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Spring Semester 2010

Date / Time Speaker Title Location
16 March 2010
17:15-18:15 		Prof. Dr. Grigor Mikhalkin
University of Geneva, Switzerland
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Zurich Colloquium in Mathematics

Title (p,q)-homology classes in tropical geometry
Speaker, Affiliation Prof. Dr. Grigor Mikhalkin, University of Geneva, Switzerland
Date, Time 16 March 2010, 17:15-18:15
Location KO2 F 150
Abstract 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.
(p,q)-homology classes in tropical geometryread_more
KO2 F 150
30 March 2010
17:15-18:15 		Prof. Dr. Camillo De Lellis
University of Zurich, Switzerland
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Zurich Colloquium in Mathematics

Title Multiple valued functions
Speaker, Affiliation Prof. Dr. Camillo De Lellis, University of Zurich, Switzerland
Date, Time 30 March 2010, 17:15-18:15
Location KO2 F 150
Multiple valued functions
KO2 F 150
13 April 2010
17:15-18:15 		Prof. em. Dr. Freddy Delbaen
ETH Zurich, Switzerland
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Zurich Colloquium in Mathematics

Title Risk Measures: the mathematcis behind capital requirements for financial institutions
Speaker, Affiliation Prof. em. Dr. Freddy Delbaen, ETH Zurich, Switzerland
Date, Time 13 April 2010, 17:15-18:15
Location KO2 F 150
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.
Risk Measures: the mathematcis behind capital requirements for financial institutionsread_more
KO2 F 150
27 April 2010
17:15-18:15 		Prof. Dr. Alfio Quarteroni
EPFL Lausanne/Politecnico di Milano
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Zurich Colloquium in Mathematics

Title Complexity reduction in PDEs: geometric multiscaling, Steklov-Poincare operators, applications
Speaker, Affiliation Prof. Dr. Alfio Quarteroni, EPFL Lausanne/Politecnico di Milano
Date, Time 27 April 2010, 17:15-18:15
Location KO2 F 150
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.
Complexity reduction in PDEs: geometric multiscaling, Steklov-Poincare operators, applicationsread_more
KO2 F 150
11 May 2010
17:15-18:15 		Prof. Dr. Donald Geman
Johns Hopkins University, Baltimore, USA
Details

Zurich Colloquium in Mathematics

Title Computational Molecular Medicine
Speaker, Affiliation Prof. Dr. Donald Geman, Johns Hopkins University, Baltimore, USA
Date, Time 11 May 2010, 17:15-18:15
Location KO2 F 150
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.
Computational Molecular Medicineread_more
KO2 F 150

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