifolds. I & II by C. Guillarmou and A. Hassell.
Q-Curvature Equation in Dimension 1
Dienstag, 25.6.19, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
Die Erstellung von Erklärvideos im Mathematikunterricht
Dienstag, 25.6.19, 19:30-20:30, Hörsaal II, Albertstr. 23b
Online- und Erklärvideos gewinnen nicht nur in der Freizeitbeschäftigung von Jugendlichen, sondern auch im schulischen Kontext an Bedeutung: Sogenannte Social Media Teacher erhalten von Schülern mehrere Millionen Klicks für ihre Mathematik-Erklärvideos. Doch welches Potenzial haben Erklärvideos im Mathematikunterricht? Im Vortrag wird ein praxiserprobtes Konzept vorgestellt, in dem Schüler der Eingangsklasse eines beruflichen Gymnasiums von YouTube-Konsumenten zu Produzenten von eigenen Erklärvideos werden. Fokus liegt auf der Fragestellung, inwieweit die Videoproduktion den Schülern dabei hilft, ihr mathematisches Vorwissen zu aktivieren und strukturieren und ob die Lernprodukte von der Lehrkraft als Diagnoseinstrument genutzt werden können.
Constructible sheaves
Freitag, 28.6.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Given a stratified topological space, we answer the question whether the functor from the derived category of constructible sheaves to the derived category of sheaves with constructible cohomology is an equivalence.\nBasic facts on locally constant sheaves and constructible sheaves will be explained. This is joint work with Valery Lunts and Jörg Schürmann.