Pacific Institute for the Mathematical Sciences - PIMS

Complex Geophysical Gravity Currents

Scientific Event

Almost-primes represented by quadratic polynomials

Dirichlet's theorem on primes in arithmetic progressions characterizes those linear polynomials which take on prime values infinitely often. However, this is where the current state of knowledge ends. For the case of polynomials with higher degree   more››

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Goldton-Yildirim-Pintz and small gaps between primes

I'll give an expository talk, following the recent article of Soundararajan, on the theorem of Goldston, Yildirim, and Pintz that there are infinitely many primes p such that the next prime q satisfies q – p = o(log p).   more››

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On Card Shuffling

I will talk about some famous results of Bayer and Diaconis (1992) which permit a rigorous answer to the following question: given a deck of n cards, how many times should it be shuffled so that the deck is in approximately random order? The goal   more››

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Littlewood-Richardson coefficients: Reduction formulae and a conjecture by King, Tollu and Toumazet

Littlewood-Richardson coefficients are structural constants of the cohomology ring of Grassmannians and the ring of Schur functions, and they are counted by the number of skew tableaux with certain properties. In this talk, we introduce well   more››

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Detecting Spillover: A dynamical systems modeling approach to glutamatergic synaptic signaling

The connectivity of neurons in the hippocampus depends in part on whether neurotransmitter from one release site can leak out and activate receptors in another synapse or extrasynaptic patch. The existence of such 'spillover' is under debate in th   more››

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Computational Studies of the Motion of a Nematic LCP in a Simple Shear Device

TBA   more››

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Twisted K-theory (old and new), Part II

Twisted K-theory in terms of Banach algebras and Fredholm operators in an Hilbert space. Some computations.   more››

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Twisted K-theory (old and new), Part I

The Brauer group of a space and of a finite group. How are they related to K-theory?   more››

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Homological Stability, Part II

Homological stability theorems have been proved for many families of groups like symmetric groups, linear groups, mapping class groups of surfaces and of 3-manifolds. I will review some examples and explain how such theorems are proved. As a more   more››

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Smooth Surfaces and Sharp Junctions

Because of their ability to form blends, respond to contact and produce both organic shapes as well as man made objects, implicit surfaces have the potential for uses other than the traditional clouds and water droplets. Models can be built with e   more››

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On Robust Utility Maximization

We study the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be achieved for loga   more››

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The lace expansion and the enumeration of self-avoiding walks

The lace expansion is an elegant combinatorial construction that provides a recursion relation for the number of self-avoiding walks. We first give an introduction to the lace expansion, and then explain how it has been used recently (in joint wor   more››

Scientific Event

Homological Stability, Part I

Homological stability theorems have been proved for many families of groups like symmetric groups, linear groups, mapping class groups of surfaces and of 3-manifolds. I will review some examples and explain how such theorems are proved. As a more   more››

Scientific Event

Leray-type regularizations of the Burgers and the isentropic Euler equations

We start from the Burgers equation vt + vvx = 0 and investigate a smoothing mechanism that replaces the convective velocity v in the nonlinear term by a smoother velocity field u. This type of regularization was first proposed in 1934 by Leray, wh   more››

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Essential dimension and algebraic stacks

The talk will be preceded by an organizational meeting. I will discuss recent work with Z. Reichstein and A. Vistoli on the subject of essential dimension.   more››

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Episodic Slow Slipping of Seafloor under Cascadia: What Physical Processes cause Aseismic Deformation Transients?

In several shallow-dipping subduction zones, including Cascadia, the seafloor undergoes episodes of more rapid than usual creep-slippage under the overlying margin, but at rates vastly slower than usual earthquake slip. In some locations, also inc   more››

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Culler-Shalen (semi-)norms

Let M be a 3-manifold with boundary consisting of one torus. I will show how Culler and Shalen defined a norm on the (real) Dehn-surgery space R2=H_1(partial M; R) associated to the canonical component of the character variety of M. I will then sh   more››

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Descriptive Complexity

Neil Immerman is one of the key developers of 'descriptive complexity', which he is currently applying to research in model checking, database theory, and computational complexity theory. Immerman is the winner, jointly with Róbert Szelepcsényi,   more››

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The term structure of interest rates

The interest rate r(t,t+x) between time t and time t+x is a smooth function of x, say ho_t(x). We consider ho_t as a stochastic process on (0,infty) into a suitable Hilbert space of curves, and we seek to define it as the solution of   more››

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