Sep 08 
Anschel SchafferCohen 
 Nonstandard analysis: calculus without limits 

Nonstandard analysis studies problems of calculus using modern logic rather than epsilons and deltas. We'll go through a gentle introduction to nonstandard reasoning, and include a somewhat less gentle discussion of the construction that makes it rigorous.

Sep 15 
Prof. Angela Gibney (Rutgers) 
 How to prepare for an academic job interview and what to do before you go on the academic job market 
Sep 22 
Dominick Villano 
 The Polynomial Method 

Somewhat recently, polynomials have been used to provide brief and elegant solutions to problems that had previously been considered very hard. I'll talk about some of these problems/solutions.

Sep 29 
Prof. Philip Gressman 
 Affine Curvature in Harmonic Analysis 

In the 1970s, E. Stein and other mathematicians studying fundamental questions related to pointwise convergence of Fourier series discovered surprising new links between this very old problem and the geometry of submanifolds of Euclidean space. These discoveries paved the way for many of the questions at the forefront of modern harmonic analysis. A common element in many of these areas is the role of a strange sort of curvature condition which arises naturally from Fouriertheoretic roots but is poorly understood outside the extreme cases of curves and hypersurfaces. In this talk, I will discuss recent work which combines elements of Geometric Invariant Theory, Convex Geometry, Signal Processing, and other areas to shed light on this problem in intermediate dimensions
