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May 21 to 25, 2012

Monday, May 21

13:15-14:15

Advanced Seminar in Algebraic Geometry (uzh)
Unramified cohomology
Prof. Dr. Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York University

Uni Irchel
Y27 H 28

Speakers:

Prof. Dr. Yuri Tschinkel (Courant Institute of Mathematical Sciences, New York University)

15:15-16:15

Symplectic Geometry Seminar
Lagrangian correspondences - a toric case study
Dr. Ana Cannas da Silva, ETH Zürich
Dr. Meike Akveld, ETH Zürich, Switzerland

ETH Zentrum
HG G 43

Abstract:

This is a review talk given jointly by Meike Akveld and Ana Cannas da Silva.

Speakers:

Dr. Ana Cannas da Silva (ETH Zürich)

Dr. Meike Akveld (ETH Zürich, Switzerland)

E-Mail:

Homepage: http://www.math.ethz.ch/people/akveld

16:30-18:00

Optimization and Applications Seminar
No Seminar in favor of the Farewell Lecture of Hans-Jakob Lüthi

ETH Zentrum
HG G 19.1

17:15-18:00

Farewell Lectures
Ausgerechnet Operations Research
Prof. Dr. Hans-Jakob Lüthi, ETH Zurich, Switzerland

ETH Zentrum
HG F 30

Speakers:

Prof. Dr. Hans-Jakob Lüthi (ETH Zurich, Switzerland)

Tuesday, May 22

15:15-16:15

Analysis Seminar
Two uniqueness results for the two-dimensional continuity equation with velocity having L^1 or measure curl
Prof. Dr. Gianluca Crippa, Universität Basel

ETH Zentrum
HG G 43

Abstract:

In this seminar I will present two results regarding the uniqueness
(and further properties) for the two-dimensional continuity equation
and the ordinary differential equation in the case when the vector
field is bounded, divergence free and satisfies additional conditions
on its distributional curl. Such settings appear in a very natural way
in various situations, for instance when considering two-dimensional
incompressible fluids. I will in particular describe the following two
cases:
(1) The vector field is time-independent and its curl is a (locally
finite) measure (without any sign condition).
(2) The vector field is time-dependent and its curl belongs to L^1.
Based on joint works with: Giovanni Alberti (Universita' di Pisa),
Stefano Bianchini (SISSA Trieste), Francois Bouchut (CNRS &
Universite' Paris-Est-Marne-la-Vallee) and Camillo De Lellis
(Universitaet Zuerich).

Speakers:

Prof. Dr. Gianluca Crippa (Universität Basel)

17:15-18:15

Zurich Colloquium in Mathematics
Fibrations in rational surfaces and their sections
Brendan Hassett, Rice University, Houston, TX, USA

UZH Zentrum
KO2 F 150

Abstract:

A fibration is a surjective morphism from a smooth projective variety to a smooth curve, all defined over a field k. Assume the fibers are rational surfaces. Then every fibration admits a section, when k is algebraically closed. There is a conjectural framework for deciding whether there is a section when k is finite, expressed in terms of the Brauer group and the existence of local sections.

Our approach to these questions hinges on understanding the geometry of the scheme parametrizing all sections of our fibration, especially in contexts where the rational surfaces are relatively simple, e.g., quadric surfaces and intersections of two quadric hypersurfaces. The main application is the existence of sections provided the fibration is sufficiently general, in a sense that can be made precise.

(Joint with Yuri Tschinkel)

Speakers:

Brendan Hassett (Rice University, Houston, TX, USA)

Wednesday, May 23

13:00-15:00

FIM Minicourse
Stochastic Variational Analysis
Prof. Dr. Roger Wets, University of California, Davis, USA

ETH Zentrum
HG G 43

Abstract:

Stochastic Variational Analysis emerged in response to the need of solving (generalized) equations systems, optimization and variational problems whose parameters are, in part, stochastic. Problems of this type arise in stochastic optimization, stochastic equilibrium problems, uncertainty quantification, statistical estimation problems that turn up in a broad variety of engineering, economics, finance, energy networks, signal processing, ecology and biological problems. These lectures will be introductory in nature, and as much as time will allow, will concentrate on applications. Because the solutions to such systems arent generally unique, one cant rely on classical probabilistic techniques to either describe their solutions or find (probabilistic) approximations that might, in turn, be based on standard laws of large numbers and associated asymptotic analysis. The foundations of the theory lie in an understanding of the geometry and the analytic (topological) properties of random sets, including a suitable translation to a functional setting, coupled with both appropriate laws of large numbers, i.e., what can be learned from large samples, and fundamental inequalities, i.e., what can be learned from small samples. This dual approach is fundamental to the potential applications of the theory in practical settings.

Speakers:

Prof. Dr. Roger Wets (University of California, Davis, USA)

15:00-16:00

FIM Announcements
FIM Tea

ETH Zentrum
HG G 69

15:45-16:45

Geometry Seminar
Essential manifolds and macroscopic dimension
Prof. Dr. Alexander Dranishnikov, University of Florida, USA, and FIM

ETH Zentrum
HG G 43

Abstract:

Gromov introduced the notion of macroscopic dimension to study manifolds with positive scalar curvature. He conjectured that the rational essentiality of an n-manifold implies that its universal cover has macroscopic dimension equal n. We will discuss this and some other related conjectures.

Speakers:

Prof. Dr. Alexander Dranishnikov (University of Florida, USA, and FIM)

16:15-17:15

Colloquium in Applied and Numerical Mathematics
Boundary value problems on polyhedral domains and applications to quasi-optimal rates for the Finite Element Method
Prof. Dr. Victor Nistor, Penn State University, USA

ETH Zentrum
HG E 1.2

Abstract:

I will first review some of the issues and earlier results on boundary value problems on polyhedral domains. The main lesson is that there is a 'loss of regularity' for boundary value problems on singular domains if the usual Sobolev spaces are used. This is inconvenient however in practical applications such as the Finite Element Method. An alternative approach is to use 'weighted Sobolev' spaces. Then one can then restore full regularity for elliptic problems on such domains under the additional condition of that there are no 'Newmann-Newmann' corners or edges (joint result with Bacuta, Mazzucato, and Zikatanov). The case of 'Newmann-Newmann' corners requires some additional ideas. I will then present some results in this case in two dimensions and how they can be used to construct sequences of Finite Element Spaces that provide quasi-optimal approximation rates for transmission and pure Neumann problems (joint work with Mazzucato and Li). This method is then generalized to three dimensions.

Speakers:

Prof. Dr. Victor Nistor (Penn State University, USA)

17:15-18:15

Seminar on Stochastic Processes
A trajectorial interpretation of entropy dissipation and a non-intrinsic Bakry-Emery criterion
Joaquin Fontbona, University of Santiago de Chile

UZH Irchel
Y27 H 25

Abstract:

We develop a pathwise description of the dissipation of general convex entropies for continuous time Markov processes, based on simple backward martingales and convergence theorems with respect to the tail sigma field. The entropy is in this setting the expected value of a backward submartingale. In the case of (non necessarily reversible) Markov diffusion processes, we use Girsanov theory to explicit its Doob-Meyer decomposition, thereby providing a stochastic analogue of the well known entropy dissipation formula, valid for general convex entropies (including total variation). Under additional regularity assumptions, and using Itô calculus and some ideas of Arnold, Carlen and Ju, we obtain a new Bakry Emery criterion which ensures exponential convergence of the entropy to 0. This criterion is non-intrinsic since it depends on the square root of the diffusion matrix, and cannot be written only in terms of the diffusion matrix itself. We provide an example where the classic Bakry Emery criterion fails, but our non-intrinsic criterion ensuring exponential convergence to equilibrium applies without modifying the law of the diffusion process. Joint work with Benjamin Jourdain (Cermics ENPC, Paris).

Speakers:

Joaquin Fontbona (University of Santiago de Chile)

Thursday, May 24

15:15-16:15

Talks in Mathematical Physics
Universality in Lie algebras and Chern-Simons theory
Alexander Veselov, Loughbourough University, UK

ETH Zentrum
HG G 43

Speakers:

Alexander Veselov (Loughbourough University, UK)

16:00-17:00

Seminar in Partial Differential Equations and Numerics (uzh)
A space-time boundary integral equation approach for the numerical solution of exterior wave equation problems
Prof. Dr. Giovanni Monegato, Politecnico di Torino

Uni Irchel
Y27 H 12

Speakers:

Prof. Dr. Giovanni Monegato (Politecnico di Torino)

16:15-17:30

Zurich Graduate Colloquium (uzh)
Cluster algebras and Grassmannians
Sira Gratz, Leibniz Universität Hannover

ETH Zentrum
HG G 19.2

Speakers:

Sira Gratz (Leibniz Universität Hannover)

17:15-18:15

Talks in Financial and Insurance Mathematics (CANCELLED)
Arrow-Debreu Equilibria for Rank-Dependent Utilities
Prof. Dr. Xunyu Zhou, University of Oxford

ETH Zentrum
HG G 43

Abstract:

We provide conditions on a single period, two-date pure exchange economy with rank-dependent utility agents under which Arrow-Debreu equilibria exist. When such an equilibrium exists, we derive the state-price density explicitly, which is a weighted marginal rate of substitution between initial and end-of-period consumption of a representative agent, while the weight is expressed through the differential of the probability weighting function. A key step in our derivation is to obtain an analytical solution to the individual consumption problem that involves the concave envelope of
certain non-concave function. Our results indicate that, under a "weighting-neutral probability" that is an appropriate modification of the original probability measure, assets can be priced in the same way as in an economy with expected utility agents.

Speakers:

Prof. Dr. Xunyu Zhou (University of Oxford)

Friday, May 25

14:15-15:15

Number Theory Seminar
Bounding sup norms of automorphic forms
Dr. Guillaume Ricotta, ETH Zurich

ETH Zentrum
HG G 43

Abstract:

I will describe one possible way to bound the sup-norm of GL(n)-automorphic forms in several aspects including the spectral parameter and the level.

Speakers:

Dr. Guillaume Ricotta (ETH Zurich)

Homepage: http://www.math.u-bordeaux1.fr/~ricotta/

Saturday, May 26
No events scheduled today!
No events scheduled today!

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