10/02: Chris Hammond

Title: Equi-Affine Geometry of Real Hypersurfaces in $\mathbb{C}^{2}$

Abstract: We study the equi-affine geometry of strongly pseudoconvex real hypersurfaces in $\mathbb{C}^{2}$ via Cartan's method of moving frames. We generalize a result of M. Bolt, which states roughly that if the lowest order invariant is constant on a "nondegenerate" hypersurface, then the hypersurface is equi-affinely equivalent to a member of a particular family of equi-affinely homogeneous hypersurfaces.

10/09: Chris Hammond

Title: Equi-Affine Geometry of Real Hypersurfaces in $\mathbb{C}^{2}$ II

Abstract: We study the equi-affine geometry of strongly pseudoconvex real hypersurfaces in $\mathbb{C}^{2}$ via Cartan's method of moving frames. We generalize a result of M. Bolt, which states roughly that if the lowest order invariant is constant on a "nondegenerate" hypersurface, then the hypersurface is equi-affinely equivalent to a member of a particular family of equi-affinely homogeneous hypersurfaces.

10/16: Al Boggess

Location: Milner 216

Title: The fundamental solution to the Box_b heat equation on quadrics (joint work with Andy Raich)

10/23: Al Boggess

Location: Milner 216

Title: The fundamental solution to the Box_b heat equation on quadrics (joint work with Andy Raich), part II.

10/30: Harold Boas

Title: Julius and Julia: Mastering the art of the Schwarz lemma

Abstract: This is an expository and historical talk about the Schwarz lemma at the boundary.

11/13: Alex Tumanov, Univ. of Illinois.

"Deformations and transversality of pseudo-holomorphic discs."
Abstract:
Singularities of holomorphic curves can be perturbed away locally. The corresponding result for pseudoholomorphic curves was proved (McDuff, 1991-94) by analyzing singularities of the curves. We prove a global version for pseudo-holomorphic discs. Following the proof in the smooth category, we derive the result from a version of Thom's transversality theorem. The main difficulty in the proof is that the equation for infinitesimal perturbations of big pseudo-holomorphic discs a priori involves an integral operator with nontrivial kernel. This is a joint work with A. Sukhov.

11/18: Mikael Passare

Room: M 317

Title: Coamoebas and Mellin transforms

Abstract: The coamoeba of a complex polynomial $f$ is defined to be the image of the hypersurface defined by $f$ under the mapping $\text{Arg}$ that sends each coordinate $z_k$ to its argument $\arg z_k$. We shall discuss the connection between coamoebas and the multidimensional Mellin transforms of rational functions. It turns out that there is some amusing combinatorics involved here.