 |
|
FIM Weekly Bulletin
May 20 to 24, 2013
| Monday, May 20 |
| No events scheduled today! |
| No events scheduled today! |
| Tuesday, May 21 |
| 15:15-16:15 |
Analysis Seminar
Paralinearization theorem on manifolds
Dr. Yannick Sire, Université Aix-Marseille
|
ETH Zentrum
HG G 43 |
| Abstract: |
In this joint work with F. Bernicot, we introduce a new bilinear operator which allows, on a manifold with sub-laplacian structure, to derive a paralinearization theorem. I will give an application to a quasi-linear wave equation. |
| Speakers: |
Dr. Yannick Sire
(Université Aix-Marseille)
|
|
| 15:15-16:15 |
Talks in Mathematical Physics
Ricci flow and the space of quantum field theories
Dr. Ryan Grady, Boston University
|
ETH Zentrum
HG G 19.2 |
| Abstract: |
In this talk I aim to make precise the statement of Friedan (1980's) that the \beta function of the nonlinear \sigma model is given by the Ricci curvature of the target manifold. Working in Costello's approach to perturbative field theory, I will define a version of the nonlinear \sigma model, set up the machinery of the \beta function, and give a proof of Friedan's result. If time permits I will also discuss work on the observables in this nonlinear \sigma model. The talk is based on joint work with Si Li (Boston U). |
| Speakers: |
Dr. Ryan Grady
(Boston University)
|
|
| 17:15-18:30 |
Zurich Graduate Colloquium (uzh)
What is... 1+1?
Dr. Thomas Preu, Universität Zürich
|
Uni Zentrum
KO2 F 150 |
| Speakers: |
Dr. Thomas Preu
(Universität Zürich)
|
|
| Wednesday, May 22 |
| 10:00-12:00 |
FIM Minicourse
Quantitative stochastic homogenization of Hamilton-Jacobi equations
Dr. Scott N. Armstrong, Université Paris Dauphine, Ceremade (France)
|
ETH Zentrum
HG G 19.1 |
| Abstract: |
We will consider the stochastic homogenization of first-order and viscous
Hamilton-Jacobi equations. These are the master equations which describe
(in the first order case) continuum analogues of first-passage percolation and
(in the viscous case) large deviations of diffusions in heterogeneous environments.
In the main part of the course, we will review a new homogenization
procedure which leads to quantitative results. |
| Speakers: |
Dr. Scott N. Armstrong
(Université Paris Dauphine, Ceremade (France))
|
|
| 13:15-14:15 |
Talks in Mathematical Physics
Rational homotopy theory of automorphisms of highly connected manifolds
Prof. Dr. Alexander Berglund, University of Copenhagen
|
ETH Zentrum
HG G 43 |
| Abstract: |
I will talk about joint work with Ib Madsen on the cohomology of automorphism groups of high dimensional manifolds, and on the rational homotopy types of their classifying spaces. We prove an analog of Harer's stability theorem for a family of highly connected manifolds. When calculating the stable cohomology of their homotopy automorphisms, certain Lie algebras of symplectic derivations show up that have appeared before in Kontsevich's work on the homology of outer automorphism groups of free groups. |
| Speakers: |
Prof. Dr. Alexander Berglund
(University of Copenhagen)
|
|
| 15:00-16:00 |
FIM Announcements
FIM Tea
|
ETH Zentrum
HG G 69 |
|
|
| 15:45-16:45 |
Geometry Seminar
Thermodynamical Formalism at the boundary of hyperbolicity for Henon maps
Dr. Samuel Senti, UFRJ
|
ETH Zentrum
HG G 43 |
| Abstract: |
In this joint work with Hiroki Takahasi, we establish the existence and uniqueness of equilibrium measures for the geometric potential -t\log|df| for the Henon map at the first bifurcation parameter. |
| Speakers: |
|
|
| 16:15-17:15 |
Colloquium in Applied and Numerical Mathematics
Sparse Adaptive Tensor Galerkin Approximations of Parametric PDE-Constrained Control Problems
Prof. Dr. Angela Kunoth, Universität Paderborn
|
ETH Zentrum
HG E 1.2 |
| Abstract: |
Optimization problems constrained by linear parabolic evolution PDEs are challenging from a computational point of view, as they require to solve a system of PDEs coupled globally in time and space. For their solution, conventional time-stepping methods quickly reach their limitations due to the enormous demand for storage. For such a coupled PDE system, adaptive methods which aim at distributing the available degrees of freedom in an a-posteriori-fashion to capture singularities in the data or domain, with respect to both space and time, appear to be most promising. Employing wavelet schemes for full weak space-time formulations of the parabolic PDEs, we can prove convergence and optimal complexity. Yet another level of challenge are control problems constrained by evolution PDEs involving stochastic or countably many infinite parametric coefficients: for each instance of the parameters, this requires the solution of the complete control problem. Our method of attack is based on the following new theoretical paradigm. It is first shown for control problems constrained by evolution PDEs, formulated in full weak space-time form, that state, costate and control are analytic as functions depending on these parameters. Moreover, we establish that these functions allow expansions in terms of sparse tensorized generalized polynomial chaos (gpc) bases. Their sparsity is quantified in terms of p-summability of the coefficient sequences for some 0 < p <= 1. Resulting a-priori estimates establish the existence of an index set, allowing for concurrent approximations of state, co-state and control for which the gpc approximations attain rates of best N-term approximation. These findings serve as the analytical foundation for the development of corresponding sparse realizations in terms of deterministic adaptive Galerkin approximations of state, co-state and control on the entire, possibly infinite-dimensional parameter space. The results were obtained jointly with Christoph Schwab. |
| Speakers: |
Prof. Dr. Angela Kunoth
(Universität Paderborn)
|
|
| 17:15-19:00 |
Seminar on Stochastic Processes
The geometric Robinson-Schensted correspondence and the Whittaker process for crystallographic root systems
Reda Chhaibi, Universität Zürich
|
UZH Irchel
Y27 H 25 |
| Abstract: |
The Robinson-Schenstend correspondence is originally a bijection between words and pairs of tableaux. It can be used to define a dynamic on partition called the Schur process. A diffusive limit of the Schur process gives Dyson's Brownian motion. Here, we will present a "geometric Robinson-Schensted correspondence". by taking Brownian motion as input, one finds the Whittaker process, which can be seen as an integrable system of weakly repulsive particles. The construction works in the full generality of arbitrary crystallographic root systems. |
| Speakers: |
Reda Chhaibi
(Universität Zürich)
|
|
| Thursday, May 23 |
| 15:00-17:00 |
ProDoc Seminar
An introduction to motivic homotopy theory
Dr. Marc Levine, Universität Duisburg-Essen, Deutschland
|
ETH Zentrum
HG G 19.2 |
| Abstract: |
There have been a number of constructions of various kinds of categories of motives, ranging from Grothendieck's construction of motives of smooth projective varieties to Voevodsky's trinagulated category of motives over a field and more recently triangulated categories of motives over a base-scheme. In fact, there is a much more basic and simple construction: the motivic unstable homotopy category. In this lecture we will recall the elementary construction of the classical unstable homotopy category and explain how (originally by Morel and Voevodsky) one can extend this construction to give a homtopy theory that contains information about algebraic varieties. We will describe some of the basic features of this theory, give some examples and present some interesting computations. |
| Speakers: |
Dr. Marc Levine
(Universität Duisburg-Essen, Deutschland)
|
|
| 15:15-16:15 |
Talks in Mathematical Physics
From Pauli's Principle to Fermionic Entanglement
Matthias Christandl, ETH Zurich
|
ETH Zentrum
HG G 43 |
| Abstract: |
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected for decades, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Surprisingly, these constraints are linear: they cut out a geometric object known as a polytope. This is a beautiful mathematical result, but are there systems whose physics is governed by these constraints?
In order to address this question, we studied a system of a few fermions connected by springs. As we varied the spring constant, the occupation numbers moved within the polytope. The path they traced hugs very close to the boundary of the polytope, suggesting that the generalized constraints affect the system. I will mention the implications of these findings for the structure of few-fermion ground states and then discuss the relation between the geometry of the polytope and different types of fermionic entanglement. |
| Speakers: |
Matthias Christandl
(ETH Zurich)
|
|
| 16:15-17:15 |
ZüKoSt Zürcher Kolloquium über Statistik
Laplace deconvolution in Regression - Application to angiogenosis follow-up in cancer
Yves Rozenholc, University Paris Descartes, Paris
|
ETH Zentrum
HG G 19.1 |
| Abstract: |
In the context of anti-angiogenic cancer treatments, a major issue is to follow the drug effect. If parametric models have been developed to achieve this goal, they suffer from being tissue-related and, moreover, if their pertinence is already questionable in heathy tissue, they are certainly wrong in tumors where the cell growth changes the nature of the tissue. In order to face these problems, nonparametric modeling of the blood flow exchanges has been imagined early in the 80's and started to be used in the second half of the 90's with the availability of high-frequency imaging techniques. Unfortunately, to date the estimation in such nonparametric models is highly unstable due to high level of ill-posedness.
After recalling the medical context which has motivated our study and describing the associated models, I will present two new nonparametric estimators for Laplace deconvolution in the regression setting. The first estimator is derived from the statistical analysis of Volterra equations of the first type intimately linked to Laplace deconvolution. This point-wised estimate is shown to be adaptive in the sense that it achieves optimal rates of convergence up to the regularity of the unknown function even if this regularity is also unknown. Because this estimator needs the knowledge of the roots of a polynomial, it remains hardly usable from a practical point of view. The second estimator relies on a decomposition of the functions of interest on the basis of the Laplace functions. This global estimator tuned by model selection satisfies an oracle inequality and is easily implementable. This theoretical study is completed by simulations which show the proper behavior of this two estimators.
Collaboration with Charles-A. Cuénod (MD-PhD), Felix Abramovich, Fabienne Comte and Marianna Pensky.
|
| Speakers: |
Yves Rozenholc
(University Paris Descartes, Paris)
|
|
| 17:15-18:15 |
Talks in Financial and Insurance Mathematics
Insider Trading, Stochastic Liquidity and Equilibrium Prices
Prof. Dr. Pierre Collin-Dufresne, EPF Lausanne
|
ETH Zentrum
HG G 43 |
| Abstract: |
We extend Kyles (1985) model of insider trading to the case where liquidity provided by
noise traders follows a general stochastic process. Even though the level of noise trading
volatility is observable, in equilibrium, measured price impact is stochastic. If noise
trading volatility is mean-reverting, then the equilibrium price follows a multivariate
stochastic bridge process, which displays stochastic volatility. This is because insiders
choose to optimally wait to trade more aggressively when noise trading activity is
higher. In equilibrium, market makers anticipate this, and adjust prices accordingly.
More private information is revealed when volatility is higher. In time series, insiders
trade more aggressively, when measured price impact is lower. Therefore, execution
costs to uninformed traders can be higher when price impact is lower. |
| Speakers: |
Prof. Dr. Pierre Collin-Dufresne
(EPF Lausanne)
E-Mail:
|
|
| Friday, May 24 |
| 14:15-15:15 |
Number Theory Seminar
Motives underlying classical homotopy theory
Dr. Marc Levine, Universität Duisburg-Essen
|
ETH Zentrum
HG G 43 |
| Abstract: |
A basic invariant of classical homotopy theory are the stable homotopy groups of spheres. Up to now, no complete computation of these groups is available, but one of the main tools for their computation, the Adams-Novikov spectral sequence, reveals a deep connection with arithmetic aspects of (rank 1 commutative) formal groups. Voevodsky conjectured that the start of this spectral sequence is closely related to another spectral sequence that converges to the motivic analog of the stable homotopy groups of spheres. this second spectral sequence, known as the slice spectral sequence, is a close analog of Grothendieck's filtration by codimension on the cohomology of an algebraic variety. Recently, I uncovered a closer relation between these two constructions, establishing that the motivic slice spectral sequence and the Adams-Novikov spectral sequence agree in all their terms, not just the initial ones. This gives a new, algebro-geometric structure to the Adams-Novikov spectral sequence and conversely, the arithmetic of formal groups is surprisingly present in the slice spectral sequence. We will explain some of the ingredients that go into this connection, interesting in their own right.
|
| Speakers: |
Dr. Marc Levine
(Universität Duisburg-Essen)
|
|
| 16:00-17:00 |
Algebraic Geometry and Moduli Seminar
Compact moduli spaces for slope semistable sheaves
Prof. Dr. Daniel Greb, Universität Bochum
|
ETH Zentrum
HG G 43 |
| Abstract: |
While the variation of moduli spaces of H-slope/Gieseker-semistable sheaves on surfaces under change of the ample polarisation H is well-understood, research on the corresponding question in the case of higher-dimensional base manifolds revealed a number of pathologies. After presenting these, I will discuss recent joint work with Matei Toma (Nancy), which resolves some of these pathologies by looking at curves instead of divisors. This naturally leads to the question whether higher-dimensional analogues of the Donaldson-Uhlenbeck compactification exists, and I will discuss our construction of such a compactification. |
| Speakers: |
Prof. Dr. Daniel Greb
(Universität Bochum)
|
|
| Saturday, May 25 |
| No events scheduled today! |
| No events scheduled today! |
Wichtiger Hinweis:
Diese Website wird in älteren Versionen von Netscape ohne
graphische Elemente dargestellt. Die Funktionalität der
Website ist aber trotzdem gewährleistet. Wenn Sie diese
Website regelmässig benutzen, empfehlen wir Ihnen, auf
Ihrem Computer einen aktuellen Browser zu installieren. Weitere
Informationen finden Sie auf
folgender
Seite.
Important Note:
The content in this site is accessible to any browser or
Internet device, however, some graphics will display correctly
only in the newer versions of Netscape. To get the most out of
our site we suggest you upgrade to a newer browser.
More
information
