The usual Katz-Mazur model for the modular curve $X(p^n)$ has
horribly singular reduction. For large n there isn't any model of
$X(p^n)$ which has good reduction, but after extending the base one
can at least find a semistable model, which means...
In this talk I will describe a real-variable method to extract
long-time asymptotics for solutions of many nonlinear equations
(including the Schrodinger and mKdV equations). The method has many
resemblances to the classical stationary phase method...
In the talk, I will describe recent attempts to understand the
mysterious and beautiful geometry of nodal lines of random
spherical harmonics and of random plane waves. If time permits, I
will also discuss asymptotic statistical topology of other...
The cd-index is a noncommutative polynomial which compactly
encodes the flag vector data of a polytope, and more generally, of
a regular cell complex. Ehrenborg and Readdy discovered the
cd-index has an inherent coalgebraic structure which...
This will be an introduction to special value formulas for
L-functions and especially the uses of modular forms in
establishing some of them -- beginning with the values of the
Riemann zeta function at negative integers and hopefully arriving
at...
Let p and l be two distinct prime numbers, and fix a positive
integer d . I will explain how the F_l-cohomology complex of the
Lubin-Tate tower of height d of a p-adic field K realizes mod l
versions of both the semi-simple Langlands correspondence...