Zurich colloquium in mathematics

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Date / Time

Speaker

Title

Location

16 March 2010
17:15-18:15

Prof. Dr. Grigor Mikhalkin
University of Geneva, Switzerland

Event Details

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

Event Details

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

Event Details

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

Event Details

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

Event Details

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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