Inferring Demographic Histories using Coalescent Hidden Markov Models
Friday, 3.5.19, 12:00-13:00, Raum 232, Ernst-Zermelo-Str. 1
Inference of historical demographic events from contemporary genomic sequence data has received a lot of attention in recent years. A particular focus has been on the recent exponential growth of population size in humans. This recent growth strongly impacts the distribution of rare alleles, which are of importance when studying disease related genetic variation. The popular method PSMC (Li and Durbin, 2011) is used to infer population sizes from a sample of two chromosomes. However, the small sample size severely limits the power of this method in the recent past.\n\nTo improve inference in the recent past, we extend the Coalescent Hidden Markov model approach of PSMC to larger sample sizes. Since using the full genealogical trees relating the sample at each locus is computationally prohibitive, we introduce a flexible mathematical framework to employ different representations of these local trees. In partciular, we present the implementation of this framework using the height of the local trees (TMRCA), corresponding to PSMC for sample size 2, and using the total branch length of the local trees. \n\nWe evaluate the different representations in simulation studies and applications to genomic variation data from diverse human populations. We discuss potential extension of the framework to infer divergence times and migration rates in structured populations, and employing the posterior distribution of the local trees to detect regions under selection.
Workshop on Analysis, Simulation, and Modeling of Elastic Curves
Monday, 6.5.19, 09:00-10:00, Raum 226, Hermann-Herder-Str. 10
String mass spectra, Lecture I
Monday, 6.5.19, 12:15-13:15, Hörsaal I, Physik-Hochhaus, Hermann-Herder-Straße 3
In the first lecture, we will retrace the journey of the theoretical physicists\nwho set out the basic principles of string theory, taking their inspiration from the theory of a \nrelativistic point particle. We shall use the classical Polyakov action to establish the equations\nof motion of the free boson string, which are differential equations subject to some constraints.\nThese constraints yield the first string mass formula we shall encounter during this mini course.
Elliptic Genera of ADE singularities
Monday, 6.5.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
In a paper by Harvey, Lee and Murthy, the authers calculated the elliptic genera of ADE singularities as the partition of some gauged linear sigma models using the technique called supersymmetric localization. In this talk, I will give a free field construction of these elliptic genera and talk about the geometric interpretation.
String mass spectra, Lecture II
Tuesday, 7.5.19, 12:15-13:15, Hörsaal II, Albertstr. 23b
The second lecture aims at quantising the bosonic string (using the light cone gauge\nformalism) and showing how quantisation alters the string mass formula obtained in Lecture 1. We will\nuse this mass formula to analyse the spectrum of a single, free closed boson string.
Wer wagt, gewinnt? Wie wir Kindern und Jugendlichen Risikokompetenz vermitteln können
Tuesday, 7.5.19, 19:30-20:30, Hörsaal II, Albertstr. 23b
Der Vortrag behandelt das Thema RISIKO aus verschiedenen Perspektiven. \nEs werden die vier Komponenten der Risikokompetenz beschrieben und anhand von empirischen Resultaten über Schulinterventionen diskutiert.\nDabei spielen die Informationsformate eine wichtige Rolle, die das Verständnis von\nWahrscheinlichkeiten und Erwartungswerten erleichtern und fördern.\n
String mass spectra, Lecture III
Thursday, 9.5.19, 12:15-13:15, Hörsaal II, Albertstr. 23b
The third lecture focusses on the quantisation of open bosonic strings and on how the \nmass formula is modified in a theory of open strings. This will give us an opportunity to see how Dirichlet \nbranes enter the game and to elaborate on the fact that string theory is not just a theory of strings, but also of higher \ndimensional objects.
Thursday, 9.5.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
Knörrer type equivalences for cyclic quotient surface singularities
Friday, 10.5.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Asymptotic behavior of flows by powers of the Gaussian curvature
Monday, 13.5.19, 16:00-17:00, Raum 125, Ernst-Zermelo-Str. 1
In this talk, I will introduce the ideas of\nBrendle-Choi-Daskaspoulos' paper "Asymptotic behavior of flows by powers of the Gaussian curvature".\nAnd I will try to use their idea to treat some other similar problems and show where the difficulities are.
Introduction to the spinor flow
Monday, 13.5.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Geometric flows are a natural non-perturbative approach to the construction of special holonomy metrics. Several flows have been proposed in different settings, such as the Kähler--Ricci flow and the Laplacian flow. The spinor flow is a unified approach for all Ricci flat special holonomy manifolds based on the spinorial characterization of such metrics. In this talk I will discuss its definition (due to Ammann, Weiß, Witt), its relationship to other flows and several recent results concerning its behavior.
Continuous K-theory and cohomology of rigid spaces
Friday, 17.5.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Continuous K-theory is a variant of algebraic K-theory for rigid spaces (nonarchimedean analytic spaces). In this talk, I will relate the bottom K-theory group of a rigid space with its top cohomology group with integral coefficients. I will begin with some recollections about algebraic K-theory for schemes and then introduce continuous K-theory for rigid spaces, as defined by Morrow and further studied by Kerz-Saito-Tamme. Afterwards, I will present an easy proof of my result in the regular case assuming resolution of singularities. This will be done in terms of Berkovich spaces and their skeleta (which will be used as a black box). The general result avoids the assumption of resolution of singularities and works with Zariski-Riemann type spaces instead which are defined as the limit over all models. Despite not a scheme anymore, these Zariski-Riemann type spaces behave, due to a result by Kerz-Strunk, from the K-theoretic point of view similar as a regular model does. The content of this talk is based on my PhD thesis advised by Moritz Kerz and Georg Tamme.
Lecture Series 'Hypoelliptic laplacian and applications'
Monday, 20.5.19, 10:15-11:15, Raum 125, Ernst-Zermelo-Str. 1
Eine Verallgemeinerung des Martin-Axioms
Monday, 20.5.19, 14:15-15:15, Raum 404, Ernst-Zermelo-Str. 1
In dem Bachelorvortrag wird eine Version eines verallgemeinerten Martin-Axioms behandelt. Es\nwird gezeigt, warum es eine schwache Version ist, und ein Beweis mittels\niterierten Forcings für diese dargestellt werden.\n
On the space of initial value pairs satisfying the dominant energy condition strictly
Monday, 20.5.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The dominant energy condition implies an inequality for the induced initial value pair on a spacelike hypersurface of a Lorentzian manifold. In this talk, we want to study the\nspace of all initial value pairs that satisfy this inequality strictly. In order to do so, we introduce a Lorentzian alpha-invariant for initial value pairs, and compare it to its classical counterpart. Recent non-triviality results for the latter will then imply that this space has non-trivial homotopy groups.
Lecture Series 'Hypoelliptic laplacian and applications'
Tuesday, 21.5.19, 10:15-11:15, Raum 125, Ernst-Zermelo-Str. 1
wird noch bekanntgegeben
Tuesday, 21.5.19, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Schritte zum Problemlösen - auch in der Sekundarstufe II
Tuesday, 21.5.19, 19:30-20:30, Hörsaal II, Albertstr. 23b
Im Vortrag geht es um Forschungsergebnisse und Konzepte zu problemorientiertem und problemzentriertem Mathematikunterricht. Welche Möglichkeiten hat man als Lehrperson, den Unterricht stärker auf das Problemlösen auszurichten und dies auch in Prüfungen zu berücksichtigen? Ein Schwerpunkt wird dabei auf den – oft vernachlässigten – Bereich der Sekundarstufe II gelegt.
Lecture Series 'Hypoelliptic laplacian and applications'
Wednesday, 22.5.19, 10:15-11:15, Raum 125, Ernst-Zermelo-Str. 1
Lecture Series 'Hypoelliptic laplacian and applications'
Thursday, 23.5.19, 10:15-11:15, Raum 125, Ernst-Zermelo-Str. 1
Hypoelliptic Laplacian, index theory and the trace formula
Thursday, 23.5.19, 17:00-18:00, Hörsaal II, Albertstr. 23b
The hypoelliptic Laplacian is a family of operators, indexed by b ∈ R^∗_+ ,\nacting on the total space of the tangent bundle of a Riemannian manifold, that\ninterpolates between the ordinary Laplacian as b → 0 and the generator of\nthe geodesic flow as b → +∞ . These operators are not elliptic, they are not\nself-adjoint, they are hypoelliptic.\nThe hypoelliptic deformation preserves subtle invariants of the Laplacian. In\nthe case of locally symmetric spaces, the deformation is essentially isospectral.\nIn a first part of the talk, I will describe the geometric construction of the\nhypoelliptic Laplacian in the context of de Rham theory. In a second part, I\nwill explain applications to the trace formula.
Schüler-Info-Tag
Friday, 24.5.19, 08:30-09:30, Raum 404, Ernst-Zermelo-Str. 1
Sie überlegen, Mathematik zu studieren? Am 24. Mai bietet das Mathematische Institut einen Informationstag an, der sich gezielt an Studieninteressierte richtet.\n\nWir möchten einen vertiefenden Zugang zu mathematischen Fragestellungen und ihren Lösungen verschaffen, möchten Freude an der Mathematik bestärken und die Möglichkeit eröffnen, Gleichgesinnte und Ansprechpartner kennen zu lernen. Sie hören Vorlesungen, besuchen einen längeren Workshop und ein Seminar und erhalten konkrete Informationen zu Studium und Beruf.
Lecture Series 'Hypoelliptic laplacian and applications'
Friday, 24.5.19, 10:15-11:15, Raum 125, Ernst-Zermelo-Str. 1
Grothendieck groups of isolated quotient singularities
Friday, 24.5.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
We study the Grothendieck group of the Buchweitz-Orlov singularity category for quasi-projective algebraic schemes. Particularly, we show for isolated quotient singularities that the Grothendieck group of its singularity category is finite torsion and that rational Poincare duality is satisfied on the level of Grothendieck groups. We consider also consequences for the resolution of singularities of such quotient singularities. More concretely we prove a conjecture of Bondal and Orlov on the derived category of rational singularities in the case of quotient singularities.
Generalised Spencer cohomology and supersymmetry
Monday, 27.5.19, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
It is a fact of life that the Lie algebra of isometries of a riemannian manifold is a filtered Lie algebra whose associated graded Lie algebra is a subalgebra of the euclidean algebra: the Lie algebra of isometries of the flat model of riemannian geometry. It is also a fact of life, more recently understood, that the Lie superalgebras which arise as supersymmetries of supergravity backgrounds too are filtered Lie superalgebras whose associated graded Lie superalgebra is a subalgebra of the Poincaré superalgebra: the supersymmetry algebra of the flat supergravity background. The cohomology theory governing such filtered deformations is generalised Spencer cohomology. In this talk I will review these facts and describe some consequences of the calculations of generalised Spencer cohomology for Poincaré superalgebras in different dimensions: including what could be considered a cohomological derivation of eleven-dimensional supergravity and a determination of the possible lorentzian 4- and 6-dimensional manifolds admitting rigid supersymmetry. This is based on collaborations with Andrea Santi and Paul de Medeiros.
Gorensteinness and iteration of Cox rings
Friday, 31.5.19, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
We show that finitely generated Cox rings have trivial canonical class. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of Fano type and Kawamata log terminal quasicones, iteration of Cox rings is finite with factorial master Cox ring.\n