Michael Deveau, Department of Pure Mathematics, University of Waterloo
“Computable Functors and Effective Interpretability”
Stephen Wen, Department of Pure Mathematics, University of Waterloo
“Applications of the zeta function over function fields.”
Anthony McCormick, Department of Pure Mathematics, University of Waterloo
“The Spencer Complex Part 3”
Vilmos Komornik, University of Strasbourg
"Topological and fractal properties of non-integer base expansions"
Given a base $1<q\le 2$, following R\'enyi (1957) we consider expansions of the form
\begin{equation*}
x=\sum_{i=1}^{\infty}\frac{c_i}{q^i}
\end{equation*}
with digits $c_i$ belonging to $\{0,1\}$. In case $q=2$ of the familiar binary expansions every $x\in [0,1]$ has an expansion, and this is unique except the dyadic rational numbers that have two expansions.
Ertan Elma, Department of Pure Mathematics, University of Waterloo
“Brun’s Sieve, Part 2”
We will finish the proof of the main theorem of Brun’s sieve (section 6.2 of the book An Introduction to Sieve Methods and Their Applications, by R. Murty, C. Cojocaru).
MC 5403
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
“A new construction of compact G2 manifolds by glueing Eguchi-Hanson spaces, Part III: Fibrewise blow-up by a family of Eguchi-Hanson spaces”
Trevor Gunn, Department of Pure Mathematics, University of Waterloo
“Hyperfields for Tropical Geometry”
Letian Chen, University of Waterloo
"Algebraic Function Fields and the Riemann-Roch Theorem"
We will introduce the concept of algebraic function fields and state the Riemann-Roch theorem. We will see some natural analogues between number fields and algebraic function fields. In particular we will define primes and divisors and study how prime factorization works in the function field case. As a consequence we will be able to prove that the class number of a function field over finite field is finite. Time permitting we will also talk about ramifications.
Panagiotis Gianniotis, Department of Pure Mathematics, University of Waterloo
"Relating diameter and mean curvature for submanifolds of Euclidean space"
Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Effective Bi-interpretability"
We extend the definition of effective interpretability presented last time to get the notion of effective bi-interpretability, and prove that a number of useful properties hold when two structures are effectively bi-interpretable.
MC 5403