Transformation Groups Seminar

Speaker: Tao Gong (Western)

"Introduction to root systems and Weyl groups (continued)"

Time: 10:30

Room: MC 108

In a Euclidean space, a (crystallographic) root system is special set of nonzero vectors, called roots. Each root determines a reflection in the Euclidean space, and these reflections generate a finite group, called the Weyl group. I will show some interesting facts about root systems and Weyl groups. In particular, I will talk about classification of root systems, and group actions of (extended) Weyl groups on the Euclidean space.

Topology and geometry seminar

Speaker: Michael Francis (Western)

"Detecting the orientation class of a singular foliation"

Time: 15:30

Room: MC 107

Given a foliated smooth manifold, you'd like to do analysis/topology on the space of leaves. Bad news: this quotient is poorly-behaved! Instead, you can work with a smooth proxy called the holonomy groupoid (which defines the same stack). Using this gadget, Connes defined things like the orientation class and fundamental class of the leaf space. Trying to do similar things with singular foliations, one encounters weird and interesting phenomena such as "continuous holonomy". We'll explore these ideas by concentrating on a special class of examples.

Colloquium

Speaker: Michael Albanese (Waterloo)

" The Yamabe Invariant of Complex Surfaces"

Time: 15:30

Room: MC 108

To any suitable geometric space (closed smooth manifold), one can associate a real number called the Yamabe invariant which arises from considerations in Riemannian geometry. For surfaces, this number is a familiar quantity, but in higher dimensions, it is less understood. However, as we will see, more can be said if one restricts to those spaces which admit a complex structure, e.g., orientable surfaces. This talk is partly based on joint work with Claude LeBrun.

Ph.D. Public Lecture

Speaker: Tianyu Cheng (Western)

"Study of Behaviour Change and Impact on Infectious Disease Dynamics by Mathematical Models"

Time: 09:00

Room: MC 107

This work uses mathematical models to study human behavior changes' effects on infectious disease transmission dynamics. It centers on two main topics. The first concerns how behavior response evolves during epidemics and the effects of adaptive precaution behavior on epidemics. The second topic is how to build general framework models incorporating human behavior response in epidemiological modelling.

Graduate Seminar

Speaker: Nathan Kershaw (Western)

"Closed symmetric monoidal structures on the category of graphs"

Time: 15:30

Room: MC 107

Discrete homotopy theory is a relatively new area of mathematics, concerned with applying methods from homotopy theory in topology to the category of graphs. In order to do this, a notion of a product between graphs is required. Classically two products have been considered, the box product and the categorical product. These products lead to two different homotopy theories, namely A-theory and X-theory, respectively. This leads us to the question of why these two products are considered, and if one can define other products to study discrete homotopy theory with instead. In this talk, we will answer this question by fully characterizing all closed symmetric monoidal products on the category of graphs. 

This talk will be based on joint work with C. Kapulkin (arxiv:2310.00493).