Karos, Orakel und ein Typenübergehungssatz
Wednesday, 2.11.16, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 3.11.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Elliptic surfaces
Friday, 4.11.16, 10:15-11:15, Raum 404, Eckerstr. 1
Elliptic surfaces form a central part of the classification of algebraic surfaces. In my talk, I will give a brief review of the theory of elliptic surfaces, especially those with section such that the theory of Mordell-Weil lattices applies. Then I will discuss old and new applications in several directions such as sphere packings, K3 surfaces of large Picard number, the maximum number of lines on quartic surfaces in P^3, Enriques surfaces containing a given configuration of smooth rational curves.
On Stokes matrices for Frobenius manifolds
Monday, 7.11.16, 16:15-17:15, Raum 404, Eckerstr. 1
In this talk we will discuss how to compute the Stokes matrices for some semisimple Frobenius manifolds by using the so-called monodromy identity. In addition, we want to discuss the case when we get integral matrices and their relations with mirror symmetry. This is a part of an ongoing project with M. Smirnov and previous joint work with Marius van der Put. \n
Boundary and interior vortices in thin film micromagnetics
Tuesday, 8.11.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Ferromagnetic materials are described by a nonlocal and nonconvex variational principle. For certain regimes, it is possible to rigorously derive simplified models using Gamma-convergence. In my talk I will concentrate on models that contain point defects carrying a topological charge, and will discuss static and dynamical results for these defects as well as some of the underlying analytical tools.\n
Steklov-eigenvalue bounds and minimal surface I
Tuesday, 8.11.16, 16:15-17:15, Raum 404, Eckerstr. 1
We present results by Frasier and Schoen written down in their paper "Sharp eigenvalue bounds and minimal surfaces in the ball". In the first talk we discuss properties of the first Steklov eigenvalue and lay the requirements to prove in the second talk that under all annulus' the critical one gives the maximal Steklov eigenvalue.
Strolling through paradise
Wednesday, 9.11.16, 16:30-17:30, Raum 404, Eckerstr. 1
Thursday, 10.11.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
The b-semiampleness conjecture on surfaces
Friday, 11.11.16, 10:15-11:15, Raum 404, Eckerstr. 1
An lc-trivial fibration f:(X,B)->Y is, roughly speaking, a\nfibration such that the log-canonical divisor of the pair (X,B) is trivial along the fibres of f.\nAs in Kodaira’s canonical bundle formula for elliptic fibrations, the log-canonical divisor can be expressed as the sum of the pull-back of three divisors: the log-canonical divisor of Y; a divisor, called discriminant, containing informations on the singular fibres; and a\ndivisor called moduli part related to the birational variation of the fibres.\nBy analogy with the case of elliptic fibrations, the moduli part is conjectured to be semiample.\nAmber proved the conjecture when the base Y is a curve.\nIn this talk we will explain how to prove the conjecture when Y is a surface.\nThis is a joint work with Vladimir Lazić.
Reconstructing branching lineages in single cell genomics
Friday, 11.11.16, 12:00-13:00, Raum 404, Eckerstr. 1
Single-cell technologies have recently gained popularity in developmental biology because they allow resolving potential heterogeneities due to asynchronicity of differentiating cells. Popular multivariate approaches for analyzing such data are based on data normalization, followed by dimension reduction and clustering to identify subgroups. However, in the case of cellular differentiation, we cannot expect clear clusters to be present - instead cells tend to follow continuous branching lineages.\n\nWe show that modeling the high-dimensional state space as a diffusion process, where cells move to close-by cells with a distance-dependent probability well reflects the differentiating characteristics. Based on the underlying diffusion map transition kernel, we then propose to order cells according to a diffusion pseudo time, which measures transitions between cells using random walks of arbitrary length. This allows for a robust identification of branching decisions and corresponding trajectories of single cells. We demonstrate the method on single-cell qPCR data of differentiating mouse haematopoietic stem cells as well as on RNA sequencing profiles of embryonic stem cells.\n\nAs outlook if time permits, I will outline how to use this pseudotime in combination with dynamic models to construct a mechanistic understanding of the regulatory process, based on recent work regarding ODE-constrained mixture modeling.
Rigidity problems for manifolds with foliated boundary
Monday, 14.11.16, 16:15-17:15, Raum 404, Eckerstr. 1
Joint work with Georges Habib, Fida El Chami and Roger Nakad. We will show that, starting with an integral inequality due to O. Hijazi and S. Montiel, particular geometries for compact Riemannian spin or spin\(^c\) manifolds with foliated boundary may be characterized purely in terms of curvature.
Building countable generic structures with the algebraic closure property
Wednesday, 16.11.16, 16:30-17:30, Raum 404, Eckerstr. 1
In this talk we introduce a new method of building countable\ngeneric structures with the algebraic closure property. This method\ngeneralizes the well-known construction method of building generic\nstructures using a pre-dimension function. Using this method it is very easy\nto build a generic structure that its theory is not simple. The initial\nmotivation for such a generalization was to build a generic structure that\nis NTP2 but not simple. Time permitting, we investigate TP2 property of\nthe non-simple generics that are obtained from this method.\n
Thursday, 17.11.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Application of homology in quantum fault-tolerance
Friday, 18.11.16, 10:15-11:15, Raum 404, Eckerstr. 1
It has been realized by Richard Feynman, Peter Shor and others that by exploiting the laws of quantum mechanics some computational problems may be solved exponentially faster than on 'classical' computers. Building a so-called quantum computer is a difficult undertaking due to the fragility of quantum mechanical systems.\n\nWe will discuss how homology can help in designing fault-tolerant quantum computing architectures. In particular, we introduce a simple procedure which turns a cell complex into a quantum mechanical system in which information can be protected against noise, a so-called homological quantum code. A nice feature of this construction is that it relates geometric properties of the cell complex to properties of the quantum code. We will focus on cell complexes which are tilings of closed 2D and 4D (hyperbolic) manifolds.\nLastly, we will discuss certain no-go theorems which prove that quantum codes with certain desirable properties can never be obtained by this procedure.
Octonionic Line Bundles
Monday, 21.11.16, 16:15-17:15, Raum 404, Eckerstr. 1
Octonionic line bundles do not exist. Nevertheless, they can be used to describe an invariant needed to classify highly connected 15-manifolds. I will give a little introduction to the octonionic projective plane, and then describe this invariant.
Steklov-eigenvalue bounds and minimal surface II
Tuesday, 22.11.16, 16:15-17:15, Raum 404, Eckerstr. 1
Strolling through paradise
Wednesday, 23.11.16, 16:30-17:30, Raum 404, Eckerstr. 1
Aspherical manifolds, what we know and what we do not know
Thursday, 24.11.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Aspherical closed manifolds arise very often in topology, for\ninstance in low dimensional topology,\nclosed Riemannian manifolds with non-positive sectional curvature and so on. We\nwant to give a survey about open problems (and their status) such as the\nBorel Conjecture about topological rigidity, the Novikov Conjecture about the\ntopological invariance of higher signatures,\nthe Singer Conjecture about the distribution of L^2-Betti numbers,\napproximation of L^2-torsion,\nand the realizablility of Poincare duality groups as fundamental groups of\naspherical closed manifolds. Moreover, we present results about the rational\nhomotopy groups of\nthe group of diffeomorphisms and homeomorphisms of aspherical closed manifolds\nand the problem which hyperbolic groups have the standard sphere as boundary.\n\n\n\n\n\n\n
Hyperbolicity of moduli spaces of abelian varieties with a level structure
Friday, 25.11.16, 10:15-11:15, Raum 404, Eckerstr. 1
For any positive integers g and n, let Ag(n) be the moduli space of principally polarized abelian varieties with a level-n structure (it is a smooth quasi-projective variety for n>2). Building on works of Nadel and Noguchi, Hwang and To have shown that the minimal genus of a curve contained in Ag(n) grows with n. We will explain a generalization of this result dealing with subvarieties of any dimension. In particular, we show that all subvarieties of A_g(n) are of general type when n > 6g. Similar results are true more generally for quotients of bounded symmetric domains by lattices.
Analytische und numerische Betrachtung lokaler und nicht-lokaler Phasenfeldmodelle
Tuesday, 29.11.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Introduction to first variation of varifolds
Tuesday, 29.11.16, 16:15-17:15, Raum 404, Eckerstr. 1
Paare algebraisch abschlossener Körper sind äquational
Wednesday, 30.11.16, 16:30-17:30, Raum 404, Eckerstr. 1