Pacific Institute for the Mathematical Sciences - PIMS

The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus

Let x and y be points chosen uniformly at random from the four-dimensional discrete torus with side length n. We show that the length of the loop-erased random walk from x to y is of order n2 (log n)^{1/6}, resolving a conjecture of Benjamini and   more››

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Ionic and Metabolic Mechanisms in Pulsatile Insulin Secretion

Insulin is secreted in pulses with a period of about 5 minutes from the beta-cells of the pancreas. These pulses are in turn driven by oscillations of cytosolic calcium. Two parallel streams of investigation over more than two decades have studied   more››

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Subfactors and (1+1)-dimensional TQFTs (Part 2)

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Subfactors and (1+1)-dimensional TQFTs (Part 1)

In this joint work with Vijay Kodiyalam (IMSc, Chennai) and Vishwambhar Pati (ISI, Bangalore), we construct a certain 'cobordism category' D whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-man   more››

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Linearly reductive finite group schemes

I will report on joint work with Dan Abramovich and Martin Olsson. We classify linearly reductive finite group schemes in positive or mixed characteristic, and use this to define a good replacement for the notion of orbifold in positive or mixed c   more››

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System Level Mathematical Analysis of Mitosis

Mitotic spindle goes through distinct morphological states characterized by increasing spindle length and distances between chromosomes. A complete picture of how the spindle assembles is still lacking. We performed an In Silico model screen to id   more››

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Prime numbers, Riemann, and Langlands

Prime numbers have held a mystery over number theory since before Euclid. To introduce a powerful new tool to the subject, Riemann defined his analytic zeta function; with it, he described the Prime Number Theorem and conjectured Riemann's Hypothe   more››

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Geometric flow in Kahler manifold

We will discuss some recent results on the Calabi flow, short time existence, stability and extension theorem. The Calabi flow is a 4th order parabolic flow which is gradient flow of certain convex functional in infinite dimensional space. If we h   more››

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Characterizing projective spaces

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Gravitational allocation of Lebesgue measure to Poisson points

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Summer School on Frontiers in Mathematics and Economics

The summer school brings together graduate students, postdoctoral fellows and young faculty members from business schools, economics, mathematics and operations research with leading economists and mathematicians. It exposes students in business a   more››

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Modelling homotopy n-types in algebraic topology and category theory

Homotopy n-types are topological spaces with trivial homotopy groups in dimension greater than n. They arise naturally in algebraic topology and category theory. Both these areas of mathematics have seen the development of models of n-types. In th   more››

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DIGITAL SNOWFLAKES

Several mathematical models of snow crystal growth will be discussed. For a popular class of cellular automata known as Packard's Snowflakes, one can develop a fairly complete rigorous theory, addressing limiting density, fractal shapes and   more››

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Quantification of Blow-up Levels for a 2-D Elliptic Equation with Critical Exponential Nonlinearity

We study sequences of solutions of some elliptic PDE’s, on 2-dimensional bounded domain, with critical Moser-Trudinger exponential nonlinearity. We prove that lack of compactness occur only when standard bubbles appear and thus we can quantify t   more››

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Motives and Periods

The conference is intended to cover recent developments in the study of motives and periods with an emphasis to the connections to physics, arithmetic and algebraic cycles. The conference has an instructional component which consists of a series   more››

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Probability Seminar 2006

On the existence of cut points for Brownian motion on fractals   more››

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Quantum Information Theory for Mathematicians

In this talk I will give an overview of quantum information theory, with an emphasis on some of the underlying mathematics. In particular, quantum algorithms depend on a physical property of quantum systems,entanglement, which may be characterized   more››

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MITACS Math Biology Seminar 2006

Rolling is an important manifestation of biological cell adhesion, especially for the leukocyte cell in the immune process. It combines several phenomena such as the affinity, the junction and failure between specific adhesion molecules, and an ac   more››

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On simplicity of the second Neumann eigenvalue: What every mathematician should know about analysis on

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Algebraic Topology Seminar 2006

We study the concepts of homotopy disjointness and homotopy disjointness by small deformation for mappings between spheres. Joint work with Daciberg Goncalves produced the following result. The existence of a mapping f: S^(4n-2)   more››

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