Transformation Groups Seminar

Speaker: Shubhankar (Western)

"Polyhedral products"

Time: 10:30 - 12:00

Room: MC 107

Talk 3.5 of the learning seminar on Pontryagin rings in toric topology.

Transformation Groups Seminar

Speaker: Matthias Franz (Western)

"Formality of Davis-Januszkiewicz spaces"

Time: 10:30 - 12:00

Room: MC 107

I will present a proof that the Davis-Januszkiewicz space DJ(K) is integrally formal, meaning that its integral cochain algebra is quasi-isomorphic to its cohomology (which is the Stanley-Reisner ring of K). If time permits, I will sketch a proof that toric manifolds (or, more generally, equivariantly formal toric varieties) are formal in the sense of rational homotopy theory.

Colloquium

Speaker: Jurek Lewandowski (University of Warsaw)

"The Normal Conformal Cartan Connection and spacetime"

Time: 15:30 - 16:30

Room: MC 107

NCCC is by no means a popular tool in physics, and certainly the possibilities of its application have not been fully exhausted. The spinor equivalent of NCCC appears in the literature as a local twistor connection. Thus, using NCCC, spacetimes admitting covariantly constant twistor fields were once found and identified as conformal metrics constructed earlier by Fefferman and used in the geometric approach to the Cauchy-Riemann structures. A new application of NCCC is the construction of conformally invariant symplectic potential on the space of Bach flat geometries. These include all Einstein spacetimes. NCCC provides new charges and currents well-defined both at points in spacetime and at its conformal boundary. Relevant examples will be demonstrated in the Graham-Fefferman coordinates.

Transformation Groups Seminar

Speaker: Matthew Staniforth (University of Southampton)

"Higher Whitehead maps in polyhedral products"

Time: 10:30 - 11:30

Room: MC 107 and Zoom

We define generalised higher Whitehead maps in polyhedral products and study their properties and the relations among them. By investigating the interplay between the homotopy theoretic properties of polyhedral products and the combinatorial properties of simplicial complexes, we describe new families of relations among these maps, while recovering and generalising known identities among Whitehead products.

Zoom Meeting ID: 93798234275, Passcode: 520011

Colloquium

Speaker: Ilias Kotsireas (Wilfred Laurier University)

"20+ years of Legendre pairs"

Time: 15:30 - 16:30

Room: MC 107

(Coffee @ 3:00) Legendre pairs were introduced in 2001 by Seberry and her students, as a means to construct Hadamard matrices via a two-circulant core construction. Legendre pairs of every odd prime length exist, via a simple construction using the Legendre symbol. We will review known constructions for Legendre pairs. We will discuss various results on Legendre pairs during the past 20+ years, including the concept of compression, introduced in a joint paper with D. Z. Djokovic, as well as the computational state-of-the-art of the search for Legendre pairs. Finally, we will discuss a Coding Theory reformulation of the problem of enumerating Legendre pairs for a given odd length ell, via computing the weight enumerator of a binary code, based on work of S. Eliahou. The importance of Legendre pairs lies in the fact that they constitute a promising avenue to the Hadamard conjecture.

Analysis Seminar

Speaker: Blake Boudreaux (Western)

"Convexity in Several Complex Variables"

Time: 15:30 - 16:30

Room: MC 107

Abstract: In 1906, F. Hartogs discovered the existence of domains in $\mathbb{C}^n$ for which every holomorphic function can be extended to a larger domain. Domains that do not admit this extension phenomenon satisfy a complex type of convexity, known as pseudoconvexity. This type of convexity can be viewed as convexity "with respect to holomorphic functions", as opposed to classical convexity which is convexity "with respect to linear functions". $$ $$ In this talk, we will motivate and define pseudoconvexity. We will also compare and contrast its many equivalent formulations with that of classical convexity. We will also introduce a class of "pseudoconvex" manifolds known as Stein manifolds and discuss their many properties. Notions of convexity with respect to other classes of functions will also be discussed.

Transformation Groups Seminar

Speaker: Sayantan Roy Chowdhury (Western)

"Loop spaces of Davis-Januszkiewicz spaces"

Time: 10:30 - 12:00

Room: MC 107

Talk 6 of the learning seminar on Pontryagin rings in toric topology.