Robert Cornea, Department of Pure Mathematics, University of Waterloo
A basic Introduction to Higgs Bundles and Vafa-Witten Bundles, Part Two
Gian Cordana Sanjaya, Department of Pure Mathematics, University of Waterloo
"Elliptic Curves"
We switch our discussion to elliptic curves over finite fields. We prove Hasse’s bound and Weil conjecture, and we discuss more structures on elliptic curves over finite fields.
MC 5403
Scott Wilson, City University of New York
"Homotopical obstructions to the existence of certain complex structures on smooth manifolds"
Rachael Alvir, Department of Pure Mathematics, University of Waterloo
"Effectively closed sets - Part VI"
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 start proving an effective version of the perfect set theorem.
MC 5403
Jintao Deng, Department of Pure Mathematics, University of Waterloo
"The K-theory of relative group C*-algebras"
Amanda Petcu, Department of Pure Mathematics, University of Waterloo
"A History of Women in Math"
Xingchi Ruan, Department of Pure Mathematics, University of Waterloo
"Singular Series in the Hilbert-Kamke Problem"
The Hilbert-Kamke problem is a well-known problem in number theory. It looks for the solubility of a certain type of system of equations. We talk about how the singular series will provide solubility to the Hilbert-Kamke problem, and we will find a lower bound of the number of variables to ensure the sum of the singular series is positive.
MC 5403
Liam Orovec, Department of Pure Mathematics, University of Waterloo
"Unique Representations of Real Numbers in Non-Integer Bases"
Natasha Dobrinen, University of Notre Dame
"Infinite-dimensional Ramsey theory for binary relational free amalgamation classes"
Eric Boulter, Department of Pure Mathematics, University of Waterloo
"Co-isotropic foliations in holomorphic symplectic manifolds"