Schoenfieldabsolutheit
Mittwoch, 1.2.17, 16:30-17:30, Raum 404, Eckerstr. 1
Nonlinear Optimization Methods for Model Predictive Control of Mechatronic Systems
Donnerstag, 2.2.17, 10:00-11:00, Raum 125, Eckerstr. 1
Model Predictive Control (MPC) for mechatronic systems is based on the online\nsolution of medium scaled constrained nonlinear optimal control problems, with\nsampling times in the milli and microsecond range. This poses specific challenges\nfor the problem formulation and the numerical solution methods. This talk pres-\nents and discusses algorithms and open source software implementations that are\ndesigned to address these challenges, and reports on experimental tests with me-\nchatronic, aerospace and automotive applications. The focus is on recent progress\non numerical integration and derivative generation, as well as embedded quadratic\nprogramming methods.
Effective behavior of random media: From an error analysis to elliptic regularity theory
Donnerstag, 2.2.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Heterogeneous media, like a sediment, are often naturally described in statistical terms. \nHow to extract their effective behavior on large scales, like the permeability in Darcy's law, from the\nstatistical specifications? A practioners numerical approach is to sample the medium \naccording to these specifications and to determine\nthe permeability in the Cartesian directions by imposing simple boundary conditions.\nWhat is the error made in terms of the size of this "representative volume element''?\nOur interest in what is called "stochastic homogenization'' grew out of this error analysis.\n\nIn the course of developing such an error analysis, connections with the classical\nregularity theory for elliptic operators have emerged. It turns out that the\nrandomness, in conjunction with statistical homogeneity, of the coefficient field (which can be seen as a Riemannian metric)\ngenerates large-scale regularity of harmonic functions (w.r. t.the corresponding Laplace-Beltrami operator). \nThis is embodied by a hierarchy of Liouville properties: \nAlmost surely, the space of harmonic functions of given but arbitrary growth rate\nhas the same dimension as in the flat (i.e. Euclidean) case. \nClassical examples show that from a deterministic point of view, this Liouville property fails \nalready for a small growth rate:\nThere are (smooth) coefficient fields, which correspond to the geometry of a cone at infinity,\nthat allow for sublinearly growing but non-constant harmonic functions
Curvature of higher direct images
Freitag, 3.2.17, 10:15-11:15, Raum 404, Eckerstr. 1
The differential geometric properties of the classical Hodge bundles were\nfirst studied by Griffiths in the context of the period map and variation of\nHodge structures. This can be used to show the hyperbolicity of the moduli\nspace of polarized Calabi-Yau manifolds. In the talk we consider generalized\nHodge bundles which are twisted by a relative ample line bundle. An intrinsic\ncurvature formula can be given. This generalizes a result of Berndtsson on\nthe\nNakano positivity of the direct image of the ample twisted relative canonical\nbundle of a fibration as well as the curvature formula for higher direct\nimages\nof Schumacher in the canonically polarized case.
Geometric approaches to constrained Variational Calculus and Control Theory
Montag, 6.2.17, 10:15-11:15, Raum 318, Eckerstr. 1
We look at variational constrained and controlled systems through the lens of their\ngeometrical entanglement. For Hamiltonian systems with holonomic constraints we define a co-isotropic submanifold on the configuration space and then work on it through\nreductions, with the purpose of obtaining a reduced Hamiltonian system which may be\nsimpler to study in some practical situations. In particular, we see how, on a co-isotropic\nsubmanifold, it is always possible to find a symplectic reduction. For controlled systems, a\ngeometric approach not only allows to look at the variables in a physical meaningful way,\nbut it also provides useful tools that can be used to determine the state of the system after\njumps of discontinuity of the control. In particular, we see how a well precise Riemannian\nproperty of the kinetic metric allows us to detect the continuity of the input-output map\neven when the control is discontinuous.
Einfache Expansionen von Körpern
Mittwoch, 8.2.17, 16:30-17:30, Raum 404, Eckerstr. 1
Donnerstag, 9.2.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
tba.
Freitag, 10.2.17, 10:15-11:15, Raum 404, Eckerstr. 1
Arithmetic hyperbolicity
Freitag, 10.2.17, 10:15-11:15, Raum 404, Eckerstr. 1
I will explain what it means for a variety to be arithmetically hyperbolic. I will then explain that Lang-Vojta's conjecture implies that any variety with an immersive period map is arithmetically hyperbolic. In this joint work with Daniel Loughran we extend the latter statement to algebraic stacks by rigidifying stacky period maps.
Value, Size, Momentum and the Average Correlation of Stock Returns
Freitag, 10.2.17, 12:00-13:00, Raum 404, Eckerstr. 1
Dynamic average correlations of stock returns are predicted by the volatility of the market excess return and moving average returns of value, size and momentum portfolios. While the influence of market volatility on average correlation is well-known, the role of value, size and momentum appears to be underappreciated. Correlations of stock returns and stock returns share sources of risk like the market volatility, but there are other sources that are distinct. In particular, correlations are increased when value or momentum returns are roughly zero, while strongly negative returns of value or momentum are associated with lower correlations. Using the market volatility and a moving average return of the value portfolio as predictors of average correlation, we obtain a global minimum variance portfolio with a Sharpe ratio that is 1.5% higher relative to the one based on a Dynamic Equicorrelation Garch model, and the difference in portfolio volatility is statistically significant"
Segal approach for algebraic structures
Freitag, 10.2.17, 14:00-15:00, Raum 125, Eckerstr. 1
Abstract: The operads are considered today as a conventional tool to describe homotopy algebraic structures. However, for the original problem of delooping, another formalism exists, bearing the name of Segal. This approach has proven advantageous in certain situations, such as, for example, modelling higher categories.\n\nIn this talk, we will discuss how one can illuminate and arguably simplify the proof of Deligne conjecture, the existence of E_2-structure on Hochschild cochains, using the language of Segal objects and operator categories of Barwick. We will then elaborate on our solution to the problem of extending the Segal approach to arbitrary monoidal structures, which employs the language of Grothendieck fibrations and an extension of Reedy theorem to families of model categories.\n\nWhile the second part of the talk is technical, the first one will require only basic knowledge of categories and topology.\n
Boundary triples, Krein formula, and resolvent estimates for one-dimensional high-contrast periodic problems
Dienstag, 21.2.17, 14:00-15:00, Raum 226, Hermann-Herder-Str. 10