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SCU Mathematics Colloquium Series Schedule
Spring 2004
SCU Mathematics Colloquium Series Schedule
Spring 2004
Unless noted otherwise, talks will be at 4:00pm Tuesdays. Room TBA. There will be refreshments before all talks in O'Connor 31 starting around 3:45pm.
Title: A Protocol for Scalable, Peer-to-Peer Resource Sharing on Networks
A peer-to-peer network distributes the holdiing of resources equally among its members. CHORD, a protocol for such a network, provides a mechanism that permits stable network performance as members and resources join and leave in such a way that resources and transactions are uniformly distributed across the membership.
Title: How much mathematics can be for all?
In my book The Math Gene, I presented an evolutionary argument to show that the basic capacity for mathematical thinking is present in everyone as part of our genetic inheritance. But how much mathematics comes in this way? Is there a point beyond which most people will simply never "get it"? I believe there is sufficient evidence to indicate that the answer is yes. Moreover, among those parts of mathematics that can be mastered only by a few are some topics taught in the middle school. This talk is a sequel to Devlin's book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. (Basic Books, 2000)
Title: Fluid Equations and their Asymptotic Behavior
Phenomena arising in fluid dynamics often evolve driven by some form of diffusion. In this lecture we will consider different types of systems of nonlinear partial differential equations which describe such models. Due to the dissipative mechanism of the systems the corresponding solutions can be shown to decay at different speeds in appropriately chosen norms or energies spaces. The models I will discuss are represented by the Navier-Stokes, the Magneto-Hydrodynamics, the Convection Diffusion and the Quasi-Geostrophic equations. Attention will be focused on the long time behavior of the solutions to these systems. We will discuss methods that will give upper and lower bounds on the rates of decay. In particular we want to explore common features regardless of the nonlinearity of the corresponding system. In this direction we will show cases were the solutions and their underlying linear counterpart decay at the same rate which as such will be optimal.
Title: The World of Microscopic Geometric Tiles in the Dynamics of Piecewise Isometries
In this talk, accessible to beginning undergraduate students, we will illustrate a class of dynamical systems that give rise to intriguing microscopic geometric structures. Dynamical Systems is an an active area of mathematics in which objects of interest the behavior of orbits. Given a space X and a function acting on this space, f, an orbit is a sequence, {x, f(x), f(f(x))}, etc. While the talk will be augmented by a multimedia presentation and the computer is central in the visualization aspect, the talk will be rigorous in nature and it will include an illustration of number theoretic and geometric tools. The archive of multimedia used is located at: math.sfsu.edu/goetz/
Title: Systems of Orthogonal Polynomials Arising from the Modular j-function
Let $S_p (x) \in F_p[x] $ be the polynomial whose zeros are the $j$-invariants of supersingular elliptic curves over $\overline{F}_p$. Generalizing a construction of Atkin described in a recent paper by Kaneko and Zagier, we define an inner product ${\left\langle , \right\rangle_{\psi}}$ on $R[x]$ for every $\psi(x) \in Q[x]$. Suppose a system of orthogonal polynomials $\{P_{n,\psi}(x) \}_{n=0}^{\infty}$ with respect to ${\left\langle , \right\rangle_{\psi}}$ exists. We prove that if $n$ is sufficiently large and $\psi(x)\P{n}(x)$ is $p$-integral, then $S_p (x) \mid \psi(x) P_{n,\psi}(x)$ over $F_p[x]$
Title: Cayley Graphs and Expanders
Expanders are certain families of graphs that have many important applications to computer science. A hard open question is whether Cayley graphs of the symmetric groups can contain an expanding family. We consider the special case of Cayley graphs generated by reversals (a reversal is an involution that reverses the order of an entire subinterval of 1234...n).
The list of talks from previous quarters are available via this archive link.
Last Updated: 7 March 2005
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