## Scientific Lectures

- 11-Jun-07

- 4-Jun-07

- 28-May-07

- 25-May-07

Mathematics: An experimental Science

We'll discuss some recent results that were conjectured via computer experiments and then proved. The examples will be drawn from number theory, Young tableaux, hypergeometric determinant evaluation, theory of matrices of 0s and 1s, etc. Several u more››

University of British Columbia

- 23-May-07

Invasion percolation on regular trees

Invasion percolation is a dynamic process closely linked to critical percolation, but without an external parameter. In joint work with Omer Angel, Frank den Hollander and Gord Slade we showed that the cluster of inva more››

University of British Columbia

- 23-May-07

Making a Splash, Breaking a Neck: The development of complexity in physical systems

The fundamental laws of physics are very simple. They can be written on the top half of an ordinary piece of paper. The world about us is very complex. Whole libraries hardly serve to describe it. Indeed, any living organism exhibits a degree of c more››

University of Washington

- 22-May-07

The Good, the Bad, and the Awful: Scientific Simulation and Prediction

Worthwhile computer simulations are done to explore uncharted territory, resolve a well-posed scientific or technical question, or to make a design choice. Some excellent work is reviewed. Some less happy stories are recounted. I th more››

University of Washington

- 22-May-07

Eigenvalue Problem and a New Product in Cohomology of Flag Varieties

This is a report on my joint work with P. Belkale. We define a new commutative and associative product in the cohomology of any flag variety G/P (which still satisfies the Poincaré duality) and use this product to generate certain inequalities wh more››

University of Washington

- 21-May-07

- 18-May-07

Markov Chains and Web Ranking: a Multilevel Adaptive Aggregation Method

Google's PageRank method for ranking web pages models how a `random surfer' follows links between web pages in a random fashion. The stationary probability vector of the resulting Markov chain provides a ranking of all the pages in the network. Ca more››

University of British Columbia

- 17-May-07

- 16-May-07

Oscillating random walk on Z driven by its occupation time at zero

I will consider a nearest-neighbor random walk X_n on integers with the drift at time n (conditional on the past expectation of $X_{n+1}-X_n$) equals to $-sign(X_n)f^{-1}(eta_n),$ where eta_n is the number of visits to zero by time n and f(n) is a more››

University of British Columbia

- 15-May-07

Differences of semigroups, eigenvalue bounds, and their application to Schroedinger operators

TBA more››

University of British Columbia

- 11-May-07

Non-reductive group actions and symplectic implosion

Given a linear action of a complex reductive group on a projective variety X, geometric invariant theory provides us with an open subset of X (the set of stable points) which has a well-behaved quotient, and a compactification of this quotie more››

University of Washington

- 9-May-07

Boundary Value Problems for Elliptic PDEs and the Morse Index

A symplectic view of linearized elliptic problems leads naturally to the formulation of an appropriate Maslov Index. This is well-known in one space dimension and is generalized here to domains in higher space dimensions. The result is a Morse Ind more››

University of British Columbia

- 9-May-07

Gamma-Convergence and Saddle Points

We prove a theorem asserting, roughly speaking, that if a sequence of functionals converges to a limiting functional (in the sense of Gamma-convergence, a natural and widely-used notion in the calculus of variations), and if the limiting functiona more››

University of British Columbia

- 8-May-07

Going with Flow and Updating Ocean Models

Much data in the ocean come from Lagrangian instruments that float or drift. Mathematical issues arise from the need to assimilate these and other data into ocean models. more››

University of Washington

- 7-May-07

We analyze portfolio credit risk in light of dynamic "frailty," in the form of incompletely observed covariates. Common dependence by firms on unobservable time-varying default covariates is estimated to cause large changes in conditiona more››

University of British Columbia

- 4-May-07

In these two lectures I will survey my recent work with Lupercio and Xicotencatl on the properties of the homology of the free loop space of an orbifold. In the first lecture I will review the work of Chas and Sullivan on string topology and I wil more››

University of British Columbia

- 2-May-07

Spanning Trees, Random Graphs, and Random Walks

In the usual Erdõs-Rényi model of random graphs, each pair of n vertices is connected by an edge independently with probability c/n for some constant c. When c > 1, it has a unique 'giant' component. How quickly does the number of spannin more››

University of British Columbia