Events by month

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.

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

"Introduction"

This term some of us will be working through sections 2 and 3 (and  maybe 4?) of a recent paper of Bakker-Brunebarbe-Tsimerman in which a definable version of Serre's GAGA is developed (and then applied to solve an old problem of Griffiths). It is a kind of compromise between algebraic geometry and local complex analytic geometry facilitated by model theory (it seems to involve very little of the last).

Tobias Fritz, Perimeter Institute

"A separation theorem for order unit modules, with applications to random walks and the Laplace transform"

Rémi Jaoui, Department of Pure Mathematics, University of Waterloo

"Pseudo-finite sets and dimension, Part 6"

In this first session of the reading group for 2019, I will summarize some results of the previous lectures on probability logic and explain some applications to the study of ultraproducts of k-approximate subgroups.

MC 5403

Andriy Haydys, University of Freiburg

"The blow up set of the Seiberg-Witten equation with multiple spinors"

David McKinnon, Department of Pure Mathematics, University of Waterloo

"Definable complex analytic spaces"

I'm going to talk about definable spaces, and then start on a discussion of section two of the paper of Bakker-Brunebarbe-Tsimmerman.

MC 5479

Daniel Smertnig, Department of Pure Mathematics, University of Waterloo

"On basic and Bass quaternion orders"

Christopher Hawthorne, Department of Pure Mathematics, University of Waterloo

"Cryptographic primitives and applications"

Guy Salomon, Department of Pure Mathematics, University of Waterloo

"Hyperrigid subsets of Cuntz–Krieger algebras and the property of rigidity at zero”

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"The Isomorphism Problem for Pregeometries"

Ross Willard, Department of Pure Mathematics, University of Waterloo

"Dualizing structures that are necessarily of infinite signature"

Patrick Speissegger, McMaster University

"Limit cycles of planar vector fields, Hilbert’s 16th problem and o-minimality"

Pop by the Mathematics 3 (M3) Atrium any time throughout the day and watch as the omnitruncated dodecaplex comes together. Piece-by-piece the 3D polytope model will be put together by Professor Benoit Charbonneau and student, staff, and faculty volunteers. At the end of the day it will rise up and be a permanent art installation in M3.

Siddharth Mathur, University of Arizona

"Azumaya Algebras and the Resolution Property"

Azumaya algebras, are (etale) twisted forms of matrix rings. These objects are of great utility because they give rise to Brauer classes. Fifty years ago, Grothendieck asked whether every cohomological Brauer class has a corresponding Azumaya algebra. This question is still open even for smooth separated threefolds over the complex numbers!

Michael Lipnowski, McGill University

"Algorithms for the topology of arithmetic groups"

Integer matrix Lie groups \Gamma carry extremely deep arithmetic information.  Topological invariants of \Gamma are particularly interesting.  I will describe an algorithm which, given \Gamma, computes the homology of \Gamma together with the action of certain correspondences on it (Hecke operators).  Joint work with Aurel Page.

MC 5501

Levon Haykazyan, Department of Pure Mathematics, University of Waterloo

"Coherence"

We discuss sections 2.2 and 2.3 of the Bakker-Brunebarbe-Tsimerman paper.

MC 5479

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"The Isomorphism Problem for Pregeometries"

We show that the isomorphism problem for rice pregeometries in which dependent elements are dense (Condition B)  is $\Pi^0_3$-hard.

MC 5413

Ross Willard, Department of Pure Mathematics, University of Waterloo

"Dualizing structures that are necessarily of infinite signature, part 2: proof of duality"

In this lecture I will give Pitkethly’s proof that her schizophrenic pair (described in the seminar the previous week) is in fact a dualizing pair.

MC 5479

Rémi Jaoui, Department of Pure Mathematics, University of Waterloo

"Pseudo-finite sets and dimension, Part 7"

In my talk, I will explain a proof of the stabilizer theorem in the combinatorial setting  (Sanders' Theorem) using the independence theorem of probability logic.

MC 5403