Donnerstag, 4.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Riemannian shape analysis
Montag, 8.1.18, 16:15-17:15, Raum 404, Eckerstr. 1
Shape analysis aims at a mathematical description and\nanalysis of geometric data such as e.g. curves or surfaces. The key\nparadigm is to view these data as elements of an infinite-dimensional\nRiemannian manifold, which is called shape space. I will give an\nintroductory talk to shape spaces and Riemannian metrics thereon. Some\nmain results to be covered are (non-)degeneracy of the Riemannian path\nlength functional and wellposedness of the geodesic equation.
Kac-Moody algebras and derived algebraic geometry
Dienstag, 9.1.18, 09:15-10:15, SR 119, Eckerstr. 1
Kac-Moody algebras are usually used in physics to describe\nsome 2-dimensional conformal field theories. In this talk, we will introduce a new version of Kac-Moody algebras supposed to describe some physical phenomenons in higher dimensions.\n\nThose new algebras are in fact Lie algebras up to homotopy and we will study them using tools from algebraic topology and derived algebraic geometry.
Ein Färbungssatz
Mittwoch, 10.1.18, 16:30-17:30, Raum 404, Eckerstr. 1
Sei \(k \bgeq 1\) eine natürliche Zahl. Gowers' Satz über eine Partition der Menge der \(k\)-wertigen Blöcke in endlich viele Teile sagt, dass in einem Teil der Partition eine gegen die Tetrisoperation abgeschlossene Unterhalbgruppe liegt. Die partiell definierte Gruppenoperation auf den Blöcken ist die stellenweise Addition, die auf hintereinanderliegenden Blöcken mit der Konkatenation übereinstimmt. Wir verallgemeinern Gowers' Satz, indem wir den Grundraum auf Blocksequenzen, deren Projektionen auf \(\bomega\) aus bestimmten selektiven Koidealen über \(\bomega\) stammen, einschränken. Diese neue Variante führt dazu, dass es in Forcingserweiterungen durch Gowers-Matet-Forcing erweiterte Ramseyräume gibt. Der Vortag wird sich auf die Beweisschritte ohne Forcing konzentrieren. \n
Adelic formal neighborhoods and chiral modules with support
Donnerstag, 11.1.18, 09:15-10:15, SR 119, Eckerstr. 1
In this talk I will explain how one can use Ind-Pro objects\nto consider the restriction to formal and punctured formal\nneighborhoods of a subvariety Z in a variety X. This restriction functor can then be applied to give a description of modules for a chiral algebra over X supported at Z in terms of modules for an associative algebra object over Z. This is work in progress.\n\n\n(no worries, the speaker will explain what a "chiral algebra" is...)
Donnerstag, 11.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Complete intersections in varieties with finite-dimensional motive
Freitag, 12.1.18, 09:30-10:30, Hörsaal II, Albertstr. 23b
We consider complete intersections inside a variety with finite-dimensional motive for which the Lefschetz standard conjecture B holds. We show how conditions on the (modified) niveau filtration on homology influence the Chow groups. This leads to a generalization of results of Voisin and Vial on injectivity of cycle class and Abel-Jacobi maps. Using a variant involving group actions, we obtain several new examples of complete intersections with finite-dimensional motive. This is joint work with Robert Laterveer and Chris Peters.
The generalized Franchetta conjecture for hyperkaehler varieties
Freitag, 12.1.18, 11:15-12:15, Hörsaal II, Albertstr. 23b
The generalized Franchetta conjecture as formulated by O’Grady is about algebraic cycles on the universal K3 surface. It is natural to consider a similar conjecture for algebraic cycles on universal families of hyperkaehler varieties. This has close ties to Beauville’s conjectural ``splitting property’’, and the Beauville-Voisin conjecture (stating that the Chow ring of a hyperkaehler variety has a certain subring injecting into cohomology). I will attempt to give an overview of these conjectures, and present some cases where they can be proven. This is joint work with Lie Fu, Mingmin Shen and Charles Vial.
Derivator Six Functor Formalisms
Freitag, 12.1.18, 14:45-15:45, Hörsaal II, Albertstr. 23b
Grothendieck, Verdier, and Deligne in the 60's observed that classical duality theorems like Poincaré, or Serre duality can be most elegantly expressed, and vastly generalized, by a formalism of the six functors. This makes essential use of derived categories. The latter are, however, not sufficient for the purpose of descent. Descent is essential to define equivariant (co)homology and for equivariant duality theorems, and more generally to extend six-functor-formalisms to stacks, which is very important in applications. The problem with (co)homological descent is that the ``glueing data'' has a higher-categorical nature. In this talk we explain how our theory of fibered derivators, based on the idea of derivator due to Grothendieck and Heller (will be explained as well !), solves the problem of (higher-categorical) descent in a way closely related to the classical theory of cohomological descent (due to Deligne in SGA4). However, it is, in contrast, completely self-dual, making it very suitable for the descent of six-functor-formalisms.
Stability of Ricci flow on singular spaces
Montag, 15.1.18, 16:15-17:15, Raum 404, Eckerstr. 1
We discuss recent results on the Ricci flow for spaces with incomplete edge singularities. In the special case of isolated cones we establish stability of the flow near Ricci flat metrics.
Dynamics of fronts in some singularly coupled Allen-Cahn equations
Dienstag, 16.1.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
When coupling the scalar Allen-Cahn model for phase separation with large scale linear fields, the dynamics of interfaces can be rather intriguing. We consider the one-dimensional situation and apply methods from spatial dynamics to identify and unfold singularities that complex motion even for a single interface. Specifically, we can imbed scalar singularities such as a butterfly catastrophe that yield accelerated and direction reversing fronts. In recent work we unfold a degenerate Takens-Bodganov point with additional oscillatory dynamics.
Fortsetzung des Vortrags vom 10.1.2018 über Färbungen
Mittwoch, 17.1.18, 16:30-17:30, Raum 404, Eckerstr. 1
INVERSE CURVATURE FLOWS AND GEOMETRIC INEQUALITIES
Donnerstag, 18.1.18, 16:00-17:00, Hörsaal II, Albertstr. 23b
In recent years curvature flows have played a crucial role in proving important geometric theorems. For instance, the Ricci flow lead to a proof of the Poincare conjecture, and the inverse mean curvature flow (IMCF) was crucial in the proof of the Riemannian Penrose inequality. In this talk we present further applications of the IMCF. First we review, how classical geometric inequalities, such as the Minkowski inequality for closed convex hypersurfaces, can be generalised to a wider class of hypersurfaces using curvature flows. Secondly, we present new estimates for a Willmore-type energy of hypersurfaces with boundary, satisfying a perpendicular Neumann-type condition on the unit sphere. The crucial ingredient is the IMCF with boundary conditions.
Homologie linearer Gruppen und die Vermutung von Quillen
Donnerstag, 18.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
Unlikely intersections between isogeny orbits and curves
Freitag, 19.1.18, 10:15-11:15, Hörsaal FRIAS, Albertsstr. 19
In the spirit of the Mordell-Lang conjecture, we consider the intersection of a curve in a family of abelian varieties with the images of a finite-rank subgroup of a fixed abelian variety A0 under all isogenies between A0 and some member of the family. After excluding certain degenerate cases, we can prove that this intersection is finite. This proves the so-called André-Pink-Zannier conjecture in the case of curves. We can even allow translates of the finite-rank subgroup by abelian subvarieties of controlled dimension if we strengthen the degeneracy hypotheses suitably. In my talk, I will try to explain the motivation for this problem and give an outline of the proof, which follows a strategy due to Pila-Zannier.
Chronological Age Determination for Forensic Applications using Random Forest Regression and DNA Methylation Analysis
Freitag, 19.1.18, 12:00-13:00, Raum 404, Eckerstr. 1
Over the last few years it became clear that additional information is hidden wi-\nthin epigenetic modifications of the DNA, and that especially DNA methylation\n(DNAm) could provide useful evidence to the criminal justice system. Within this\nproject, specific changes in DNAm levels upon age progression at selected loci were\nused to develop an objective scientific tool to determine the chronological age of\nan (unknown) individual. This information can be used to narrow down the list\nof suspects during criminal investigations or to determine the age of a person in\nother legal contexts such as human trafficking. A model for age prediction based\non whole blood samples, 13 selected age-dependent DNAm markers, and a ran-\ndom forest regression (RFR) approach was developed. The analysis of the DNAm\nwas performed using amplicon based massive parallel sequencing (MPS) and the\nRFR model created with the R package RandomForest. The performance of the\nmodel was evaluated using cross-validation for the training set and by indepen-\ndent analysis of an additional test set. Within the seminar, a short introduction\ninto the field of forensic (epi-)genetics, the marker selection and development of\nthe DNA methylation tool based on RFR and MPS as well as the results of the\nage-determination tool will be presented. Furthermore, the potential and (current)\nlimitations of the experimental and machine learning approach in respect to the\nimplementation into forensic investigations will be discussed. The here presented\nproject of the University of Amsterdam in cooperation with the Netherlands Fo-\nrensic Institute was funded by the NCTV grant of the Dutch Ministry of Security\nand Justice.
Crystal graphs and semicanonical functions for symmetrizable Cartan matrices
Freitag, 19.1.18, 14:00-15:00, Raum 404, Eckerstr. 1
In joint work with B. Leclerc and J. Schröer we propose a 1-Gorenstein algebra H, defined over an arbitrary field K, associated to the datum of a symmetrizable Cartan Matrix C, a symmetrizer D of C and an orientation Ω. The H-modules of finite projective dimension behave in many aspects like the modules over a hereditary algebra, and we can associate to H a kind of preprojective algebra Π. If we look, for K algebraically closed, at the varieties of representations of Π which admit a filtration by generalized simples, we find that the components of maximal dimension provide a realization of the crystal B(-∞) corresponding to C. For K being the complex numbers we can construct, following ideas of Lusztig, an algebra of constructible functions which contains a family of "semicanonical functions", which are naturally parametrized by the above mentioned components of maximal dimensions. Modulo a conjecture about the support of the functions in the "Serre ideal" those functions yield a semicanonical basis of the enveloping algebra U(n) of the positive part of the Kac-Moody Lie algebra g(C).
BPS-states and automorphic representations of exceptional groups
Freitag, 19.1.18, 15:45-16:45, Raum 404, Eckerstr. 1
Automorphic forms on exceptional Lie groups appear naturally in string theory compactifications. They manifest themselves as couplings in higher derivative corrections and in terms of generating functions of BPS-states. I will explain how to treat automorphic forms in the modern theory of automorphic representations, which can be directly connected to BPS-states in string theory. Various recent results, conjectures and open problems are outlined.
Twisted intertwining operators and nonabelian orbifold theories
Freitag, 19.1.18, 17:00-18:00, Raum 404, Eckerstr. 1
The study of two-dimensional conformal field theories can in fact be reduced to the study of intertwining operators. In particular, the study of orbifold conformal field theories corresponds to the study of twisted intertwining operators (intertwining operators among twisted modules). However, for more than twenty years, there was even no mathematical definition of twisted intertwining operators when the twisted modules involved are associated to non-commuting automorphisms of the vertex operator algebra. In this talk, I will discuss a recently introduced notion of twisted intertwining operator and the basic properties of such operators. I will also present the main conjecture on nonabelian orbifold theories in terms of these operators and discuss the applications.
On the algebraic approach to QFT
Montag, 22.1.18, 16:15-17:15, Raum 404, Eckerstr. 1
Residual-type a posteriori estimator for a quasi-static contact problem.
Dienstag, 23.1.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
tba
Mittwoch, 24.1.18, 16:30-17:30, Raum 404, Eckerstr. 1
The dp-rank of an abelian group
Mittwoch, 24.1.18, 16:30-17:30, Raum 404, Eckerstr. 1
Abstract: Abelian groups form an archetypical example of stable groups. Their model theory is well-understood and in fact, distinct degrees of stability can be easily described for abelian groups in terms of the lattice of definable subgroups. For instance, an abelian group is omega-stable if and only if it satisfies the descending chain condition on definable subgroups.\n\nIn this talk, I will characterise the notion of dp-rank, which originates in Shelah's work on NIP theories, for abelian groups. Furthermore, I will explain how to compute it explicitly. This is joint work with Yatir Halevi.\n\n
On the motivic Tamagawa number of number fields
Donnerstag, 25.1.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
The Tamagawa number of a linear algebraic group is a classical arithmetic invariant.\nIt was computed and related to special values of L-functions in the second half of the 20th century.\nIn 1990 Bloch and Kato proposed a Tamagawa number of a (certain kind of) motive, related it to special L-values of motives and stated a conjecture on their value in the spirit of the classical case. We will discuss motivic Tamagawa numbers for the (seemingly easiest) unknown case, namely the twisted motive of a number field. I will present precise formulas relating these two notions of Tamagawa numbers to one another and to Borel regulators.
Invariance of closed convex cones for stochastic partial differential equations
Donnerstag, 25.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
The goal of this talk is to clarify when a closed convex cone is invariant for a stochastic partial differential equation (SPDE) driven by a Wiener process and a Poisson random measure, and to provide conditions on the parameters of the SPDE, which are necessary and sufficient. As a particular example, we will show how the Heath-Jarrow-Morton-Musiela (HJMM) equation from Financial Mathematics, which models the evolution of interest rate curves, fits into the present SPDE setting. Moreover, we will apply our result about the invariance of closed convex cones in order to investigate when the HJMM equation produces nonnegative interest rate curves.\n\n
Invariance of closed convex cones for stochastic partial differential equations
Donnerstag, 25.1.18, 17:00-18:00, Hörsaal II, Albertstr. 23b
The goal of this talk is to clarify when a closed convex cone is\ninvariant for a stochastic partial differential equation (SPDE) driven\nby a Wiener process and a Poisson random measure, and to provide\nconditions on the parameters of the SPDE, which are necessary and\nsufficient. As a particular example, we will show how the\nHeath-Jarrow-Morton-Musiela (HJMM) equation from Financial Mathematics,\nwhich models the evolution of interest rate curves, fits into the\npresent SPDE setting. Moreover, we will apply our result about the\ninvariance of closed convex cones in order to investigate when the HJMM\nequation produces nonnegative interest rate curves.
The Koszul duality between D-modules and Omega-modules
Freitag, 26.1.18, 10:30-11:30, Hörsaal FRIAS, Albertstr. 19
Koszul duality between D-modules and Omega-modules (dg modules over the algebraic de Rham complex) has first been studied by Kapranov, and subsequently by various authors including Beilinson-Drinfeld and Positselski. In this talk, I will report on work in progress (joint with Dmitri Pavlov) on a refinement of Koszul duality. An application of this refinement is a presentation of the derived pushforward and pullback functors for D-modules which avoids the usual mixing of right and left adjoints.
Higher Order Elicitability
Freitag, 26.1.18, 12:00-13:00, Raum 404, Eckerstr. 1
Elicitability of a statistical functional means that it can be obtained as the minimizer of an expected loss function. Such a loss function leads to a natural way of forecast comparison or model selection, and allows for M-estimation and generalized regression.\n\nPrime examples of elicitable functionals are the mean or quantiles of a random variable. Independently, Weber (2006, Mathematical Finance) and Gneiting (2011, JASA) have shown that expected shortfall (ES), an important risk measure in banking and finance, is not elicitable. However, it turns out that ES is jointly elicitable with a certain quantile, that is, it is elicitable of second order.\n\nIn this talk, we present our results on higher order elicitability of ES and some other functionals, and we provide characterizations of the associated classes of consistent scoring functions. We illustrate the usefulness of scoring functions for forecast comparison.
Pollicott-Ruelle-Resonanzen
Montag, 29.1.18, 14:00-15:00, Bibliothek Angewandte Mathematik, R216, RZ, Hermann-Herder-Strasse 10
Pollicott-Ruelle-Resonanzen werden auch klassische Resonanzen genannt. Sie lassen sich definieren als Eigenwerte des erzeugenden Vektorfelds des geodätischen Flusses auf dem (ko)-Sphärenbündel einer geeigneten Riemannschen Mannigfaltigkeit, wobei das Vektorfeld als Operator auf einem sogenannten anisotropen Sobolevraum aufgefasst wird. Das Gegenstück zu klassischen Resonanzen sind Quantenresonanzen, d.h. die Eigenwerte des Laplace-Beltrami-Operators. Wir betrachten, zunächst anhand eines einfachen Beispiels, Resultate und Forschungsfragen zu der Beziehung zwischen klassischen und Quanten-Resonanzen und den zugehörigen Resonanzzuständen.
Hadamard states for quantum Abelian duality
Montag, 29.1.18, 16:15-17:15, Raum 404, Eckerstr. 1
Cohomological properties of OT manifolds
Dienstag, 30.1.18, 11:00-12:00, SR 119
Conical spherical metrics: Lecture I
Dienstag, 30.1.18, 13:00-14:00, SR 119, Eckerstr. 1
Cone spherical, flat and hyperbolic metrics are conformal metrics with constant curvature +1, 0 and −1, respectively, and with finitely many conical singularities on compact Riemann surfaces. The Gauss-Bonnet formula gives a natural necessary condition for the existence of such three kinds of metrics with prescribed conical singularities on compact Riemann surfaces. The condition is also sufficient for both flat and hyperbolic metrics. However, it is not the case for cone spherical metrics, whose existence has been an open problem over twenty years.
Gradient Flow for a phase Field Model of the Willmore Energy
Dienstag, 30.1.18, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
\nWe consider a phase field model for Willmore’s energy originally proposed by de Giorgi. In essence, the energy of this phase field model is given by taking the first variation of the well known Modica-Mortola energy and integrating the square of this variation. A Gamma-convergence result was proved in 2006 by Röger and Schätzle. In this presentation, we examine the viscous gradient flow of de Giorgi’s energy and prove existence of weak solutions using a Galerkin approximation. Finally, we give an outlook to the addition of further constraints for the energy, for example using a term to control certain topological properties of the phase field.
Conical spherical metrics: Lecture II
Mittwoch, 31.1.18, 10:15-11:15, SR 119, Eckerstr. 1