### Monday March 6, 2006, 4:00 PM

### tea at
3:40 PM at the Math Department lounge (Goldsmith 300)

**Speaker**: Maxim Braverman (NEU)

**Title**: Index Theory, Old and New

**Abstract**: One of the most exciting achievements of mathematics in
the second half of the 20th century is the Atiyah-Singer index
theorem, asserting that the analytical and topological index of an
elliptic operator on a compact manifold coincide.

In the talk I will review the definitions of analytical and
topological index and some of their generalizations, including the
index of transversally elliptic operators, constructed by Atiyah
in 1974. Then I'll discuss some extensions of these notions to
non-compact manifolds, due to Atiyah, Vergne, Paradan and myself,
and will state an index theorem for equivariant Dirac operator on
a non-compact manifold.