Transformation Groups Seminar

Speaker: Lewis Stanton (University of Southampton)

"Loop spaces of moment-angle complexes associated to flag complexes"

Time: 10:30

Room: Zoom

Polyhedral products are natural subspaces of the Cartesian product of spaces, which have a diverse range of applications across mathematics. One particular special case is the moment-angle complex. Work of various authors has identified families of simplicial complexes for which the loop space of their corresponding moment-angle complex is homotopy equivalent to a product of spheres and loops on spheres. In this talk, I will survey the current progress in this direction, and then expand the family of simplicial complexes for which such a decomposition is known - namely simplicial complexes which are the k-skeleton of a flag complex.

Analysis Seminar

Speaker: Rasul Shafikov (Western)

"Rational convexity and symplectic geometry"

Time: 14:30

Room: MC 108

In this talk I will define Liouville vector fields, Weinstein domains, contact type submanifolds and discuss their connection with Stein structures and rational convexity in $\mathbb C^n$.

Geometry and Topology

Speaker: Lukas Muller (Perimeter Institute)

"Quantum representations of handlebody groups"

Time: 15:30

Room: MC 107

Mapping class groups of surfaces and handlebody groups are fundamental objects in low-dimensional topology. Quantum algebra and mathematical physics provide large classes of finite dimensional representations for both. In this talk, I will discuss examples of those representations and their properties. An important feature is that they are local under cutting and gluing of handlebodies. I will sketch an approach to a precise formulation of this property and present a complete classification result. The talk is based on joint work with Lukas Woike.

Colloquium

Speaker: Craig Kaplan (Waterloo)

"Aperiodic Monotiles"

Time: 15:30

Room: MC 107

A set of shapes is called aperiodic if they admit tilings of the plane, but none that have translational symmetry. Starting in the 1960s, progress in our understanding of such tilings produced progressively smaller aperiodic sets, but failed to arrive at a single shape that tiles aperiodically, also known as an aperiodic monotile. In 2023, we resolved that open question by proving that the "hat", a union of eight kites, is an aperiodic monotile. In this talk I provide background on aperiodicity and related topics in tiling theory, review the history of the search for for an aperiodic monotile, and present the new monotiles that we discovered.

Graduate Seminar

Speaker: Alejandro Santacruz Hidalgo (Western)

"Hardy's inequality: a brief review, some extensions and applications"

Time: 15:30

Room: WSC 187

In 1915 G.H Hardy needed an estimate for arithmetic means to find a proof of Hilbert's inequality for sequences, a continuous version of that inequality followed in 1925. Since then, extensions have been made in many directions; more general domains, weighted norm inequalities, general measures, among others. In this talk we will review the classic statement of Hardy's original inequality. We will explore some of the extensions of this important inequality and review some of its implications, such as, Sobolev inequalities and boundedness of the Fourier transform in weighted Lorentz spaces.