David McKinnon, Department of Pure Mathematics, University of Waterloo
"Gaussian integers and gcds"
Jeremy Champagne, Department of Pure Mathematics, University of Waterloo
"Geometry of numbers as a tool for Diophantine approximation"
Anybody who has taken a course on algebraic number theory, has probably seen Minkowski's convex body theorem as a mean to prove the finiteness of class groups. However, less people know about Minkowski's second convex body theorem, which gives much more insight into this problem of finding integer points with certain properties.
Nicolas Banks, Department of Pure Mathematics, University of Waterloo
"Dual Isogenies, the Weil Pairing, and the Structure of Endomorphism Rings"
We conclude our review of the geometry of elliptic curves by studying dual isogenies. This allows us to prove important results on torsion elements on elliptic curves, culminating in the construction of the Weil pairing and the algebraic structure of rings of isogenies.
MC 5403
Robert Martin, University of Manitoba
"Non-commutative measure theory"
Sean Monahan, Department of Pure Mathematics, University of Waterloo
"Spot it! and why it! (works)"
Do you like to play games? Can you easily distinguish different shapes? Are you at least 6 years old? Well then I've got the perfect game for you! It's called Spot it! (or Dobble if you're not from 'Merica). Fundamentally, the game is about quickly spotting the common symbol displayed on a given pair of cards. In this talk we will see the math behind why this game works. Spoiler: it's projective geometry!
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"Nearly Kahler 6-manifolds have SU(3)-structures"
Michael Albanese, Department of Pure Mathematics, University of Waterloo
"Spin^h and further generalisations of spin"
Ian Hambleton, McMaster University
"Euler Characteristics and 4-manifolds"
The topology and total curvature of a Riemann surface is determined by a single integer, the Euler characteristic (Leonhard Euler, 1707-1783). In dimension four and higher, the Euler characteristic gives an interesting invariant for finitely presented groups. The talk will survey some recent joint work with Alejandro Adem on this theme.
MC 5501
Elliot Kaplan, McMaster University
"Hilbert polynomials for finitary matroids"
Owen Sharpe, Department of Pure Mathematics, University of Waterloo
"Diophantine Techniques in Bourgain's Discrete Restriction Conjecture"
We continue the last talk about Bourgain's discrete restriction conjecture, and explain the Diophantine techniques used in the recent progress on the conjecture by Hughes and Wooley.
This seminar will be held both online and in person: