TBA
Montag, 1.2.16, 16:15-17:15, Raum 404, Eckerstr. 1
The cotangential and the derived de Rham complex in the h-topology
Dienstag, 2.2.16, 10:15-11:15, Raum 404, Eckerstr. 1
Orientation Reversing Gauge Transformations
Dienstag, 2.2.16, 12:00-13:00, Raum 404, Eckerstr. 1
The talk presents topological obstructions to defining an automorphism of vector bundles with negative determinant. Concrete calculations for vector bundles over spheres are presented. The problem is then analysed using obstruction theory and characteristic classes from algebraic topology, where a definite answer using the Euler class can be given in some situations.
Symmetry breaking in indented elastic cones
Dienstag, 2.2.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry, and modeling the compression by suitable Dirichlet boundary conditions at the center and the boundary of the sheet, we identify the energy scaling law in the von-Karman plate model. Specifically, we find that three different regimes arise with increasing indentation: initially the energetic cost of the logarithmic singularity dominates, then there is a linear response corresponding to a moderate deformation close to the boundary of the cone, and for larger indentation a localized inversion takes place in the central region.\nThen we show that for large enough indentations minimizers of the elastic energy cannot be radially symmetric. We do so by an explicit construction that achieves lower elastic energy than the minimum amount possible for radially symmetric deformations.\n\nJoint work with S. Conti (IAM Bonn) and I. Tobasco (CIMS New York)
Hessian metrics and local Lagrangian immersions
Dienstag, 2.2.16, 16:15-17:15, Raum 125, Eckerstr. 1
Mixed Tate Motives
Donnerstag, 4.2.16, 09:00-10:00, Raum 119, Eckerstr. 1
I my talk I will consider categories of Tate motives over\nbase schemes which satisfy the Beilinson-Soule vanishing property.\nI will construct t-structures and show that these also induce\nt-structures on compact objects, both with integral and\ncertain finite coefficients, thereby producing\nsmall abelian categories of mixed Tate motives. As an ingredient I will discuss\nthat triangulated Tate motives can be described as modules\nover a motivic E-infinity dga.\n
ERROR BOUNDS AND QUANTIFIABLE CONVERGENCE OF PROXIMAL METHODS FOR NONSMOOTH/(NON)CONVEX OPTIMIZATION
Donnerstag, 4.2.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
For iterative methods in nonconvex optimization, a central question is when to stop. And when the decision has been made to stop, what is the relation, if any, between the point that the algorithm delivers and the desired solution(s) to the optimization problem? Quantification of the convergence of algorithms is the key to providing error bounds for stopping crieria, and at the heart of quantifiable convergence rates lies theory of regularity, not only of the underlying functions and operators, but of the critical points of the optimization model. We survey progress over the last several years on sufficient conditions for local linear convergence of fundamental algorithms applied to nonconvex problems, and discuss challenges and prospects for further progress. The theory is local by nature and contains the convex case as an example where the local neighborhood extends to the whole space. We demonstrate the use of the tools we have developed on applications to image processing and matrix completion.
Freitag, 5.2.16, 10:00-11:00, Raum 404, Eckerstr. 1
Abundance conjecture for varieties with many differential forms
Freitag, 5.2.16, 10:00-11:00, Raum 404, Eckerstr. 1
The abundance conjecture and the existence of good models are the main open problems in the Minimal Model Program in complex algebraic geometry. Even though it is completely proved in dimension 3, almost nothing has been known in higher dimensions. In this talk, I will discuss my recent joint work with Thomas Peternell, where we prove that the abundance conjecture holds on a variety with mild singularities if it has many reflexive differential forms with coeffi cients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions. Under this assumption, the result has several consequences: for instance, that hermitian semipositive canonical divisors are almost always semiample. When the numerical dimension of the canonical sheaf is 1, our results hold unconditionally in every dimension.
Hamiltonian field theory: Where Geometry meets Physics
Freitag, 5.2.16, 14:15-15:15, Hörsaal Weismann-Haus (Albertstr. 21a)
The lecture surveys the state-of-art of global Hamiltonian field theory\nwith a particular stress to geometric structures associated with\nEuler-Lagrange and Hamilton equations. With help of a new concept of\nLepage manifold one obtains a covariant Hamilton theory related with an\nEuler-Lagrange form (representing variational equations) rather than\nwith a particular Lagrangian. This approach substantially extends the\nfamily of variational problems which possess a canonical multisymplectic\nHamiltonian formulation, and can be thus treated without using the Dirac\nconstraint formalism. To illustrate the results we present an\nunconstraint Hamiltonian theory of gravity and electromagnetism.
Regularität von Laminationen der Kodimension 1
Montag, 8.2.16, 16:15-17:15, Raum 404, Eckerstr. 1
Remarks on the convergence of pseudospectra
Dienstag, 9.2.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Pseudospectra help to understand general properties of non-normal matrices and operators, e.g. spectral instabilities or decay rates of associated semigroups.First we give a summary of basic notions and results. Then we discuss the question whether a linear operator can have constant resolvent norm on an open set and present several results that exclude this phenomenon. Finally we show the convergence of pseudospectra for operators acting in different Hilbert spaces and mention applications to Schroedinger operators.The talk is based mainly on joint work with Sabine Boegli
Symmetrische Namen fuer Paare von Vitaliklassen reeller Zahlen
Mittwoch, 10.2.16, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 11.2.16, 17:00-18:00, Hörsaal II, Albertstr. 23b
Effective Matsusaka for surfaces in positive characteristic
Freitag, 12.2.16, 10:00-11:00, Raum 404, Eckerstr. 1
The problem of determining an effective bound on the multiple which makes an ample divisor D on a smooth variety X very ample is natural and many results are known in characteristic zero. In this talk, based on a joint paper with Gabriele Di Cerbo, I will discuss this problem on surfaces in positive characteristic, giving a complete solution in this setting. \nOur strategy requires an ad hoc study of pathological surfaces, on which Kodaira-type theorems can fail. A Fujita-type theorem and a vanishing result for big and nef divisors on pathological surfaces will also be discussed.
The Rearrangement Algorithm: Properties and Applications
Freitag, 12.2.16, 14:00-15:00, Raum 404, Eckerstr. 1
t.b.a
Freitag, 12.2.16, 14:15-15:15, Raum 127, Eckerstr. 1
Integration in Differential Cohomology
Freitag, 12.2.16, 14:15-15:15, Raum 127, Eckerstr. 1
A differential extension of a generalized cohomology theory provides a\nmethod to combine the topological information about a smooth manifold coming\nfrom the cohomology theory with the geometric information coming from the\ndifferential forms.\nOn the level of the differential extension there are integration maps\ncomplementing the integration of forms along the S^1-fiber of trivial circle\nbundles.\nIn this talk I will present two results on the uniqueness of such\nintegration maps. Firstly, for ordinary cohomology with integer coefficients\nthe integration is uniquely determined. Secondly, there are sufficient\nconditions for the uniqueness in the general case.
Fractional Levy processes: Theory, statistical inference and applications
Freitag, 12.2.16, 15:00-16:00, Raum 404, Eckerstr. 1
Controlling the false discovery rate for discrete data
Freitag, 12.2.16, 16:15-17:15, Raum 404, Eckerstr. 1
Optimal Transport from Random Allocation to Ricci Flow
Freitag, 12.2.16, 17:00-18:00, Raum 404, Eckerstr. 1
Equilibrium equations in Resource Dependent Branching Processes with immigration
Samstag, 13.2.16, 09:30-10:30, Raum 404, Eckerstr. 1
Polya Urns Via the Contraction Method
Samstag, 13.2.16, 10:30-11:30, Raum 404, Eckerstr. 1
Bernoulli and tail-dependence compatibility
Samstag, 13.2.16, 11:45-12:45, Raum 404, Eckerstr. 1
Quantization of Hitchin spectral curves and G-opers
Montag, 22.2.16, 16:15-17:15, Raum 404, Eckerstr. 1
There are particularly nice holomorphic Lagrangian subvarieties in the moduli space of Higgs pairs on a compact Riemann surface, called Hitchin sections. Physicist Gaiotto conjectured that there should be a canonical procedure to quantize the Hitchin spectral curves of the Higgs pairs on this Lagrangian into a family of holomorphic connections, called "opers," on the same Riemann surface. Recently this conjecture has been solved in a joint work by Dumitrescu-Fredrickson-Kydonakis-Mazzeo-Mulase-Neitzke. In this talk a holomorphic construction of the conjectured opers will be given. We will see that the quantum deformation parameter, the Planck constant, is identified as the coordinate of a sheaf cohomology group naturally associated with the Hitchin section.
Absolute instability of spatially developing/temporally oscillating unbounded flows and media
Dienstag, 23.2.16, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We present our recent results on the absolute instability of spatially developing/temporally oscillating unbounded flows and media. In the treatment of temporally oscillating\nflows, the Floquet theory is applied. As an example of the application of the treatment a nonlinear Schrodinger equation is analyzed on absolute instability. The spatially\ndeveloping flows treated include localized flows and flows with the tails that decay algebraically sufficiently rapidly, when x goes to + or - infinity: Flows having the same limit state, when x goes to + or - infinity as well as those having different limit states, when x goes to infinity and\nx goes to - infinity, i.e. fronts, are considered. In the treatment, no restriction of the rate of\nvariability of the base state in the finite domain is imposed and no approximations are used. The initial-value stability problem is treated by using the Laplace transform.\nThe resulting boundary-value problem with spatially variable coecients is treated as a dynamical system by using the exact asymptotic expressions, when x goes to + or - infinity for\nthe fundamental matrix of the problem. In the non-localized case, the derivation of\nthe asymptotics of the fundamental matrix is based on the application of the Levinson theorem. The boundary-value problem is solved formally and a set of the dispersion relation functions, Dn(w); for the global normal modes, for the corresponding regions,\nin complex domain, n >= 1, is obtained, where w is a frequency (and a Laplace transform parameter).\nThe solution of the stability problem is given by an inverse Laplace transform\nof the solution of the boundary-value problem. By using this solution, the conditions for the absolute instability of the \now in each case considered are obtained in terms of\nthe global dispersion-relation functions, the dispersion-relation functions of the limit states at + or - infinity and the matrix-functions entering into the asymptotics of the fundamental matrix of the boundary-value problem. Since all the objects controlling the instabilities are essentially global properties of the \nflow, it is maintained that the concept\nof local stability cannot be consistently defined for the \nows treated. A procedure for computing the instabilities is suggested.