Pacific Institute for the Mathematical Sciences - PIMS

The Rotor-router model and Diaconis-Fulton Addition

Given two sets A and B in the lattice, the Diaconis-Fulton sum is a random set obtained by putting one particle in every point of the symmetric difference, and two particles in every point of the intersection, of A and B. Each 'extra particle' per   more››

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Computation of plurigenera of a canonical threefold

For a canonical threefold, there are few known results about plurigenera. We know that a sufficient multiple of canonical divisor generates a nontrivial linear system and that there is a universal multiple. In this talk, we are going to introduce   more››

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For making genetic networks operate robustly, unintelligent non-design suffices

Five years ago we (George von Dassow, Ed Munro, Eli Meir, and Garrett Odell) made mathematical/computer models of two ancient and famous genetic networks that act early in diverse embryos to establish spatial gene expression patterns prefiguring t   more››

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Micro Fluid Mechanics: Some Interface Dynamics Problems

Interface dynamics is of considerable importance in multiphase microfluidic devices such as microheat pipes, and in dewetting dynamics. We consider a liquid meniscus inside a wedge of included angle [pic] that wets the solid walls with a contact a   more››

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A Geometric Proof of the Blakers-Massey Theorem

In this talk we give a geometric proof of the Blakers-Massey Theorem using Mather's Cube Theorems. As an application, we use this result to compute the James Splitting of Omega S^n.   more››

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Multi-level Micro-Finite Element Analysis for Human Bone Structures

Using microarchitectural bone imaging, it is possible to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. In combination with microstructural finite element (microFE) analysis this could p   more››

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Generic subsets of Thompson's group

Richard Thompson constructed an example of a group which is called 'F'that has many unusual properties. One way to consider its elements is in terms of pairs of rooted binary trees. This viewpoint lends itself nicely to counting subsets of el   more››

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Modeling relapse in infectious diseases

An integro-differential equation is proposed to model a general relapse phenomenon in infectious diseases including herpes. The basic reproduction number Ro for the model is identified and a threshold property of Ro established. For the case of a   more››

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A Galois correspondence for reductive groups and applications to the First Fundamental Theorems

Following some unpublished ideas of Lex Schrijver we will explain a new approach to the First Fundamental Theorems (FFTs) from classical invariant theory. It uses the tensor product of the two tensor algebras $T(V)$ and $T(V^*)$ with the aim to se   more››

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Open problems related to certain mathematical models for MEMS: The dynamical case

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SL(2,C) Character Varieties of 3-Manifold Groups

In continuation of the intro from last time, I will give an overview of some applications of SL(2,C) character varieties to 3-manifold topology. We will then discuss possible topics for the following seminars and will assign speakers.   more››

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Random walk in random environment on a strip

I am going to define the model, discuss briefly an interesting particular case of it, and present some limit theorems recently obtained for RWRE on strips. I am going to build my talk around the comparison of this model to the well-studied RWRE on   more››

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Finite subset spaces of the circle and a theorem of Bott

By considering the circle as the boundary of the hyperbolic plane we are able to describe the first three unordered configuration spaces of the circle by considering them as particular quotients of the group of isometries of the hyperbolic plane.   more››

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Galloping instability of viscous shock waves

This is joint work with Kevin Zumbrun (Indiana University). Motivated by physical and numerical observations of time oscillatory galloping, spinning, and cellular instabilities of detonation waves, we study Poincare--Hopf bifurcation of traveling-   more››

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Dynamic Asset Allocation: a Portfolio Decomposition Formula and Applications

This paper establishes a new decomposition of the optimal portfolio policy in dynamic asset allocation models with arbitrary vNM preferences and Ito prices. The formula rests on a change of num'{e}raire which consists in taking pure discount bonds   more››

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A stochastic two-state signalling module with negative feedback

Motivated by the negative feedback calcium exerts on the gating dynamics of a calcium-conducting ion channel in olfactory receptor neurons, we develop an abstract two-state (open/closed) signalling module with negative feedback. The coupling betwe   more››

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Stochastic control and optimal design of a heat mill.

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Perfect Matchings under Vertex Deletion

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Hedging Under Jump Diffusion with Transaction Costs

In this talk, we consider the problem of hedging a contingent claim, where the underlying asset follows a jump diffusion process. The no-arbitrage value of the claim is given by the solution of a Partial Integro-Differential Equation (PIDE), which   more››

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Canonical metrics and collapsing manifolds

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