## 2008 DG-MP-PDE Seminar - 04

- Date: 02/07/2008

Lecturer(s):
Michael Greenblatt (University of Illinois at Chicago)

Location:

University of British Columbia

Topic:

Newton Polyhedra and Sharp Estimates for Oscillatory Integrals

Description:

Varchenko described how one can obtain sharp estimates for scalar

oscillatory integrals when the Newton polyhedron of the phase satisfies

a certain nondegeneracy condition. These estimates can be described in

a nice geometric way in terms of this Newton polyhedron. We will

describe how these estimates still hold under weaker conditions; the

proof uses resolution of singularities methods. We then will describe a

class of functions for which the weaker conditions can not be weakened

further. Further generalizations will also be discussed.

Schedule:

3:30pm, WMAX 110