University of Lethbridge

It is a classical problem to understand the set of Jacobians of curves among all abelian varieties, i.e., the image of the map Mg→Ag which sends a curve X to its Jacobian JX. In characteristic p, Ag has interesting filtrations, and we can ask how the...

In his famous '86 paper, Andrews made several conjectures on the function σ(q) of Ramanujan, including that it has coefficients (which count certain partition-theoretic objects) whose sup grows in absolute value, and that it has infinitely many...

Mathematical transcendence refers to objects (usually numbers or functions) that do not satisfy any polynomial equation, that is, they are not algebraic. The numbers $\pi$ and $e$ are famous transcendental numbers, and $e^x$ and the Gamma function...

I will describe a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel-Walfisz theorem, Hoheisel's asymptotic for short intervals, a Brun-Titchmarsh bound and Linnik's bound for the least prime...

Given a Galois extension of number fields L/K, the Chebotarev Density Theorem asserts that, away from ramified primes, Frobenius automorphisms equidistribute in the set of conjugacy classes of Gal(L/K). In this talk we report on joint work with D...

The exciting and rapidly-growing field of topological materials has brought with it unexpected new connections between physics and pure mathematics. As the name suggests, topology has played a significant role in understanding and classifying these...

Elliptic curve isogeny path finding has many applications in number theory and cryptography. For supersingular curves, this problem is known to be easy when one small endomorphism or the entire endomorphism ring are known. Unfortunately, computing...

Given coprime integers $a,b$, the classical identity of Bezout provides integers $u,v$ such that $au-bv = 1$. We consider refinements to this identity, where we ask that $u,v$ are norms from a quadratic extension. We then find ourselves counting...

For an integer k≥3; Δk (x) :=∑n≤xdk(n)-Ress=1 (ζk(s)xs/s), where dk(n) is the k-fold divisor function, and ζ(s) is the Riemann zeta-function. In the 1950's, Tong showed for all large enough X; Δk(x) changes sign at least once in the interval [X, X +...

In 1979, Erdős conjectured that for k≥9, 2k is not the sum of distinct powers of 3. That is, the set of powers of two (which is 2-automatic) and the 3-automatic set consisting of numbers whose ternary expansions omit 2 has finite intersection. In the...