Events

Francisco Villacis, Department of Pure Mathematics, University of Waterloo

"Integrable systems on smooth projective toric varieties"

Let X be a smooth projective toric variety of complex dimension n. We can endow X with a symplectic form coming from the Fubini-Study form on projective space. We will show that we have an action of a real n-torus on X which is Hamiltonian and gives rise to an integrable system on X.

This seminar will be held both online and in person:

The intent of this seminar is to cover some of the basic theory of elliptic curves. Our first objective is to cover chapters 2, 3 and 6 from Joseph Silverman’s book (The Arithmetic of Elliptic Curves). Later in the semester, we will switch our focus towards more specific topics in the theory of elliptic curves. 

This week's presenter is Yash Singh, Department of Pure Mathematics, University of Waterloo.

MC 5403

Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets - Part III"

An effectively closed set (or $\Pi^0_1$ class) in Baire space $\omega^\omega$ is the set $[T]$ of infinite branches through a computable tree $T$. This semester in the computability seminar, we will be studying $\Pi^0_1$ classes from Cenzer \& Remmel's textbook. This week, we will conclude chapter 2 by discussing some applications of $\Pi^0_1$ classes in computability theory.

MC 5403

Erik Seguin, Department of Pure Mathematics, University of Waterloo

"Amenability and stability for discrete groups"

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

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.

Elliot Kaplan, McMaster University

"Hilbert polynomials for finitary matroids"

Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo

"Nearly Kahler 6-manifolds have SU(3)-structures"

David McKinnon, Department of Pure Mathematics, University of Waterloo

"Gaussian integers and gcds"

Changho Han, Department of Pure Mathematics, University of Waterloo

"A Brief Introduction to the General MMP Part 2"

Continuing from where we left off last time, I will discuss singularities of the MMP. Then, I will give a brief explanation of how the higher-dimensional MMP works; note that there will be some key differences from the surface case, including flips.

This seminar will be held jointly online and in person: