Ross Willard, Department of Pure Mathematics, University of Waterloo
"Examples of dualizable and nondualizable algebras"
Having established useful criteria, I will illustrate their use in proving finite algebras are, or are not, dualizable.
MC 5403
Andrej Vukovic, Department of Pure Mathematics, University of Waterloo
"Fundamental Group of the Circle and Other Highlights"
Today we construct the circle type and show that its fundamental group is Z, using synthetic homotopy theory. As requested at the last meeting, we also show that function extensionality implies weak function extensionality.
MC 5413
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Pseudo-finite sets and dimension, Part 6"
I will discuss the pseudo-finite Larsen-Pink inequality, which compares pseudo-finite dimension to algebraic dimension in simple algebraic groups.
MC 5403
Sascha Troscheit, Department of Pure Mathematics, University of Waterloo
"Quasi self-similarity and the dimension drop conjecture for self-conformal sets"
Sven Raum, Stockholm University
"Superrigidity for group operator algebras"
Dmitry Zakharov, Central Michigan University
"Maps to trees and loci in the moduli space of tropical curves"
David Marker, University of Illinois at Chicago
"Logical Complexity of Schanuel's Conjecture"
Schanuel's Conjecture is naturally a \Pi^1_1-statement. We show that it is equivalent to a \Pi^0_3-statement in arithmetic by showing that if there are counterexamples, then there are computable counterexamples. The main ideas come from the work of Johnathan Kirby on exponential algebraic closure and exponential derivations.
MC 5403
Ruizhang Jin, Pure Mathematics, University of Waterloo
"Model-theoretic Analysability in Differentially Closed Fields"
Julius Ross, University of Illinois at Chicago
"Dualities between Complex PDEs and Planar Flows"
Andriy Haydys, University of Freiburg
"G2 instantons and the Seiberg-Witten monopoles"
G2 manifolds constitute a class of Einstein seven-manifolds and are of substantial interest both in Riemannian geometry and theoretical physics. At present a vast number of compact G2 manifolds is known to exist. In this talk I will discuss a gauge-theoretic approach to the construction of invariants of compact G2 manifolds. I will focus on an interplay between gauge theories in dimensions 7 and 3 and how this can be used for the construction of the invariants.