Boundary value problems on noncompact manifolds
Monday, 3.12.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
We consider Poisson problems on manifolds with boundary and\nbounded geometry and assume that they have finite width (that is, that the distance from any point to the boundary is bounded uniformly). We include Robin boundary conditions. As an application, we establish the connection to the Poisson problem on certain domains in the plane and\nhigher dimensional stratified spaces. In particular we get the well-posedness of strongly elliptic equations on domains with oscillating conical singularities, a class of domains\nthat generalizes the class of bounded domains with conical points. \nThis is joint work with Bernd Ammann (Regensburg) and Victor Nistor (Metz).
On the Plateau-Douglas problem for the Willmore energy
Tuesday, 4.12.18, 16:00-17:00, Raum 404, Ernst-Zermelo-Str. 1
In this talk we will introduce the Willmore energy of surfaces in the three-dimensional Euclidean space, which is the surface integral of the squared mean curvature. For a smooth closed embedded planar curve, we will consider the minimization of the Willmore energy among immersed surfaces of a prescribed genus having the given curve as boundary. Such problem can be seen as a generalization of the classical Plateau-Douglas problem, which is immediately trivial in the case of planar boundary curves. Exploiting the conformal properties of the functional and tools from the theory of varifolds with boundary, we will see that the problem does not reduce to a minimal surfaces problem and we will present some recent explicit results both of existence and non-existence of minimizers, depending on the prescribed boundary curve.
Der Häufigkeitsdoppelbaum als didaktisch hilfreiches Werkzeug von der Unterstufe bis zum Abitur
Tuesday, 4.12.18, 19:30-20:30, Hörsaal II, Albertstr. 23b
Wie wahrscheinlich ist eine Erkrankung nach einem positiven medizinischen Testergebnis? Leider scheitern selbst viele Ärzte an der Beantwortung derartiger Fragen. Glücklicherweise helfen zwei Strategien, bedingte Wahrscheinlichkeiten zu verstehen: 1. Natürliche Häufigkeiten und 2. Visualisierungen. Im Vortrag wird gezeigt, wie mithilfe eines Häufigkeitsdoppelbaumes beide Strategien genutzt werden können, um Aufgaben erfolgreich zu lösen. Der Häufigkeitsdoppelbaum kann bereits ab der Unterstufe eingesetzt werden und die Schülerinnen und Schüler bis hin zum Abitur begleiten.
Invariant geometric structures on \(G_2\) flag manifolds
Monday, 10.12.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
I will discuss invariant geometric structures on certain homogeneous spaces, known as \(G_2\) flag manifolds. Flag manifolds are known to carry interesting invariant structures, such as a complex structure with compatible Kähler-Einstein metric, as well as other (possibly non-integrable) almost complex structures. These are typically studied from a Lie-theoretic point of view, and are well-understood in that context. However, such algebraic methods shed little light on their geometric origin. In this talk, we will take a complementary, differential-topological approach to studying invariant geometric structures on these manifolds. Besides recovering results typically obtained using Lie theory, we will see that this more geometric approach reveals connections to interesting topics in complex geometry, such as rigidity theorems for Kählerian complex structures, and twistor theory for quaternionic\nKähler manifolds.
Thursday, 13.12.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Differential transcendence of special functions
Friday, 14.12.18, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
One of the goal of the difference Galois theory is to\nunderstand the algebraic relations between solutions of a linear\nfunctional equation. Recently, Hardouin and Singer developed a Galois\ntheory that aims at understanding what are the algebraic and\ndifferential relations among solution of such equations. In this talk we\nare going to see recent results ensuring that in many situations, such\nsolutions satisfy no algebraic differential relations.
Things you could call a reciprocity law
Friday, 14.12.18, 14:15-15:15, Hörsaal II, Albertstr. 23b
A number of different theorems "of similar shape" in the geometry of curves can be\nunified to a single statement in something called "K-theory". People who dream of\nnumber theory to be in analogy to curve theory want an analogous systematization.\nThis has remained a problematic issue, but starting in 2017, this is changing.
Equivariant Factorization Algebras from Abelian Chern-Simons theories
Monday, 17.12.18, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Factorization algebras are a powerful tool to encode observables in classical and quantum field theory. As suggested by Costello and Gwilliam, to the formal moduli problem describing deformations of flat G-bundles with connections on a manifold M, one can associate a factorization algebra F on M which describes the perturbative aspects of classical Chern-Simons theory on M with structure group G. In the talk I will concentrate on the case of G an abelian group, and show that the factorization algebra F comes naturally equipped with a (homotopy) action of the gauge group Maps(M,G), which can be regarded as a genuine nonperturbative aspect of Chern-Simons theory. Joint work with Corina Keller.
wird noch bekanntgegeben
Tuesday, 18.12.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The structure of stable sets
Wednesday, 19.12.18, 16:30-17:30, Raum 404, Ernst-Zermelo-Str. 1
We shall begin by explaining the idea behind the so-called "arithmetic regularity lemma" pioneered by Green, which is a group-theoretic analogue of Szemerédi's celebrated regularity lemma for graphs with wide-ranging applications. We will then describe recent joint work with Caroline Terry (University of Chicago), which shows that under the natural model-theoretic assumption of stability the conclusions of the arithmetic regularity lemma can be significantly strengthened, leading to a characterisation of stable subsets of finite abelian groups. In the latter part of the talk, we survey related work by various authors including Alon, Conant, Fox, Pillay, Sanders, Sisask, Terry and Zhao, further exploring this topic from both a combinatorial and a model-theoretic perspective.