ETH :: D-MATH :: Zurich Colloquium in Mathematics

Just like their classical (complex) counterparts, tropical manifolds carry homology theories. In the talk we will look at the simplicial and singular homology groups of tropical manifolds. However, unlike the classical case, we can directly trace (p,q)-contributions (to the h^{p,q} Hodge numbers) already in this very topological language.

In good cases a tropical manifold is approximable by a 1-parametric family of complex manifolds. The tropical homology carries not only the corresponding degenerations of the Dolbeaut (p,q)-groups, but also the corresponding monodromy operator. Its tropical manifistation, "tropical wave", looks in many ways similar to the tropical hyperplane section.

The talk is based on a work in progress joint with I. Itenberg and I. Zharkov.

Speakers:

Prof. Dr. Grigor Mikhalkin (University of Geneva, Switzerland)

Mar. 30, 2010

Camillo De Lellis

Multiple valued functions

Speakers:

Prof. Dr. Camillo De Lellis (University of Zurich, Switzerland)

Apr. 13, 2010

Freddy Delbaen

Risk Measures: the mathematcis behind capital requirements for financial institutions

Abstract:

The capital requirements for financial institutions should satisfy rules that encourage diversification, avoid risk concentration and take into account the time aspect of uncertainty. They also should allow to allocate, in a consistent way, the risk capital to the different branches of the financial institution. This is best done via convex, time consistent risk measures, a mathematical concept that is based on the theory of stochastic processes, backward stochastic differential equations and semi-linear PDE.

Speakers:

Prof. em. Dr. Freddy Delbaen (ETH Zürich, Switzerland)

E-Mail:

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

Apr. 27, 2010

Alfio Quarteroni

Complexity reduction in PDEs: geometric multiscaling, Steklov-Poincare operators, applications

Abstract:

Mathematical models of complex physical problems can be based on heterogeneous differential equations, i.e. on boundary-value problems of different kind in different subregions of the computational domain. In this presentation I will introduce some elementary examples and illustrate the way the coupling conditions between the different models can be devised. Then several solution algorithms will be proposed and a few representative applications to blood flow modeling, sports design, and the environment will be addressed.

Speakers:

Prof. Dr. Alfio Quarteroni (EPFL Lausanne/Politecnico di Milano)

May. 11, 2010

Donald Geman

Computational Molecular Medicine

Abstract:

I will talk about several projects in computational biology, including biomarker discovery, molecular network modeling and pathway-level cancer analysis. There are two objectives in each case, namely biological understanding and translational medicine, meaning bridging the gap between fundamental research and clinical practice. Both require new methodology in statistics and machine learning in order to overcome the main technical barrier: measured against the complexity of the processes (e.g., gene regulation), and the dimension of the data (e.g., DNA microarrays), the number of available samples is minuscule. Both objectives also require avoiding the "black box" decision rules generated by standard methods in computational learning. These are enormous challenges and may not be feasible without further advances in the "-omics" technologies.

Speakers:

Prof. Dr. Donald Geman (Johns Hopkins University, Baltimore, USA)

May. 18, 2010

Ed Frenkel

t.b.a. (CANCELLED)

Speakers:

Prof. Dr. Ed Frenkel (University of California, Berkeley, USA)

Alle Interessentinnen - insbesondere auch die Studierenden beider Hochschulen - sind herzlich eingeladen. Im Anschluss an das Kolloquium findet ein Apéro statt.

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