Leah Duffett, Department of Pure Mathematics, University of Waterloo
"Horned spheres and Schoenflies Theorem"
Shaoming Guo, Indiana University Bloomington
"Parsell-Vinogradov systems in higher dimensions"
I will present a few results on counting the numbers of integer solutions of Parsell-Vinogradov systems in higher dimensions. A few techniques from harmonic analysis are crucial in our approach. They are Brascamp-Lieb inequalities, multi-linear Kakeya inequalities, induction on scales, etc.
MC 5501
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"A finite pointed group with no finite basis (part 2)"
We'll continue to go over the construction of Roger Bryant. Hopefully, we'll finally see the group P, and argue that every (n-1)-generated subalgebra of Q_n is in HSP(P).
MC 5413
Mykola Matviichuk, University of Toronto
"Deformation of Dirac structures via L infinity algebras"
Henna Koivusalo, University of Vienna
"Dimensions of sets arising from iterated function systems -- with a special emphasis on self-affine sets"
In this colloquium style talk I will review the history of calculating dimensions of sets that arise as invariant sets of iterated function systems. I will, in particular, compare the theory of self-similar sets to the theory of self-affine sets.
Laurent Bienvenu, Montpelier, CNRS
"Randomized algorithms in computability theory"
Justin Laverdure, Department of Pure Mathematics, University of Waterloo
"Rational maps from reduced schemes"
I'll outline the definition of rational, dominant rational, and birational maps, and use these notions to outline the equivalence of the categories of finitely generated extensions of a field k and that of integral k-varieties. I'll also go over the classical example of rational points on the circle, in the light of rational maps.
MC 5413
Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Isomorphisms that cannot be coded by computable relations"
When we wish to show that two structures have an isomorphism of a certain degree between them, a standard technique is to carefully choose some computable set $U$ and then show that under a natural isomorphism $f$, the image $f(U)$ has the degree we are interested in. We show a case of two structures isomorphic to $(\omega, <)$ where this method of establishing the degree of the isomorphism between them will not work.
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Isolated types of finite rank"
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Branching Processes, Martingales, Kingman’s Subadditive Ergodic Theorem, and some applications. Part V: Finale — A modern branching process"
In this last talk of the seminar series, I will talk about a modern branching process: V-variable trees. I will prove the existence of its almost sure branching rate and discuss questions similar in spirit to the work we did for Galton-Watson Processes. Notably, we will discuss ‘limit measures’ on the Gromov boundary of associated trees.