Anton Iliashenko, Department of Pure Mathematics, University of Waterloo
"The third Betti number of nearly Kahler 6-manifolds"
Rasul Shafikov, Western University
"Lagrangian embeddings, rational convexity, and approximation"
A celebrated theorem of Duval and Sibony characterizes rationally convex real submanifolds in complex Euclidean spaces as those isotropic with respect to a Kahler form. I will discuss how the results in symplectic geometry can be used to obtain some new results in the approximation theory.
MC 5417
Ronnie Nagloo, University of Illinois at Chicago
"Geometric triviality in differentially closed fields"
Luke MacLean, Department of Pure Mathematics, University of Waterloo
"Effectively closed sets - Part IV"
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 begin on chapter 3.
MC 5403
Ronnie Nagloo, University of Illinois at Chicago
"Applications of model theory to functional transcendence"
Leo Jimenez, Department of Pure Mathematics, University of Waterloo
"Not pfaffian, Part II"
James Freitag has shown that the j-function is not Pfaffian using the model theory of differentially closed fields. We will work though his paper, entitled "Not pfaffian".
MC 5417
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:
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