Analysis Seminar

Speaker: Rasul Shafikov (Western)

"On local polynomial convexity of the union of two Lagrangian submanifolds in C^n"

Time: 15:30

Room: MC 108

I will discuss the property of polynomial convexity of compacts in C^n, and the outline the proof of local convexity of two Lagrangian submanifolds in C^n at a point of transversal intersection.

Geometry and Topology

Speaker: Jeffrey Morton (SUNY Buffalo State)

"Higher-Categorical Symmetries and Transport Functors in Higher Gauge Theory"

Time: 15:30

Room: MC 107

Higher Gauge Theory (HGT) studies categorical analogs of constructions in the geometry of connections on bundles. In this talk, I will describe an HGT analog of a phenomenon that occurs in gauge theory: a groupoid of such connections arises both as a category of functors and also from a group action. I will describe a 2-categorical analog of this phenomenon, showing a relation between global and local symmetry in categorical geometry.

Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"The heat equation proof of the Atiyah-Singer index theorem (1)"

Time: 14:30

Room: MC 107

I shall survey the main steps in the heat equation proof of the Atiyah-Singer index theorem for Dirac operators on spin manifolds.

Noncommutative Geometry

Speaker: Travis Ens (Western)

"NCG Learning Seminar: Feynman's diagrams and Feynman's theorem (1)"

Time: 10:30

Room: MC 107

Algebra Seminar

Speaker: Mehdi Garrousian (Western and U. Windsor)

"On the Koszulity of the algebra of reciprocal forms"

Time: 14:30

Room: MC 108

The Orlik-Terao algebra of a hyperplane arrangement is the algebra of the rational functions with poles on an arrangement of hyperplanes. This is a commutative analogue of the cohomology algebra of the complement and defines the so-called reciprocal plane which is a an irreducible projective variety. In a recent joint work with G. Denham and S. Tohaneanu, we give a decomposition result about the OT algebra whenever the underlying combinatorics has a certain genericity structure. This result implies that the OT algebra is Koszul if the arrangement is nicely filtered. As consequences, we give several other results such as characterizations for the OT algebra to be a quadratic complete intersection.