Glazebrook to Talk on “La Belle E ́poque of ODEs” Today

Abstract follows:

Following extensive developments in the theory of differential equations due to Sturm, Liouville, Abel and others, there was a further surge in activity toward the end of the nineteenth century that created substantial breakthroughs into other areas of mathematics. Much of this was inspired by the French school(s) centered around H. Poincare and E. Picard who took the theory of DEs into the realm of algebraic geometry and topology, thus creating an area of mathematics studied to the present day. Prolific contributors at that time included Fuchs, Schlesinger, Garnier, and Painleve (the latter was the French Prime Minister 1917, 1925).

In much of this work one discovers the ubiquitous ‘tau-function’, most notably in Painleve’s theory of transcendents’ which I will briefly discuss in the context of second order nonlinear ODEs. This is a topic that continues to have far-reaching consequences in mathematical physics (wave equations and ‘integrable systems’), algebraic geometry and representation theory. There is also a remarkable geometric-functional analysis slant to this theory which can be studied within the framework of ‘Convenient Geometry’, about which I will provide some background and some explanation, and reveal that ‘tau’ actually possesses a startling geometric property.

Galperin Talk Today: Billiards bouncing in gravitational field.

Assume that there is a collection of semi-circles of diameter 1 in the upper half plane centered at the integer points (n,0) on the x-axis. A released billiard ball falls down under the vertical constant gravitational force g. The ball bounces off the semi-circles according to the billiard law and describes a trajectory γ. Record the indices of the semi-circles the ball hits as a sequence

ω = (ω1, ω2, ...),

which we call the one-sided itinerary of the trajectory γ. We will investigate this dynamical system.

A Proof By Any Other Name ...

there once was a lady logician
whose trade was still liquor production
as her batch made its rounds
thru vast coil surrounds
she claimed it a "proof by induction"

More graffiti

Where there is number there is beauty

So said Proclus, a Greek geometer who wrote a commentary on
geometry and lived from about 412 to 485 AD.

Escher and Bach

William Green to Talk in Colloquium Today

Title: Schroedinger Equation in Dimension Two ...

In this talk we will discuss some recent research on mapping
properties of the Schroedinger operator in dimension two. The
majority of the talk will be discussing background issues
needed to understand these new results. See also

Math Talks

Fermat's Last Thing on the To Do List

Should I write the whole proof in the margin or what? ...
It's clear isn't it? ...
Oh well, I'll do it tomorrow...
Que sera sera.