Events

Speaker: Utkarsh Bajaj

"Klein's icosahedral function"

Can we define a rational function on the sphere? Sure we can. Can we define a rational function on the sphere so that it is invariant under the rotational symmetries under the icosahedron? Yes - by embedding the icosahedron in the Riemann sphere (and then doing some algebra). We then show how this beautiful function reveals connections between the symmetries of the icosahedron and the E8 lattice  - the lattice that gives the most efficient packing of spheres in 8 dimensions!

MC 5501

Speaker: Keira Gunn, University of Calgary

"Some Problems on the Dynamics of Positive Characteristic Tori."

The real (or characteristic zero) torus is simply R/Z, or the "decimal part" of any real number with operations of addition and integer multiplication.  With the positive characteristic integers defined to be polynomials with coefficients from a finite field, and the positive characteristic reals their Laurent series counterparts, we can similarly construct the positive characteristic tori (each torus dependent on the choice of field).  At first glance there are many similarities to how operations work in both positive and zero characteristic, but these similarities break down quickly upon further inspection, particularly from a view of dynamics on the tori.

In this talk, we will discuss results on some orbital sets and dynamics formulae on the positive characteristic tori, including the Artin-Mazur zeta function and analogous hypothesis for Furstenberg's Orbital Theorem.

MC5403

Research Area: Algebraic Geometry/Number Theory

Speaker: Cynthia Dai

"Group Varieties"

Abstract: 

We will define group varieties and study their basic properties. 

You can access the handout at https://cynthiaddai.github.io/2024/05/17/HeightSeminar/

MC 5417

Speaker: Benoit Charbonneau

"Maple for differential geometry"

While we are certainly competent to do with pen and paper the myriad of computations required by our research, refereeing and our supervision work, I find that using tools can improve speed and accuracy and reduce frustration. I will share some principles and illustrate using Maple, including packages useful for differential geometry: difforms, DifferentialGeometry, and Clifford. Code displayed for this presentation can be found at https://git.uwaterloo.ca/bcharbon/maple-demos

MC 5417

Speaker: Cynthia Dai

"Elliptic curves"

We will study elliptic curves, derive Weistrass short form, and study the law of addition.

You can access the handout at Height Study Seminar | Doing Meow-thematics (cynthiaddai.github.io)

MC 5417