University of Calgary

Let ord p ( a ) be the order of a in ( Z / p Z ) ∗ . In 1927, Artin conjectured that the set of primes p for which an integer a ≠ − 1 , ◻ is a primitive root (i.e. ord p ( a ) = p − 1 ) has a positive asymptotic density among all primes. In 1967...

Over the years, there have been several open problems involving polynomials that I would love to tell others about. This opportunity to speak at my “home ground” seems the perfect time to do so. More specifically, I will discuss the following: A...

Embedding calculus is a powerful tool which is useful in making quantitative and qualitative conclusions about the topology of embedding spaces. In this talk, we will give a geometric description of the fiber of Emb ( M , M ) → T ∞ Emb ( M , M )...

Automorphic representations, which provide a vast generalization of modular forms, are are grouped together into so-called L-packets according to the L-functions they produce. From this point of view, automorphic representations give a kind of fine...

Abstract: Recently, Machine Learning (ML) approaches to data assimilation and modeling have been very successful in interpreting large amounts of data, such as human behavior prediction, marketing, etc. However, direct applications of machine...

Let E be an elliptic curve defined over ℚ. Let p > 3 be a prime such that p - 1 is not divisible by 3, 4, 5, 7, 11. In this article, we classify the groups that can arise as E(ℚ(ζp))tors up to isomorphism. The method illustrates techniques for...

In everybody’s first course in category theory, we learn that categories have two different flavours of morphism: 0-morphisms (which are categories themselves), 1-morphisms (which are functors), and 2-morphisms (which are natural transformations). In...

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...