Alterierungen nach de Jong
Wednesday, 22.10.08, 14:15-15:15, Raum 403, Eckerstr. 1
Triangulated categories of mixed motives
Monday, 27.10.08, 11:15-12:15, Raum 404, Eckerstr. 1
Lecture 1 will deal with the explicit construction\nof the categories DM(S) for a general scheme S\nand its basic properties.
Vollständige Zylinder ohne konjugierte Punkte
Monday, 27.10.08, 16:15-17:15, Raum 404, Eckerstr. 1
Localization of mixed motives
Tuesday, 28.10.08, 11:15-12:15, Raum 403, Eckerstr. 1
Lecture 2 will be about localization in DM(S):\nif i : Z --> S is a closed immersion with complementary\nopen immersion j : U --> S, for any object M of DM(S),\nthere is a distinguished triangle of shape\nj!j^*(M) --> M --> ii^(M) --> j_!j^*(M)[1]\n(this holds with rational coefficients in general,\nand with integral coefficients if S and Z are smooth\nover a common base). Using Ayoub's thesis, localization\nallows to produce the six Grothendieck operations\non the categories DM(X) (with rational coefficients).\nThe aim of the talk is to give an idea of the proof\nof localization (which is quite tricky).\nEven if I suspect there won't be enough time to\nmention this during the talk, I mention here some other\nnice consequences: localization property also implies that\nrational motivic cohomology of regular schemes defined\nfrom DM coincide with motivic cohomology in the sense\nof Beilinson (using Adams operations on algebraic K-theory),\nby reducing to the case of a field, which is already known.\nThis and a version of Riemann-Roch in turns implies an absolute\npurity theorem in DM. These consequences have their\nrole to play in lecture 3.
Diskretisierung inkompressibler generalisierter Newtonscher Fluide
Tuesday, 28.10.08, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
l-adic completion of etale motives
Wednesday, 29.10.08, 14:15-15:15, Raum 403, Eckerstr. 1
Lectures 3 will be about the étale version DMet(X)\nof DM(X), which has nice properties (at least for schemes X\nwhich are of finite type over a an excellent regular scheme\nof Krull dimension less or equal to 1):\n- it coincides with DM(X) up to torsion\n- localization is true in DMet(X) (even with integral\ncoefficients)\n- the absolute purity theorem is true in DMet(X)\n- the torsion part of DMet(X) is essentially\nthe category of torsion l-adic sheaves\n- using the l-adic completion in DMet(X), one constructs\na nice l-adic realization from the rational version of DM(X)\ninto smooth Ql-sheaves which commutes with the\nGrothendieck six operations.
Studying brain connectivity with EEG/MEG using time delays
Friday, 31.10.08, 11:15-12:15, Raum 404, Eckerstr. 1
Studying brain connectivity form EEG/MEG data is\nextremely difficult because it is impossible to uniquely solve the 'inverse problem', i.e. to calculate the brain activity at specified brain locations from the measurement of external electric potentials and magnetic fields.\n\nAs a consequence, an estimate of brain activity corresponds to an incomplete demixing of channel signals. It is then unavoidable that different brain sites appear to be connected even if all brain sources were truly independent.\n\n\nTo overcome this problem we suggest to exploit the fact that the mapping of brain sources to external channels is essentially instantaneous while brain interactions involve measurable time delays. In this talk I will give an overview of our recent work based on this concept.\n\n\nSpecifically, this talk has the topics:\n\na) Role of imaginary part of cross-spectra/coherency for studying true interaction as opposed to 'artefacts of volume conduction'.\n\n\nb) Separation of interacting subsystems, which are mutually independent, using "Pairwise Interacting Sourse Analysis" (PISA).\n\n\nc) Localization of interactions.\n\n\nd) Estimating the direction of information flux robust to correlated and colored background noise.
Singularitäten von Shimura-Varietäten in positiver Charakteristik
Friday, 31.10.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
Existenz von Minimax-Geodätischen
Monday, 3.11.08, 16:15-17:15, Raum 404, Eckerstr. 1
Geometrie und Analysis von Knotenenergien
Tuesday, 4.11.08, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Hundert Jahre Raumzeit - Simulationen und Visualisierungen in der speziellen Relativitätstheorie
Tuesday, 4.11.08, 19:30-20:30, Hörsaal II, Albertstr. 23b
Vor hundert Jahren hat Hermann Minkowski in einem berühmten Vortrag die Einheit von Raum und Zeit postuliert. Aus diesem Anlass steht das Thema Raumzeit im Mittelpunkt dieses Doppel-vortrags, insbesondere geht es um relativistische Effekte. Wie sieht ein ruhender Beobachter ein sehr schnell fliegendes Objekt? Wie sieht ein sehr schnell fliegender Beobachter ein ruhendes Objekt? Das soll mit Hilfe von Computersimulationen vorgeführt werden. Einen Eindruck davon kann man sich auf der Webseite http://www.tempolimit-lichtgeschwindigkeit.de machen. \nErgänzt wird dieser Vortrag durch mathematikdidaktische Überlegungen: Kann man die Lorentztransformation abbildungsgeometrisch deuten? Wie lassen sich die Effekte, insbesondere die Zeitdilatation und die Längenkontraktion sowie das Zwillingsparadoxon mit Hilfe dynamischer Geometrie-Software visualisieren? Welche schulmathematischen Voraussetzungen sind dabei notwendig? Wo kann man dies im Mathe- bzw. Physikunterricht sinnvoll umsetzen? \n
Hundert Jahre Raumzeit - Simulationen und Visualisierungen in der speziellen Relativitätstheorie
Tuesday, 4.11.08, 19:30-20:30, Hörsaal II, Albertstr. 23b
Vor hundert Jahren hat Hermann Minkowski in einem berühmten Vortrag die Einheit von Raum und Zeit postuliert. Aus diesem Anlass steht das Thema Raumzeit im Mittelpunkt dieses Dop¬pel-vortrags, insbesondere geht es um relativistische Effekte. Wie sieht ein ruhender Beobachter ein sehr schnell fliegendes Objekt? Wie sieht ein sehr schnell fliegender Beobachter ein ruhen¬des Objekt? Das soll mit Hilfe von Computersimulationen vorgeführt werden. Einen Eindruck davon kann man sich auf der Webseite http://www.tempolimit-lichtgeschwindigkeit.de machen. \nErgänzt wird dieser Vortrag durch mathematikdidaktische Überlegungen: Kann man die Lorentztransformation abbildungsgeometrisch deuten? Wie lassen sich die Effekte, insbesondere die Zeitdilatation und die Längenkontraktion sowie das Zwillingsparadoxon mit Hilfe dynamischer Geometrie-Software visualisieren? Welche schulmathematischen Voraussetzungen sind dabei notwendig? Wo kann man dies im Mathe- bzw. Physikunterricht sinnvoll umsetzen? \n
Friday, 7.11.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
The implied market price of weather risk
Friday, 14.11.08, 11:15-12:15, Raum 404, Eckerstr. 1
Linear Algebraic Groups and A^1-Homotopy Theory
Friday, 14.11.08, 11:15-12:15, Raum 403, Eckerstr. 1
In this talk, I will explain how elementary matrix factorizations lead to a computation of the A^1-homotopy groups of linear algebraic groups and homogeneous spaces. Besides a better understanding of A^1-homotopy groups, these results have implications for questions on stabilization of group homology and algebraic K-theory. I will try my very best to make this talk locally accessible to anybody. There will be a couple of follow-up talks concerning model categories in general and A^1-homotopy in particular which will provide a more detailed introduction to this subject.
Friday, 14.11.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
Der Laplace-Operator auf einer Familie mit Kegelsingularität
Monday, 17.11.08, 16:15-17:15, Raum 404, Eckerstr. 1
Locally regulated spatial population model
Thursday, 20.11.08, 11:15-12:15, Raum 404, Eckerstr. 1
The tree length of an evolving coalescent
Thursday, 20.11.08, 11:15-12:15, Raum 404, Eckerstr. 1
An Introduction to Model Categories
Friday, 21.11.08, 11:15-12:15, Raum 403, Eckerstr. 1
Cancelled. This talk will be rescheduled. I apologize for any inconveniences.
Randwertprobleme für elliptische Operatoren erster Ordnung
Friday, 21.11.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
konvexe Integration I\n
Monday, 24.11.08, 16:15-17:15, Raum 404, Eckerstr. 1
Friday, 28.11.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
konvexe Integration II
Monday, 1.12.08, 16:15-17:15, Raum 404, Eckerstr. 1
The tree length of an evolving coalescent
Friday, 5.12.08, 11:15-12:15, Raum 404, Eckerstr. 1
tba
Friday, 5.12.08, 11:15-12:15, Raum 403, Eckerstr. 1
Normal and Other Limit Theorems in Stochastic Geometry
Friday, 5.12.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
Der Satz von Nash-Kuiper
Monday, 8.12.08, 16:15-17:15, Raum 404, Eckerstr. 1
Optimale Stopp-Probleme bei Modellunsicherheit
Friday, 12.12.08, 11:15-12:15, Raum 404, Eckerstr. 1
We develop a theory of robust optimal stopping problems with multiple priors. Applications are given for problems in Operations Research, Microeconomics, and Finance.
Garben auf affinen Schubert Varietäten, modulare Darstellungen und Lusztig's Vermutung
Friday, 12.12.08, 11:15-12:15, Raum 403, Eckerstr. 1
George Lusztig stellte 1980 eine Vermutung über die Charaktere einfacher Darstellungen von algebraischen Gruppen über einem Körper positiver Charakteristik auf und formulierte 1990 ein Programm, das zu einem Beweis in fast allen Charakteristiken führte. Die Ausnahmecharakteristiken sind jedoch bis heute unbekannt. Im Vortrag möchte ich einen neuen, deutlich einfacheren Beweis vorstellen, der einen Teil der Vermutung für alle relevanten Charakteristiken liefert und zudem eine obere Grenze für die Ausnahmen. Das wesentliche Hilfsmittel hierzu ist die Theorie von Garben auf Bruhatgraphen.
Optimale Stopp-Probleme bei Modellunsicherheit
Friday, 12.12.08, 11:15-12:15, Raum 404, Eckerstr. 1
We develop a theory of robust optimal stopping problems with multiple priors. Applications are given for problems in Operations Research, Microeconomics, and Finance.
Symmetrie als Leitfaden in der komplexen Geometrie
Friday, 12.12.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
Euler-Gleichungen und konvexe Integration (nach De Lellis/Szekelyhidi Jr.)
Monday, 15.12.08, 16:15-17:15, Raum 404, Eckerstr. 1
An Urn Model for Taxonomic Identification of Procaryotes
Friday, 19.12.08, 11:15-12:15, Raum 404, Eckerstr. 1
Stable couples on elliptic K3 surfaces
Friday, 19.12.08, 11:15-12:15, Raum 403, Eckerstr. 1
We consider a smooth K3 elliptic surface S with a section and we investigate the behaviour of moduli spaces of pairs on it. For a suitable choice of the framing, we get a finite family of moduli spaces related by wall crossing phenomena giving rise to birational maps. In a particular case, this allows to recover an isomorphism (described by Friedman with different techniques) between a moduli space of rank two coherent sheaves on S and the Hilbert scheme.
Friday, 19.12.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
A point-set model for noncommutative geometry
Monday, 22.12.08, 16:15-17:15, Raum 404, Eckerstr. 1
Friday, 26.12.08, 17:00-18:00, Hörsaal II, Albertstr. 23b
Friday, 2.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
Rational curves and asymptotic base locus of some divisors
Friday, 9.1.09, 11:15-12:15, Raum 403, Eckerstr. 1
I will present two joint works with Gianluca Pacienza and also Sébastien Boucksom for one of them.\n\nThe geometry of the rational curves on a variety is a fundamental tool for the classification of complex projective varieties.\nRecently, two notions of base locus attached to divisors/complex line bundles have been discovered and studied by Nakayama, Boucksom, Nakamaye and others.\nOne of them, the non-nef locus, is as suggest his name, empty if and only if the divisor (or the first chern of the line bundle) is nef. That is, it has non-negative instersection on every curve in the variety. We will show how this base loci are related to the geometry of rational\ncurves on a variety. Namely, I will give a survey of the proof of the two following statements:\nIf X is a projective variety with nef anticanonical bundle (dual of the canonical bundle) then every non-nef base locus of a divisor is uniruled. It is a generalization of a result of Takayama who proved this result in the case of varieties with (numerically) trivial anticanonical bundle.\n\nIf X is big then X is rationnally connected modulo the non-nef locus of -KX : two points of X are connected by a chain of curves which are either rational or in the non-nef locus of -KX . This a generalization of the well-known result of the rational connectedness of Fano varieties. The proof uses technics introduced by Zhang and\nHacon-McKernan for the proof of the rational connectedness of weak log Fano varieties and the proof of the Shokurov conjecture.
Rationale Kurven auf algebraischen Varietäten
Friday, 9.1.09, 16:30-17:30, Hörsaal II, Albertstr. 23b
On some applications of bi-invariant metrics on solvmanifolds
Monday, 12.1.09, 16:15-17:15, Raum 404, Eckerstr. 1
Theory and Numerics for the Navier-Stokes-Korteweg Equations and the Associated Sharp Interface Model
Tuesday, 13.1.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Del Pezzo surfaces, unprojections, and Calabi threefolds
Friday, 16.1.09, 11:15-12:15, Raum 403, Eckerstr. 1
A geometric transition between two Calabi-Yau threefolds is the composition of a degeneration a contraction and a smoothing. In my talk I would like to describe geometric transitions for which the contraction is an unprojection contracting a del Pezzo surface to a point. I shall show how using such constructions one can obtain new families of well described Calabi-Yau threefolds.
Billiards und p-adische Differentialgleichungen
Friday, 16.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
Kompetenzen und Leitideen im Mathematikunterricht der Oberstufe
Tuesday, 20.1.09, 19:30-20:30, Hörsaal II, Albertstr. 23b
Explicit Beilinson-Bernstein theorem for arithmetic D-modules
Friday, 23.1.09, 11:15-12:15, Raum 403, Eckerstr. 1
In the years 80's, Beilinson-Bernstein and Brylinski-Kashiwara proved that there is an equivalence of categories between the D-modules on the flag variety of a semi-simple algebraic group over the field of complex numbers and modules over the Lie algebra of the group, with some condition on the action of the center of the envelopping algebra. This result lead to important results in the theory of Lie Algebra representation. We will explain here an arithmetic version of this equivalence of category by considering flag varieties in car. p>0 and arithmetic D-modules of Berthelot attached to these varieties.
A monolithic FEM solver for fluid structure interaction in ALE formulation
Friday, 23.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
A monolithic algorithm to solve the problem of time dependent interaction\nbetween an incompressible, possibly non-Newtonian, viscous fluid and an\nelastic\nsolid is investigated. The continuous formulation of the problem and its\ndiscretization is done in a monolithic way, treating the problem as\none continuum and discretized by the finite elements method. The\nresulting nonlinear algebraic system of equations is solved\nby an approximate Newton method with coupled geometric multigrid\nlinear solver for solving the linear subproblems. We discuss\npossible efficient strategies of setting up the resulting system and\nits solution.\n
Aubry-Mather-Theorie fuer Lorentzmannigfaltigkeiten
Monday, 26.1.09, 16:15-17:15, Raum 404, Eckerstr. 1
A Local Discontinuous Galerkin Discretization for Shallow Incompressible Flows with Free Surface
Tuesday, 27.1.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Wednesday, 28.1.09, 09:15-10:15, Raum 404, Eckerstr. 1
Friday, 30.1.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
A generic stabilization approach for higher order Discontinuous Galerkin methods for convection dominated problems
Tuesday, 3.2.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
In this talk a stabilized Discontinuous Galerkin (DG) method for\nhyperbolic and convection dominated problems is presented.\nA detailed description of the scheme is presented as well as\na study of several test cases in two and three space dimensions on both unstructured and cartesian grids.
Wenn da ableiten steht, musste nur die Hochzahl vorne dran schreiben und oben eins weniger machen. - Oder: Was bleibt eigentlich vom Analysisunterricht?
Tuesday, 3.2.09, 19:30-20:30, Hörsaal II, Albertstr. 23b
Das Thema Differentialrechnung birgt viele fundamentale Ideen der Mathematik, die häufig als solche gar nicht erkannt werden. Die Gründe hierfür sind so vielfältig wie die einzelnen Lernbiografien aller am Mathematikunterricht Beteiligten. Es ist zu beobachten, dass die mathematischen Konzepte und Vorstellungen meist nur bruchstückhaft ausgebildet werden. \nAnhand einiger Unterrichtsbeispiele werden Möglichkeiten gezeigt, vielfältige Begegnungen mit der Differentialrechnung zu arrangieren, um so die Ausbildung der Konzepte zu unterstützen. Die Teilnehmer experimentieren im zweiten Teil der Veranstaltung mit den mitgebrachten Unterrichtsmaterialien und Exponaten.\n
Designs für Dosisfindungsstudien
Friday, 6.2.09, 11:15-12:15, Raum 404, Eckerstr. 1
Understanding and properly characterizing the dose response relationship is a fundamental step in the investigation of a compound, be it a new herbicide or fertilizer, a olecular entity, an environmental toxin, or an industrial chemical.\nIn this talk we investigate the problem of deriving effcient designs for the estimation of target doses in the context of clinical dose finding. We propose methods to determine the appropriate number and actual levels of the doses to be administered to patients, as well as their relative sample size allocations.\nIt is demonstrated that the designs derived for a fixed model are rather sensitive with respect to this assumption and robust optimal designs are constructed, which take into account a set of potential dose response profiles within classes of models commonly used in drug development dose finding practice.
"Wie oft klickt die Ratsche?" Über das Wechselspiel von deterministischer und stochastischer Dynamik in einem populationsgenetischen Modell.
Friday, 6.2.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
"Muller's ratchet" ist ein einfaches populationsgenetisches Modell:\nentlang jeder Ahnenlinie in einer haploiden Population, deren Größe über\ndie Generationen als konstant angenommen wird, werden schädliche\nMutationen akkumuliert. Je weniger solche Mutationen ein Individuum\nträgt, um so eher kommt es bei der Reproduktion zum Zug. Durch diesen\nSelektionsprozess kommt es entlang der überlebenden Linien zu einer\nkleineren Akkumulationsrate der Mutationen. Die Frage, wie diese Rate\nvon den Modellparametern abhängt, hat sich über Jahrzehnte als\nwiderspenstig erwiesen. Einen Teilaspekt dieser Frage werden wir im\nVortrag diskutieren und Lösungsansätze hierzu aufzeigen.\n\n
Functions minimizing an elliptic integral
Monday, 9.2.09, 16:15-17:15, Raum 404, Eckerstr. 1
Local projection stabilization for convection diffusion and flow problems
Tuesday, 10.2.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
A Discontinous Galerkin Method for 3D Shallow Water Equations
Tuesday, 10.2.09, 15:45-16:45, Raum 226, Hermann-Herder-Str. 10
Friday, 13.2.09, 17:00-18:00, Hörsaal II, Albertstr. 23b
A generic stabilization approach for higher order Discontinuous Galerkin methods for convection dominated problems
Tuesday, 17.2.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
In this talk a stabilized Discontinuous Galerkin (DG) method for hyperbolic and convection dominated problems is presented. A detailed description of the scheme is presented as well as a study of several test cases in two and three space dimensions on both unstructured and cartesian grids.
A convergence rate for finite volume schemes on Riemannian manifolds
Tuesday, 3.3.09, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
On the Willmore functional
Wednesday, 4.3.09, 14:00-15:00, Raum 127, Eckerstr. 1
This talk will be oriented towards establishing an alternate framework for the study of Willmore surfaces. In the first part of the presentation, I will review basic definitions and results associated with the Willmore energy functional. The second part of the talk will be devoted to stating some results recently obtained, in particular "conservation laws" satisfied by Willmore immersions. In the last part of the presentation, I will tie together the results of the first and of the second parts, by deriving the newly-obtained "conformal Willmore equation". Several corollaries pertaining to Palais-Smale sequences will be examined. This is joint work with Tristan Rivière.\n
A constrained Willmore functional arising in nonlinear elasticity
Wednesday, 4.3.09, 16:00-17:00, Raum 127, Eckerstr. 1
On the corners of the mean action in codimension one
Monday, 9.3.09, 16:15-17:15, Raum 404, Eckerstr. 1
asdf
Tuesday, 24.3.09, 18:00-19:00, Raum 201, Hermann-Herder-Str. 10