Honours Seminars

Mon., Apr. 8, 2024 1:30 p.m.

Location: AH 318

Please join us at 1:30 p.m. for the Honours Seminars. The order of presenters is to be determined.

Speakers:

Cody Antal - Title: Lie Groupoids and the Stokes Groupoids

Abstract: This talk will first introduce the category of groupoids which can be seen as a generalizationof the category of groups in which the binary operation is only partially defined. We will then discuss the basic algebraic properties of these objects followed by an informal picture of them as arrows between points in space.

Next we will add smooth structures to groupoids to obtain Lie groupoids and quickly introduce the associated notion of Lie algebroids which are to Lie groupoids as Lie algebras are to Lie groups.

Finally, we will investigate the connection between differential equations of the form

zⁿ dy/dz = A(z)y

and maps out of the Sto_k groupoid. This will provide us an example of the Lie theorems in the "oidified" case.

Layne Byrne - Title: The Dynamics of Fairness - Revisiting The Peach Stone Bowl Game

Abstract: In this seminar, we revisit 'The Peach Stone Bowl Game' from a new perspective, questioning the idealized fairness of its components. Through extensive simulation, we examine how altering the probabilities of the stones affects the game’s dynamics. Our study and statistical analyis, supported by over a quarter-million simulated games, offers a deeper understanding of the game’s probabilistic landscape.

Peter Wadel - Title: Low-dimensional SIC-POVMs

Abstract: In continuation of the previous seminar's discussion on symmetric, informationally complete positive operator-valued measures (SIC-POVMs), this talk will focus on exploring several examples of low-dimensional SIC-POVMs and their group-covariant properties.

Jeffery Xu - Title: Fock-Hilbert Spaces and their Operators

Abstract: The analysis of Fock spaces relies on the operators that live on it just as much as the spaces themselves. In particular, Fock space operators are defined in a similar fashion to the space itself, that of an infinite direct summation of n-tensor product Hilbert space operators, with summation over n. After defining annihilation operators and creation operators, this leads to the fundamental notions of Canonical Commutation Relations (CCR) for symmetric tensor spaces, and Canonical Anticommutation Relations (CAR) for antisymmetric tensor spaces. These are important in the field of quantum field theory (QFT) due to being related to various uncertainty principles.