University of Calgary

Twenty-first century mathematics has seen the rise of the proof assistant, and mathematical practice has changed significantly with the rise of these new tools. One consequence of this change, for the philosopher of mathematics, is the wider adoption...

Introduction to knowledge graph with an application in Construction Code Compliance with BIM and Linked Building Data Abstract: Knowledge graph and ontology are powerful mathematical constructs that has a lot of applications. This presentation begins...

We show that the reduction of a projective endomorphism modulo a discrete valuation naturally takes the form of a set-theoretic correspondence. This raises the possibility of classifying "reduction types" of such dynamical systems, reminiscent of the...

In 1966, Tate proposed the Artin–Tate conjectures, which expresses special values of zeta function associated to surfaces over finite fields. Conditional on the Tate conjecture, Milne–Ramachandran formulated and proved similar conjectures for smooth...

The Polya group P o ( K ) of a Galois number field K coincides with the subgroup of the ideal class group C l ( K ) of K consisting of all strongly ambiguous ideal classes. We prove that there are only finitely many imaginary abelian number fields K...

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...