Singular spin structures and Witten spinors
Wednesday, 2.11.11, 16:15-17:15, Hörsaal II, Albertstr. 23b
Unlike a 3-dimensional manifold, a higher dimensional manifold need not be spin. On an oriented Riemannian manifold the obstruction to having a spin structure is given by the second Stiefel-Whitney class. I will show that even when this obstruction does not vanish, it is still possible to define a notion of singular spin structure and associated singular Dirac operator. Then, modeling on Witten's proof of the Positive Mass Theorem, I will define the notion of Witten spinor on an asymptotically flat nonspin manifold, show their existence and describe their properties.
Specialising Aronszajn trees in a gentle manner
Wednesday, 2.11.11, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 3.11.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Nori-Motive und Tannaka-Kategorien
Friday, 4.11.11, 10:00-11:00, Raum 404, Eckerstr. 1
Universelle Konstruktionen von Nori-Motive
Friday, 4.11.11, 10:00-11:00, Raum 404, Eckerstr. 1
A coarse view on dynamics of one- dimensional quantum lattice systems
Friday, 4.11.11, 14:15-15:15, Hörsaal 1, Physik-Hochhaus, Hermann-Herder-Straße 3
I will present an analysis of the time evolutions that can be realized in one- dimensional quantum systems with discrete space and discrete time. We assume causality, in the sense that in any time step, information can propagate only a finite distance. In this setting, we find that there is a single, simple invariant - an "index" - which completely solves the following three problems:\n\n1. Classify all time evolutions up to continuous deformations\n2. Classify those dynamics which can be realized by quantum gates\n3. Classify the pairs of time evolutions U1, U2 which can be "pieced together" in the sense that there exists a single large system U which behaves like U1 in some parts an like U2 in other parts.\n\nThe index takes values in an abelian group (integers or positive rationals - depending on the lattice system), with the map sending reversible time evolutions to their index being a group homomorphism.\n\nA physical corollary of the program is that, in a certain sense, one cannot consistently talk about a particle moving in discrete space but continuous time.
Destruction of minimal foliations for finite range Frenkel-Kontorova models
Monday, 7.11.11, 16:15-17:15, Raum 404, Eckerstr. 1
Monotone variational recurrence relations such as the Frenkel-\nKontorova lattice, arise in solid state physics and as Hamiltonian\ntwist maps. Aubry-Mather theory guarantees the existence of minimizers\nof every rotation number. They constitute the Aubry-Mather set. When\nthe rotation number is irrational, the Aubry-Mather set is either\nconnected - a foliation, or a Cantor set - a lamination. It turns out\nthat when the rotation number of a minimal foliation is Liouville\n(easy to approximate by rational numbers) the foliation can be\ndestroyed into a lamination by an arbitrarily small smooth\nperturbation of the recurrence relation.
Entire graphs moving by curvature flows: mean curvature flow and beyond
Tuesday, 8.11.11, 16:15-17:15, Raum 127, Eckerstr. 1
We start with the classical results by Ecker and Huisken about mean curvature flow for entire graphs. Then we consider more general flows with speed depending on the curvatures. We are interested in understanding which statements hold for speeds that are increasing, homogenous functions of the principal curvatures. In particular if the homogeneity degree is one, we are able to deduce the asymptotic behaviour of entire graphs with linear growth at infinity.\n
Elementare Tetraedergeometrie
Tuesday, 8.11.11, 19:30-20:30, Hörsaal II, Albertstr. 23b
Asymptotic windings and entaglements of planar Brownian motion
Thursday, 10.11.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
The paths of planar Brownian motion are extremely complicated. Nonetheless, many asymptotic results, for large time, about the laws of Brownian functionals with geometric meaning, i.e. windings around a finite number of points, the length of the homotopic word of entanglement around two points, the width of the Wiener sausage, can be described completely. This will be the aim of this Colloquium talk.
Über die Qualität von Permutationstests für unbalancierte, heterogene Zweistichprobenprobleme
Friday, 11.11.11, 11:15-12:15, Raum 404, Eckerstr. 1
Klassische Permutationstests für Zweistichprobenprobleme (wie Pitman's Permutationstests zum Vergleich von Mittelwerten) besitzen im Gegensatz zu vielen anderen Resamplingverfahren den Vorteil, dass sie das Niveau auch für endliche Stichproben exakt einhalten, falls die Daten austauschbar sind.\nIn heterogenen Modellen ist dies allerdings nicht der Fall und der Test hält häufig nicht einmal asymptotisch die vorgegebene Fehlerwahrscheinlichkeit 1.Art ein. Der Vortrag gibt hierfür eine theoretische Erklärung und zeigt, wie dieses Problem in verschiedenen Situationen gelöst werden kann.
Efficient numerical approximation of the effective hamiltonian
Tuesday, 15.11.11, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Some Remarks on Huisken's Monotonicity
Tuesday, 15.11.11, 16:15-17:15, Raum 127, Eckerstr. 1
Kooperatives Lernen im Mathematikunterricht
Tuesday, 15.11.11, 16:30-17:30, Raum 404, Eckerstr. 1
Diagnostik im Mathematikunterricht vor dem Hintergrund einer sich ändernden Schullandschaft
Tuesday, 15.11.11, 17:30-18:30, Raum 404, Eckerstr. 1
Arithmetik zum Anfassen
Tuesday, 15.11.11, 18:30-19:30, Raum 404, Eckerstr. 1
Themenorientiertes Sachrechnen am Beispiel Fahrrad - Anmerkungen zu didaktischen Entwicklungen in der Schulmathematik
Tuesday, 15.11.11, 19:30-20:30, Raum 404, Eckerstr. 1
Die Automorphismusgruppe des Urysohnraums
Wednesday, 16.11.11, 16:15-17:15, Raum 404, Eckerstr. 1
Infinite matrices, schur-weyl duality and koszulity
Thursday, 17.11.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Koszulity or Koszul duality is an important and useful notion introduced by Beilinson, Ginzburg\nand S¨orgel which is based on the Koszul complex. In fact, it can be illustrated on the example of Jordan\nnormal form, and I will try to do this in the talk. Recently, Serganova, Dan-Cohen and I discovered that the\ncategory of tensor representations of the algebra of infinite, but finitary, matrices satisfies Koszul duality.\nThis category of tensor representations is defined by “sending Schur-Weyl duality to infinity”, so eventually\nthis establishes a link between Koszul duality and Schur-Weyl duality.\n
Computing descendants in symplectic field theory
Monday, 21.11.11, 16:00-17:00, Raum 404, Eckerstr. 1
Symplectic field theory (SFT) assigns to each symplectomorphism (of a closed symplectic manifold) an infinite-dimensional Hamiltonian system with an infinite number of symmetries. While the latter are obtained using descendants, for Hamiltonian symplectomorphisms this leads to the well-known integrable hierarchies of Gromov-Witten theory. In joint work with P. Rossi we study the algebraic structure of descendants, both to find richer geometrical invariants and to answer the question of integrability for general symplectomorphisms.
Existenz schwacher Lösungen für instationäre Herschel-Bulkley Fluide unter Verwendung der Lipschitz-Truncation Methode
Tuesday, 22.11.11, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds
Tuesday, 22.11.11, 16:15-17:15, Raum 127, Eckerstr. 1
Complement to the colloquium talk on asymptotic studies of planar Brownian motion
Tuesday, 22.11.11, 16:15-17:15, Hörsaal II, Albertstr. 23b
I shall discuss in some detail both the asymptotics (in law) of windings around N points, and the complexity of the entanglement word, for two points.
Bruchrechnung zeitgemäß unterrcihten - Status quo und Trends in der Didaktik der Bruchrechnung
Tuesday, 22.11.11, 19:30-20:30, Hörsaal II, Albertstr. 23b
Die Bruchrechnung bildet traditionell einen der Schwerpunkte im Mathematikunterricht der 6. Jahrgangsstufe. Ist sie noch zeitgemäß? Wenn ja, wie kann sie dann sinnvoll gestaltet werden? Empirische mathematikdidaktische Studien lieferten in den letzten Jahren zahlreiche Erkenntnisse über Lehr-Lern-Prozesse zum Arbeiten mit gemeinen Brüchen und Dezimalbrüchen. Auf dieser Basis lassen sich sinnvolle Unterrichtskonzepte entwickeln und mit der Entwicklung von Grundvorstellung sowie der Förderung des Zahlenblicks auch Leitlinien für einen zeitgemäßen Unterricht formulieren.
Fp-affine recurrent double sequences over F-q are p-automatic.
Wednesday, 23.11.11, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 24.11.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Thursday, 24.11.11, 17:00-18:00, Hörsaal II, Albertstr. 23b
Compact moduli spaces of surfaces via MMP
Friday, 25.11.11, 10:00-11:00, Raum 404, Eckerstr. 1
Polynomial Growth Harmonic Functions in Metric Spaces
Tuesday, 29.11.11, 16:15-17:15, Raum 127, Eckerstr. 1
Colding-Minicozzi solved Yau's conjecture that the dimension of the linear space of polynomial growth harmonic functions on Riemannian manifolds with nonnegative Ricci curvature is finite. The technique relies on the volume growth property of the manifold and the mean value inequality of harmonic functions. The Nash-Moser iteration gives the required properties of harmonic functions even in the metric (nonsmooth) setting. Alexandrov spaces are natural metric spaces with sectional curvature bounded below. Recently, the first and second order analysis are well understood in some aspects. Some results of harmonic functions on Alexandrov spaces will be discussed. Then we apply the Alexandrov geometry to develop the analysis on the graph with nonnegative sectional curvature.
Reducts of Ramsey structures: the canonical approach
Wednesday, 30.11.11, 16:15-17:15, Raum 404, Eckerstr. 1