***HOLIDAY***
CCMB Distinguished Lecture Series
Abstract: This talk will introduce the importance of RNA and the use of partition functions to predict the ensemble behavior of RNA structure formation. RNA secondary structure is the set of canonical base pairs (A-U, G-C, and G-U) in the structure. A set of nearest neighbor parameters, derived from experiments, exist for predicting the stability, as measured by free energy change, of a given secondary structure. The nearest neighbor parameters can be used in conjunction with dynamic programming algorithms to find the lowest free energy structure or the probabilities of all possible pairs in the folding ensemble. I will discuss our recent work with predicting structures that maximize expected accuracy, where expected accuracy is defined as the sum of the base pairing probabilities for pairs and the single-stranded probabilities for unpaired nucleotides. Maximizing expected accuracy improves the quality of structure prediction. I will also discuss our recent work with predicting effective siRNA sequences using a full equilibrium approach. An siRNA can silence the expression of message RNA by hybridizing to the target and directing cleavage via the RNA interference pathway. Here we use the statistical mechanics of hybridization to select sequences that are most likely to lead to effective silencing of a given message.
Mathematics Colloquium
Abstract: Actions of the Lie algebra sl(2) on vector spaces arise naturally in combinatorics, geometry, and algebra. Actions of sl(2) on categories are also quite natural and lead to powerful equivalences. These ideas are orginally due to Chuang-Rouquier in the context of representations of the symmetric group and have recently been used by myself, Cautis, and Licata in a geometric context.
Scientific Computing Seminar
Abstract: The basic model of atmospheric flow is the "Shallow-Water" system (on the sphere). It is a complicated system of nonlinear hyperbolic equations, involving material discontinuities, shocks and other wave patterns. The aim of this talk is an attempt to deal with some features (theoretical and computational) of the system by using a simplified scalar model, namely, a class of nonlinear scalar hyperbolic equations on surfaces. They are the "geometric" equivalents of the famous Burgers equation. The theory of existence and uniqueness is stated (uniqueness is implied by a suitable version of the entropy condition). A numerical finite-volume scheme is introduced (generalization of the Godunov method). Its convergence can be demonstrated (for the first-order version). Some numerical results are presented, showing a very rich collection of steady-state solutions, solutions confined to designated domains and more. (Joint work with J. Falcovitz and Ph. LeFloch).
PDE Seminar
Abstract: In this talk we present some global (spacetime) estimates of oscillatory integrals that serve as basic tools in the derivation of global well-posedness results for certain nonlinear dispersive equations in two space dimensions. The above-mentioned estimates are of two types: a)Generalizations of the famous Van-der-Corput lemma. b) A general class of cubic polynomial phase functions (in two dimensions). Some aspects of the (affine) classification of such polynomials go back to Newton.
<--- 2008 Index