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ALGEBRA SEMINAR

"Vector Bundles of Rank 2 on the grassmannian of lines in P3"

First, I will discuss some facts, results, and perspectives concerning vector bundles of rank 2 on the grassmannian. Then I will state a conjecture. The work I have done on this conjecture leads to the question of whether a very specific, very singular sub-scheme of the grassmannian exists. This is related to an important result in commutative algebra.

GRADUATE STUDENT COLLOQUIUM

"Determining the biomechanical response of a filiform hair array: A low Reynolds number fluid-structure model"

The cercal  system of the cricket has served as a model sensory system over the last 30 years and has been the subject of many anatomical, developmental, functional, and theoretical studies during that time. This system is composed of two antenna-like appendages covered with hundreds of filiform mechanosensory hairs, and encodes information about the direction and dynamics of low-velocity air currents. Many previous studies have characterized the biomechanics of individual filiform hairs, but only a few have considered the fluid- mediated interaction of closely-packed hairs. These few studies suffer from one of two disadvantages: either the modeled  hair arrangements are limited in extent or configuration, or the computational cost is prohibitive. I present a fast and scalable numerical model of filiform hair motion that can simulate the motion of arbitrary hair arrangements on the cricket cercus. Using this model, I perform numerical simulations that demonstrate the possibility for both damping and synergistic coupling within biologically realistic groupings of filiform hairs.

First National Forum of Young Topologists

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PROBABILITY AND STATISTICS SEMINAR

"Optimal control of a stochastic network driven by a fractional Brownian motion input"

We consider a stochastic control model driven by a fractional Brownian motion.  This model is a formal approximation to a queueing network with an ON-OFF input process.  We study stochastic control problems associated with the long-run average cost, the infinite horizon discounted cost, and the finite horizon cost. In addition, we find a solution to a constrained minimization problem as an application of our solution to the long-run average cost problem. We also establish Abelian limit relationships among the value functions of the above control problems.

ALGEBRA SEMINAR

"Vector Bundles of Rank 2 on the grassmannian of lines in P3 - PART 2"

I will continue my presentation from last week: First, I will restate and explain the rationale for a conjecture concerning rank 2 vector bundles on the grassmannian. Then I will discuss the progress I have made on a special case of the conjecture. This involves a very specific, very singular sub-scheme of the grassmannian and an important result in commutative algebra.

COLLOQUIUM

"Self-Similar Gaussian Random Fields and Their Fractal Properties"

Self-Similar Gaussian random fields are useful as stochastic models in many applied areas and their sample functions are often random fractals. In this talk we present some results on construction of Gaussian random fields and on their geometric and asymptotic properties.

Refreshments in Gibson 426 after the talk

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