Events

Viktor Majewski, University of Waterloo

Generalized Seiberg-Witten Equations and where to find them

Everywhere.

MC 5417

Michael Gregory, University of Waterloo

The Complexity of the Isomorphism Problem for Finitely Generated Algebras

We review the arithmetic hierarchy and use it to analyze the isomorphism problem for finitely generated c.e. algebras. We introduce the ascending chain condition (ACC) on congruences and explain how it restricts the complexity of isomorphism. We show that any finitely generated c.e. algebra whose congruence lattice satisfies ACC has a \(\Pi_2\) isomorphism problem. Then, we prove that the class \(UF_2\) of algebras with two unary operations has \(\Sigma_3\)-complete isomorphism problem.

MC 5403

Anton Iliashenko, Beijing Institute of Mathematical Sciences and Applications

Deformation theory of associative and coassociative Smith maps

Associative and coassociative Smith maps are generalizations of pseudo-holomorphic curves in the \(G_2\) setting. We construct the right framework for the deformation theory using the spinorial formulation. This is enough to establish generic non-existence. Then we discuss where the theory goes from there.

MC 5403

Quang-Khai Nguyen, Universite de Lyon

Generating Series in Algebraic Dynamics

In this talk, we will discuss the generating series associated with a self-map of a projective variety. This series is important in understanding the dynamical degree and plays an important role in the recent construction of the transcendental dynamical degree by Bell, Diller, and Jonsson. This talk will focus on some analytic and algebraic properties of such a series. It turns out that in some cases, rationality is rather the exception.

MC 5403

Spencer Kelly, University of Waterloo

The Sobolev Embedding Theorem and The Berger-Ebin Decomposition Theorem

Serving as a part two of my previous talk, in this talk we will begin with briefly talking about the Sobolev Embedding Theorem for \(L^2\)-based Sobolev spaces. We will then move on to deriving the Berger-Ebin decomposition theorem for differential operators with injective symbol.

MC 5417

Alexander Teeter, University of Waterloo

Freedman’s Results and Donaldson’s Exclusions: Classification of 4-manifolds by intersection forms

We look at Serre's algebraic classification of symmetric integral unimodular forms, and then Freedman's topological classification of topological 4-manifolds by their intersection forms. After, we take a turn to looking at Donaldson's exclusions, finding that smooth 4-manifolds are not as well behaved. Time permitting, we will see how Donaldson's exclusions naturally lead to the existence of exotic \(\mathbb{R}^4\)s.

MC 5417

Jack Jia, University of Waterloo

Categories of representations of groups are well-behaved: They are abelian (behave like module categories), symmetric monoidal (have tensor products), every object has a dual and is semi-simple, to name a few. A natural question to ask is whether every category that exhibits similar behaviour is a representation category. Deligne proved a remarkable theorem that shows every symmetric tensor category with some imposed growth condition is in fact a category of representations. Moreover, he constructed some symmetric tensor categories with faster-than-exponential growth-these are so-called Deligne categories, which can be interpreted as complex rank analogs of classical representation categories. In this talk, I will introduce the notion of symmetric tensor categories, state Deligne's Theorem, and construct some of the Deligne categories. 

MC 5403

Mainak Poddar, IISER Pune

Equivaraint principal bundles over toric DM stacks

We extend the classification of torus equivariant framed principal bundles over toric varieties using Tits buildings by Kaveh, Mannon, and Huang to such bundles over toric Deligne-Mumford stacks. A corollary is that any such bundle over a stacky projective line splits. This is a joint work with Chandranandan Gangopadhyay and Ramandeep Singh Arora.

MC 5479

Beining Mu, University of Waterloo

Degree of categoricity and treeable degrees

In this seminar, we will discuss treeable degrees and degree of categoricity. We will introduce past results on which degrees can or cannot be a degree of categoricity and when degrees of categoricity coincide with treeable degrees. We will also introduce a notion of \(\Pi^0_1\) singletons as an example of treeable degrees and their relation to degree of categoricity.

MC 5403

Julius Frizzell, University of Waterloo

Factors of Measure Preserving Systems

We will discuss the basic idea of homomorphisms of measure spaces and measure preserving systems and what it means for a measure preserving system to be a factor of another measure preserving system.

MC 5417