University of Calgary

Given two elliptic curves, the path finding problem asks to find an isogeny (i.e. a group homomorphism) between them, subject to certain degree restrictions. Path finding has uses in number theory as well as applications to cryptography. For...

We describe parametrizations of rings that generalize the notions of monogenic rings and binary rings. We use these parametrizations to give better lower bounds on the number of number fields of degree n and bounded discriminant.

In this talk we will cover the mathematics behind a security system that is thought to be secure against quantum computer hacking; the Supersingular Ell Isogeny Cryptosystem. Specifically the Supersingular Ell Isogeny Graph. This abstract object is...

In this talk we’ll continue to get to know bicategories by learning about what you can do inside a bicategory. We’ll learn about pasting diagrams as well as adjoints and equivalences inside bicategories before presenting some examples of what these...

Limits and colimit constructions are ubiquitous in category theory, and are one of the main tools used to understand how objects in a category relate to one another. These are very concrete and easily stated in terms of universal properties: given a...

Bicategories are an important aspect of modern category theory and provide the first instance of “category theory up to coherent isomorphism” we see when hiking up Mount Higher Category Theory. In this talk I will introduce the notion of bicategories...

Originally distributions were introduced in PDE-theory to generalize the notion of functions. However, this analytical concept also has some purely algebraic properties, which are worth considered. In particular, they are an important example of...

Hysteresis, a phenomenon in which the response of a system lags behind and depends on its past history, has been used to understand various psychosocial phenomena, including abrupt shifts in opinion dynamics, political polarization, and more. The aim...

Using Banach’s contractive principle and Leray–Schauder’s fixed point theorem, we study the uniqueness and existence for a new nonlinear fractional differential equation with functional boundary condition based on the two-parameter Mittag-Leffler...

M2PI matches graduate students and postdoctoral fellows with industry partners to engage in a two week long collaboration to solve an industrial mathematics challenge. M2PI participants gain valuable skills making them ready to work in non-academic...