Geometry and Topology

Speaker: Roy Joshua (Ohio State University )

" Notions of Purity and the Cohomology of Quiver moduli"

Time: 15:30

Room: MC 107

We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal bundles and also geometric quotients for reductive group actions. We then apply these results to study the cohomology of quiver moduli. We prove that a natural stratification of the space of representations of a quiver with a fixed dimension vector is equivariantly perfect and from it deduce that each of the l-adic cohomology groups of the quiver moduli space is strongly pure.

This is joint work with Michel Brion.

Analysis Seminar

Speaker: Ekaterina Shemyakova (Western)

"Completeness of Wronskian Formulas for Darboux transformations or order 2"

Time: 14:30

Room: MC 107

I shall report about my 2011 results, which is the resolution of one long standing problem in the theory of Darboux transformations. It is known that many Darboux transformations can be constructed using Darboux Wronskian formulas. The only known exceptions have been two transformations of order one - Laplace transformations, which are often used in applications. I shall show that for order one there is no other exceptions and that for order two Wronskian formulas are complete. History of the question as well as an introduction into the area will be provided.

Noncommutative Geometry

Speaker: Asghar Ghorbanpour (Western)

"Selberg Trace Formula and Heisenberg Group"

Time: 14:30

Room: MC 107

Colloquium

Speaker: Ram Murty (Queen's University)

"The Mathematical Legacy of Srinivasa Ramanujan "

Time: 15:30

Room: MC 107

The Indian mathematician, Srinivasa Ramanujan was largely self-taught and emerged from extreme poverty to become one of 20th century's influential mathematicians. In this talk, I will give a panoramic view of his essential contributions and show how they are shaping mathematics of this century.

Algebra Seminar

Speaker: Chester Weatherby (Queen's)

"Special values of the gamma function"

Time: 14:40

Room: MC 107

Little is known about the transcendence of special values of the Gamma function at rational points. In this talk we examine the Gamma function at points from an imaginary quadratic field. As a corollary of our analysis, we gain knowledge about values of infinite products of rational functions.