Center for Computational Molecular Biology Seminar
Abstract: The question how genetic variation and personal health are linked is one of the compelling puzzles facing scientists today. The ultimate goal is to exploit human variability to find genetic causes for multi-factorial diseases such as cancer and coronary heart disease. Recent technology improvement enables the typing of millions of single nucleotide polymorphisms (SNPs) for a large number of individuals. Consequently, there is a great need for efficient and accurate computational tools for rigorous and powerful analysis of these data. In my talk I am going to concentrate on two computational problems, which are an essential step in studying the data obtained by this technology: Accurate and efficient significance testing with a correction for population stratification and estimating local ancestries in admixed populations.
Brown Analysis Seminar
Abstract: A typical random matrix problem is concerned with the eigenvalue distributions of matrices whose elements are random variables. In the most famous, and still the most common, applications, physical considerations dictate that the matrices have a few restrictions (such as being symmetric), but the matrix elements are otherwise taken to be independently and identically distributed. However, there are many random matrix applications in which correlations between the matrix elements play a significant role. Physical problems often have conservation laws which tie together all of the elements in a row, for example. Disordered condensed matter problems, in particular, present situations in which each row corresponds to a statistically distributed physical location, meaning that there are additional correlations between matrix elements induced by the geometry of space. This talk will show how such correlated random matrix problems arise when one tries to understand the molecular behavior of liquids. It will also use numerical results and approximate analytical means to show some of what is known and unknown about the solutions to these problems.
Probability Seminar
Abstract: I will present some new developments in Mathematical Finance on optimal portfolio choice. A new concept of stochastic optimal utility is introduced. The maximal utility (forward performance process) solves a fully nonlinear SPDE whose form, in terms of market input, resembles the one arising in term-structure models. Explicit solutions for the optimal wealth and investment processes are obtained via the (subordinated) risk tolerance process which is functionally related to a fast diffusion equation. The connection of the forward performance to the classical utility is also discussed.
PDE Seminar
Abstract: In this talk I will present the Lojasiewicz-Simon approach in the study on convergence of solution to equilibrium for nonlinear evolution equations including Cahn-Hilliard equation, parabolic-hyperbolic phase-field equations, etc..
Department of Mathematics Colloquium
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