Nickolas Rollick, Department of Pure Mathematics, University of Waterloo
"Scheming with my associates"
Anthony McCormick, Department of Pure Mathematics, University of Waterloo
"Physics for Mathematicians"
David Urbanik, University of Waterloo
"Motivating the Riemann-Roch Theorem"
We attempt to motivate the Riemann-Roch Theorem for compact Riemannian surfaces by considering the concrete cases of the Riemann sphere and complex tori.
MC 5403
Jonny Stephenson, Department of Pure Mathematics, University of Waterloo
"Effective Bi-interpretability with Graphs"
Ertan Elma, Department of Pure Mathematics, University of Waterloo
"Selberg's Sieve"
We will start reading Chapter 7 of the book An Introduction to Sieve Methods and Their Applications, by R. Murty, C. Cojocaru.
MC 5403
Letian Chen, University of Waterloo
"Applications of the Riemann-Roch Theorem"
We will continue from last time and state the Riemann-Roch theorem after recalling some key definitions and results. We will then use the Riemann-Roch theorem to give a characterization of function fields of genus 0 and show the finiteness of the class group.
MC 5403
Tyrone Ghaswala, Department of Pure Mathematics, University of Waterloo
"The liftable mapping class group"
Panagiotis Gianniotis, Department of Pure Mathematics, University of Waterloo
"The Michael-Simon Sobolev inequality"
I will talk about the paper of Michael and Simon "Sobolev and Mean-Value inequalities on Generalized Submanifolds of R^n". In this paper, Michael-Simon use an elegant argument to prove a general Sobolev inequality for functions on subsets of the Euclidean space, which in particular is quite useful in the study of submanifolds.
MC 5479
Jonny Stephenson, Department of Pure Mathematics, University of Waterloo
"Effective bi-interpretability and Graphs II"
Last time we saw that every structure is effectively bi-interpretable with a structure over a simple language consisting of a unary predicate U and a symmetric binary predicate E. This week, we will show that any structure over this language is effectively bi-interpretable with a graph. This will complete the proof that every structure is effectively bi-interpretable with a graph.
MC 5403
Ertan Elma, Department of Pure Mathematics, University of Waterloo
"Selberg's Sieve II"
We will finish the proof of the main theorem of Selberg's sieve and prove the Brun-Titchmarsh theorem as an application.
MC 5403