Department of Mathematics and Statistics

Colloquia

Colloquia for the Department of Mathematics and Statistics are normally held in University Hall 4010 on Fridays at 4:00pm. Any departures from this are indicated below.

Light refreshments are served after the colloquia in 2040 University Hall.

Driving directions, parking information, and maps are available on the university website.

2017-2018 Colloquia

What follows is a list of speakers, talk titles and abstracts for the current academic year. Abstracts for the talks are also posted in the hallways around the departmental offices.

Fall Semester

Shoemaker Lecture Series September 11-13, 2017

Miroslav Englis (Mathematics Institute, Czech Academy of Sciences -- Prague)

Lecture 1: An excursion into Berezin-Toeplitz quantization and related topics

September 11 (Monday), 4:00-5:00pm in GH 5300

Abstract: From the beginning, mathematical foundations of quantum mechanics have traditionally involved a lot of operator theory, with geometry, groups and their representations, and other themes thrown in not long afterwards. With the advent of deformation quantization, cohomology of algebras and related disciplines have also entered. The talk will discuss an elegant quantization procedure which is based on methods from analysis of several complex variables. Further highlights include connections to Lie group representations or related developments for harmonic functions.

Lecture 2: Arveson-Douglas conjecture and Toeplitz operators

September 12 (Tuesday) 4:00-5:00pm in FH 1270

Abstract: A basic problems in multivariable operator theory is finding appropriate "models" for tuples of operators. For the case of commuting tuples, this is resolved by a nice theory developed by William Arveson, and the question of the "size" of the commutators of the model operators with their adjoints is the subject of the Arveson-Douglas conjecture. Though the latter is still open in full generality at the moment, we give a proof of the conjecture in a special case, using methods verging on microlocal analysis and complex analysis of several variables. The same machinery can also be used to get (criteria for traceability and) formulas for the Dixmier trace of Toeplitz and Hankel operators, a theme of importance in Connes' noncommutative geometry.

Lecture 3: Reproducing kernels and distinguished metrics

September 13 (Wednesday), 4:00-5:00pm in GH 5300

Abstract: Two classical distinguished Hermitian metrics on a complex domain are the Bergman metric, coming from the reproducing kernel of the space of square-integrable holomorphic functions, and the Poincare metric, i.e. a K"ahler-Einstein metric with prescribed (natural) behaviour at the boundary. In the setting of compact K"ahler manifolds rather than domains, the so-called balanced metrics were introduced some time ago by S. Donaldson, building on earlier works on S.T. Yau and G. Tian. The talk will discuss the questions of existence and uniqueness of balanced metrics on (noncompact) complex domains, where some answers are yet unknown nowadays even for the simplest case of the unit disc.

There will be a reception on Monday immediately following the talk at Libbey Hall from 5:00-7:00pm.

Generated on: 2017-09-20 21:43 UTC.