The theory of electromagnetic (EM) phenomena known as electrodynamics is one of the major theories in science. At macroscopic scales the interaction of the EM field with matter is described by the classical electrodynamics based on the Maxwell-Lorentz theory. Many of electromagnetic phenomena at microscopic scales are covered by the so-called semiclassical theory that treats the matter according to the quantum mechanics, whereas the EM field is treated classically. The subject of this presentation is a recently advanced by us neoclassical electromagnetic theory that describes EM phenomena at all spatial scales –microscopic and macroscopic. This theory modifies the classical electrodynamics into a theory that applies to all spatial scales including atomic and nanoscales. The neoclassical theory is conceived as one theory for all spatial scales in which the classical and quantum aspects are naturally unified and emerge as approximations. It is a classical Lagrangian field theory, and consequently it is a local and deterministic theory. Probabilistic aspects of the theory may arise in it effectively through complex nonlinear dynamical evolution. This presentation is to provide an introduction to our theory including a concise historical review.

(Joint work with Anatoli Babin)

In this talk, I will give you many ways to characterize  the unit ball

in $R^n$ or in $C^n$. It involves, differential equations, first eigenvalue of Laplace-Beltrami 

operator, etc.

Algebraic topology was invented by Poincare in 1895 to study the behavior of algebraic functions.  In his seminal ICM address 5 years later, Hilbert posed a fundamental challenge to the field: find a topological obstruction to reducing the solution of the general degree 7 polynomial to an expression in functions of two or fewer variables.  In this talk, I'll review some of the beautiful history of algebraic topology and algebraic functions, discuss Hilbert's problem(s), and outline ongoing work in applying the topology of braids and algebraic functions to this problem.  This is joint work with Benson Farb.

The last seminar of fall quarter will have Neil Donaldson bracing us for the common final exams, and then we'll discuss what worked and didn't work in our teaching this quarter.

How should you read your TA evaluations?  How do I read them?  I'd like to talk about this and I'd also like to review the first half of the seminar, talking about questions like "What was the main point of the Week ? meeting?".