# Welcome to the Math Department

Use the navigation menu on the left to browse around the site!

## Announcements

Students wanting to **add a math major** or
**switch to a math major** can do so between February 15 and
March 31, during First Summer Session, or between October 1 and the day
before Thanksgiving break.

**Force-Add information for Fall 2014**

## Featured Research

**Peter Haskell**- Professor Haskell's research area, index theory, is the study of the relationships between topology and geometry, on the one hand, and analysis. An early example is associated with the vector calculus theorems of Green and Stokes: an irrotational vector field (closed differential one-form) on a region D is guaranteed to be conservative (exact) on D only if D is simply connected (i.e., every loop in D can be contracted to a point in D). Examples of topological invariants that have analytic realizations include the winding number and the Euler characteristic. Index theory has developed from its roots in analysis on manifolds (global analysis) to include the study of singular spaces, with part of this development based on functional analytic tools such as the K-theory of algebras of linear operators on Hilbert space. Topological and analytic invariants detect twisting, like that pictured in this image generated by KnotPlot.