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GRADUATE STUDENT COLLOQUIUM

"The Holonomic Systems Approach"

The Holonomic Systems Approach was proposed in the early 1990s by D.  Zeilberger and has turned out to be extremely useful when dealing with special functions in computer algebra. Moreover, his celebrated algorithm for definite hypergeometric summation originates from this approach. We want to give an introduction to the underlying ideas---Ore algebras, Groebner bases, creative telescoping---in an intuitive and therefore non-rigorous way. We also show various examples where these concepts can be successfully applied.

ALGEBRA SEMINAR (Lecture Series)

"Lecture Series on From Sums of Squares To Secant Varieties: Evolution of an Idea" (Part I)

In these talks I would like to explain how some famous theorems of elementary number theory, which have analogues for polynomials in several variables, have given rise to interesting questions and investigations in commutative algebra and algebraic geometry.

Moreover, these purely geometric results have had practical applica tions in such diverse areas as: computational complexity (in particular,finding effcient algorithms for matrix multiplication) mathematical biology (in particular, on the genome project) and algebraic statistics.

COLLOQUIUM

"The Challenge of Simulating  Fluid Flow Accurately in the Presence of Boundaries"

Abstract:

The physical world has a rich diversity of fluid dynamics, ranging from the micron scale to the galactic scale, and varying from high Mach number compressible flows to low Mach number incompressible flows. Large variations in scales, flow properties, and surrounding environments pose many challenges for computations. These issues are particularly important in domains with boundaries. Much of the scientific and technological impact of the Navier-Stokes equations derives from the effect of no-slip boundary conditions in creating physical phenomena such as lift, drag, boundary-layer separation and vortex shedding, for which the behavior of the pressure near boundaries is of great significance. In this talk, I will present new equivalent formulations of Navier-Stokes equations (NSE) better suited for numerical computations. The emphasis will be on the enforcement of imcompressibility and the discovery of intrinsic stability properties that lead to accurate, efficient and practical computations of three dimensional problems. I will also present some efficient methods for more completed flows such as low-mach flow, MHD, kinetic equations with different scales.

Refreshments in Gibson 426 after the talk

APPLIED COMPUTATIONAL MATHEMATICS SEMINAR

"Modeling and analysis of collective behavior of self-propelled agents"

Collective behaviors of self-propelled agents (representing birds, fishes, cars, etc) such as flocking, swarming, trail formulation, attract much of recent research activities in applied mathematics. In this talk, I will discuss some of the recent developments in modeling and analysis of these emergence behaviors. In particular, I will present some analysis of flocking estimates for Cucker-Smale modes and Vicsek modes for birds and fish. 

I will also discuss the connection and passage among particle models, kinetic models, and continuum models of these self-propelled agents.

ALGEBRA SEMINAR (Lecture Series)

"Lecture Series on From Sums of Squares To Secant Varieties: Evolution of an Idea" (Part II)

In these talks I would like to explain how some famous theorems of elementary number theory, which have analogues for polynomials in several variables, have given rise to interesting questions and investigations in commutative algebra and algebraic geometry.

Moreover, these purely geometric results have had practical applica tions in such diverse areas as: computational complexity (in particular,finding effcient algorithms for matrix multiplication) mathematical biology (in particular, on the genome project) and algebraic statistics.

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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.

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