Donnerstag, 2.11.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Walks, Difference Equations and Elliptic Curves
Freitag, 3.11.17, 10:15-11:15, Hörsaal FRIAS, Albertsstr. 19
In the recent years, the nature of the generating series of walks in\nthe quarter plane has attracted the attention of many authors in\ncombinatorics and probability. The main questions are: are they\nalgebraic, holonomic (solutions of linear differential equations) or at\nleast hyperalgebraic (solutions of algebraic differential equations)? In\nthis talk, we will show how the nature of the generating function can\nbe approached via the study of a discrete functional equation over a\ncurve E, of genus zero or one. In the first case, the functional\nequation corresponds to a so called q-difference equation and all the\nrelated generating series are differentially transcendental. For the\ngenus one case, the dynamic of the functional equation corresponds to\nthe addition by a given point P of the elliptic curve E. In that\nsituation, one can relate the nature of the generating series to the\nfact that the point P is of torsion or not.\n This is a collaboration with T. Dreyfus (Irma, Strasbourg), J. Roques\n(Institut Fourier, Grenoble) and M.F. Singer (NCSU, Raleigh).
Vorträge zum 30-jährigen Bestehen des FDM-Seminars
Freitag, 3.11.17, 13:30-14:30, Raum 404, Eckerstraße 1, Freiburg i. Br.
Programm:\n\n13:30 Einführung mit Beiträgen von Rektor Prof. Dr. Hans-Jochen Schiewer und dem Mit-Gründer des FDM, Prof. Dr. Josef Honerkamp\n\n14:00 Prof. Dr. Leonhard Held (University of Zurich): Building a Statistical Model: The Endemic-Epidemic Modelling Framework\n\n15:00 Kaffee\n\n15:30 Prof. Dr. Rainer Dahlhaus (Heidelberg University): Cointegration and Phase Synchronization: Bridging Two Theories\n\n16:30 Prof. Dr. Josef Teichmann (ETH Zürich): Affine processes in mathematical Finance\n\n17:30 Schluss\n\n
Deformation problems on Calabi-Yau manifolds, Picard-Fuchs equations and potential functions
Montag, 6.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
In my talk I will explain various results concerning Calabi-Yau threefolds and geometric objects on the Calabi-Yau variety, e. g. a divisor, a curve or a coherent sheaf. I will discuss their deformation theory and the connection to Picard-Fuchs equations and potential functions. These are special holomorphic functions describing the obstructions of a deformation problem.
Bifurcation of the compressible Taylor vortex
Dienstag, 7.11.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The inverse mean curvature flow and the Riemannian Penrose inequality
Dienstag, 7.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
\(\bkappa\)-trees and the sup game
Mittwoch, 8.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
We use the so-called sup game to obtain some results about\nthe relationships between dominating \(\bkappa\)-sequences and Cohen\n\(\bkappa\)-sequences. In particular, we improve a couple of results\nconcerning the amoeba for \(\bkappa\)-Sacks forcing and \(\bkappa\)-Laver forcing\nthat I presented in some previous seminar-talk.\n
The algebraic topology of p-adic Lie groups
Donnerstag, 9.11.17, 10:15-11:15, Raum 403, Eckerstr. 1
Lazard proved that the cohomology of compact p-adic Lie groups satisfies a version of Poincare duality. This indicates an analogy between p-adic Lie groups and real manifolds. I will explain some results which develop this analogy further.
Donnerstag, 9.11.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
From elementary number theory to string theory and back again
Freitag, 10.11.17, 10:15-11:15, Hörsaal FRIAS, Albertstr. 19
I will describe some surprising interactions between number theory, algebraic geometry and mirror symmetry that have appeared in my recent work with Mircea Mustata and Chenyang Xu and that have led to a solution of Veys' 1999 conjecture on poles of maximal order of Igusa zeta functions. The talk will be aimed at a general audience and will emphasize some key ideas from each of the fields involved rather than the technical aspects of the proof.
The extended ν invariant of Joyce manifolds
Montag, 13.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
The Crowley-Nordström ν invariant and its extension ν¯ is an invariant of compact G2 manifolds. It has been computed for several kinds of connected sums by Crowley, Nordström and Goette (see next talk), in this talk we discuss strategies of computations for Joyce manifolds.
Contact and Adhesion of Fractal Interfaces
Dienstag, 14.11.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The inverse mean curvature flow and the Riemannian Penrose inequality
Dienstag, 14.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
Modular representations of sl_n with two-row nilpotent p-character
Mittwoch, 15.11.17, 10:45-11:45, Hörsaal FRIAS
We will study the category of modular representations of the\nspecial linear Lie algebra with a central p-character given by a\nnilpotent whose Jordan type is a two-row partition. Building on work of\nCautis and Kamnitzer, we construct a categorification of the affine\ntangle calculus using these categories; the main technical tool is a\ngeometric localization-type result of Bezrukavnikov, Mirkovic and\nRumynin. Using this, we give combinatorial dimension formulae for the\nirreducible modules, composition multiplicities of the simples in the\nbaby Vermas, and a description of the Ext spaces. This Ext algebra is an\n"annular" analogues of Khovanov's arc algebra, and can be used to give\nan extension of Khovanov homology to links in the annulus. This is joint\nwith Rina Anno and David Yang.
Praesentation der Masterarbeit
Mittwoch, 15.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
Lokal modulare additive Redukte von den komplexen Zahlen
Mittwoch, 15.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
Vektorräume sind modulare Strukturen, denn es gilt die Dimensionsformel. Diesen Begriff der Modularität können wir auf streng minimale Strukturen verallgemeinern, indem wir mit dem algebraischen Abschluss und dem dadurch gegebenen Dimensionsbegriff arbeiten. Eine streng minimale Struktur ist lokal modular (oder monobasiert), wenn die Dimensionsformel für alle endlich erzeugten algebraisch abgeschlossenen Mengen gilt, deren Durchschnitt positive Dimension hat.\nMarker und Pillay zeigten im Jahre 1990, dass in jedem nicht-monobasierten additiven Redukt der komplexen Zahlen die Muliplikation definierbar ist. Der Beweis erfolgt in zwei Teilen. Im ersten Teil wird mit Hilfe der Gruppenkonfiguration von Hrushovski ein unendlicher Körper im Redukt interpretiert. Wie man dann die ursprüngliche Multiplikation des Körpers im Redukt definieren kann, wird im zweiten Teil gezeigt. Im Vortrag wird der erste Teil des Beweises präsentiert und die Idee des zweiten Teils erklärt.
Donnerstag, 16.11.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Functorial test modules
Freitag, 17.11.17, 10:15-11:15, Hörsaal FRIAS, Albertstr. 19
In my talk I will report on joint work with Manuel Blickle. I will explain how one can generalize the definition of test ideals \btau to so-called Cartier modules in a functorial way. We obtain several transformation rules with respect to f^! and f_* for various classes of morphisms f: X \bto Y, e.g. for f smooth one has an isomorphism f^! \btau = \btau f^!. Part of the reason for working in this generality is that one has an equivalence with constructible etale p-torsion sheaves up to nilpotence of Cartier modules and these results further support the idea that the test module construction relates to etale nearby cycles similarly to the complex situation where multiplier ideals relate to complex nearby cycles.
Mini-Workshop on "Singular Variational Problems"
Sonntag, 19.11.17, 10:00-11:00, Raum 226, Hermann-Herder-Str. 10
Luigi Berselli (U Pisa): Time averages and Reynolds equations for dissipative equations; \nGiuseppe Buttazzo (U Pisa): Shape optimization under uncertainty;\nPatrick Dondl (U Freiburg): A phase field model for Willmore’s energy with topological constraint;\nMichael Ruzicka (U Freiburg): On a Clement type operator; \nSoeren Bartels (U Freiburg): Semi-implicit time stepping for p-Laplace equations\n
The extended \(\bnu\) invariant of exotic extra twisted connected sums
Montag, 20.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
There is nowadays a large supply of compact manifolds of special holonomy \(G_2\). The Crowley-Nordström \(\bnu\) invariant and its extension \(\bbar\bnu\) help to distinguish different connected components of the \(G_2\)-moduli space on a given manifold \(M\). We already know some manifolds \(M\) whose \(G_2\)-moduli space has at least 7 different connected components.\nHowever all examples of \(G_2\)-manifolds investigated so far turn out to be topologically \(G_2\)-nullbordant, that is, their \(\bnu\)-invariant is divisible by 3.\n\nIn this talk, we will consider Nordström's extra twisted connected sum construction with at least one \(\bmathbb Z/3\)- or \(\bmathbb Z/4\)-block. Although \(\bbar\bnu(M)\) is defined in terms of \(\beta\)-invariants, we will show that in the end it can be computed explicitly for these examples using elementary hyperbolic geometry.
The inverse mean curvature flow and the Riemannian Penrose inequality from Husiken and Imanen.
Dienstag, 21.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
\(\bkappa\)-trees and the sup game, part 2
Mittwoch, 22.11.17, 16:00-17:00, Raum 404, Eckerstr. 1
This is the continuation of the talk of November 8, 2017.
Donnerstag, 23.11.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Local systems in motivic homotopy theory
Freitag, 24.11.17, 10:15-11:15, Hörsaal FRIAS, Albertstr. 19
Local systems in motivic homotopy theory
Freitag, 24.11.17, 10:15-11:15, Hörsaal FRIAS, Albertstr. 19
This talk is first devoted to explain how Voevodsky's theory of motivic complexes is built on, and provides, a natural notion of local system. Two key players involved here are homotopy sheaves and cycle modules, which are respectively the theoretical and concrete side of the same notion. The first part of the talk will recall these two notions and their fundamental link.\n The second part of the talk will move on relative motivic complexes. I will explain the construction of a natural t-structure, analogous to the perverse t-structure (but not realized to it!), obtained in collaboration with Bondarko along ideas of Ayoub. Besides describing some of its good properties, I will explain a program to compute its heart, in terms of cycle modules.\n If time allows, I will wander a little bit on the aimed tool motivating these technicalities: the delta-homotopy Leray spectral sequence.\n
On detecting changes in the jumps of arbitrary size of a time-continuous stochastic process
Freitag, 24.11.17, 12:00-13:00, Raum 404, Eckerstr. 1
An Ito semimartingale is a superposition of a roughly fluctuating Brownian part and a pure jump process. Therefore, it is a very challenging task to disentangle the small jumps of the process from increments of the continuous part. We solve this problem by deriving a statistical procedure for inference on the general jump behaviour of an Ito semimartingale. Finally, we apply this technique to detect abrupt and gradual changes in the jumps of the underlying process using bootstrap tests, where we also allow for local alternatives.
Detection and Estimation of Local Signals
Dienstag, 28.11.17, 12:00-13:00, Raum 404, Eckerstr. 1
I will discuss a general framework for detection of local signals, primarily defined\nby change-points, in sequences of data. Changes can occur continuously, e.g., a\nchange in the slope of a regression line, or discontinuously, e.g., a jump in the\nlevel of a process. I will focus on the problem of segmentation of independent\nnormal observations according to changes in the mean. Results will be illustrated\nby simulations and applications to copy number changes and to historical weather\npatterns. Confidence regions for the change- points and some difficulties associated\nwith dependent observations will also be discussed. Aspects of this research involve\ncollaboration with Fang Xiao, Li Jian, Liu Yi, Nancy Zhang, Benjamin Yakir and\nLi (Charlie) Xia.
Numerical homogenization by localized orthogonal decomposition and connections to the mathematical theory of homogenization
Dienstag, 28.11.17, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The inverse mean curvature flow and the Riemannian Penrose inequality from Husiken and Imanen.
Dienstag, 28.11.17, 16:15-17:15, Raum 404, Eckerstr. 1
Präsentation der Masterarbeit: Grunerts gerichteter Pseudoraum
Mittwoch, 29.11.17, 16:30-17:30, Raum 404, Eckerstr. 1
Grunerts gerichteter Pseudoraum
Mittwoch, 29.11.17, 16:30-17:30, Raum 404, Eckerstr. 1
In dem Vortrag werden wir \ndie Axiome des N-Pseudoraums und einige seiner Eigenschaften besprechen, \ndie Axiomatisierung des gerichteten Pseudoraums angeben, \nbesprechen, welche Eigenschaften einen 1-Typ über der leeren Menge eindeutig\nbestimmen, \nund die Unabhängigkeitsrelation besprechen.\n\n
Donnerstag, 30.11.17, 17:00-18:00, Hörsaal II, Albertstr. 23b