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
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
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: Cynthia Dai
"Global Heights"
In this talk, we will wrap up local heights with respect to a presentation of a line bundle, then define global heights. If time permits, we will also talk about Weil heights.
MC 5417
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: Filip Milidrag, University of Waterloo
"The Classification of Irreducible Discrete Reflection Groups"
In this talk we will make a correspondence between irreducible discrete reflection groups and associated connected Coxeter diagrams. Then we will use this to classify all connected Coxeter diagrams and by extension every irreducible discrete reflection group.
MC 5501
Speaker: Paul Marriott
"Statistics and Geometry: We don't talk any more."
George Bernard Shaw once said Britain and America are two counties separated by a common language. Perhaps the same can be said for Statistics and Geometry. This talk gives a high-level overview of a recent graduate course which explored the relationship between Statistics and Geometry. It looks at what the disciplines have in common but also where there are points of substantive difference. The talk will review the long history of geometric tools finding a place in statistical practice and will highlight modern developments using ideas from convex, differential and algebraic geometry and showing applications in Neuroscience.
MC 5417
Speaker: Alex Pawelko
"Symmetry Reduction and the Quest for G2 Moment Maps"
We present an overview of the classical theory of moment maps from symplectic geometry and their use within the Marsden-Weinstein-Mayer theory of symplectic reduction, with an emphasis on the Lie theoretic considerations that arise. If time permits, we will then discuss some attempts to generalize moment maps to the setting of G2 manifolds.
MC 5417
Speaker: Nicolas Chavarria
"T-minimal Theories and Dimension II"
We continue looking at Will Johnson's work on the dimension of definable sets in t-minimal theories.
MC 5403
Algebraic Geometry/Number Theory
Speaker: Cynthia Dai
"Local Heights"
In this talk, we will wrap up heights on projective space by prove Northcott's theorem for algebraic numbers. Next, we will local heights with respect to a Cartier divisor.
MC 5417