Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo
"Effective Descriptive Set Theory 3"
We will continue to introduce effective descriptive set theory following Andrew Marks's notes.
MC 5479
Lucia Martin Merchan, Department of Pure Mathematics, University of Waterloo
"Hodge decomposition for Nearly Kähler 6-manifolds"
In this talk we discuss the paper of M. Verbitsky (arXiv:math/0510618) where he finds Kähler identities for Nearly Kähler 6-manifolds. From that, he deduces a Hodge decomposition in the compact case, as well as some restrictions on their refined Betti numbers.
MC 5403
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Bounding nonorthogonality"
In stability theory there is a natural notion for what it means for a complete type $p$ to have significant definable interaction with a definable set $X$: we say that "$p$ is nonorthogonal to $X$”. This notion allows passing to a larger set of parameters, and if we insist on fixing the base parameters we get the stronger, but easier to see, notion of "non-weak-orthogonality”. Last year, Remi Jaoui and I, proved a theorem that, in a certain particular context coming from differential fields, says something like "$p$ is nonorthogonal to $X$ if and only if $p^2$ is not weakly orthogonal to $X$”. This year, Jason Bell, Matt Satriano and I gave the same theorem in another context coming this time from difference fields. The theorems have applications to the bimeromorphic geometry of algebraic vector fields and dynamical systems, but in this talk I will stick to the abstract statement itself, attempt to make it more precise, and maybe convey something about how it is proved (in the differential case).
MC 5479
Yash Singh, Department of Pure Mathematics, University of Waterloo
"Parabolic sheaves and stacks of roots"
We study parabolic vector bundles, and more generally parabolic sheaves on schemes and their connections with sheaves on certain stacks of roots, due to Borne and Vistoli. We will also see how log structures give a natural framework for these constructions.
MC 5417
William Gollinger, University of Waterloo
"Kirby Moves"
In this talk we revisit the handle moves introduced earlier, now in the context of Kirby diagrams. We will carefully study the effects of handle slides on framings, and illustrate some handle cancellations. Lastly we'll introduce blow-ups and blow-downs as helpful tools for making Kirby diagrams more amenable.
MC 5403
Chris Schulz, Department of Pure Mathematics, University of Waterloo
"NIP"
We continue reading through Simon's "A guide to NIP theories''.
MC 5403
Chris Schafhauser, University of Nebraska-Lincoln
"Finite dimensional approximations of groups"
Blackadar and Kirchberg introduced the class of matricial field C*-algebras, which are those which approximately embed into finite dimensional matrix algebras. Specializing this property to group C*-algebras, one defies a group to be MF if it admits approximate finite dimensional representations which are approximately faithful and and approximately weakly contained in the left regular representation. I will give a survey of known examples and properties of MF groups, including a recent result showing that free products of amenable groups amalgamated over a common normal subgroup are MF.
This seminar will be held both online and in person:
Cynthia Dai, Department of Pure Mathematics, University of Waterloo
"Introduction to Grassmannians"
We will introduce Grassmannians Gr$(k,n)$, then talk about the Chow ring of Gr$(1,3)$.
This seminar will be held both online and in person:
Steven Rayan, University of Saskatchewan
“Moduli Spaces and Quantum Matter: From Materials to Pure Mathematics and Back"
The advent of topological materials, a form of physical matter with unusual but useful properties, has brought with it unexpected new connections between physics and pure mathematics. As the name suggests, topology has played a significant role in understanding and classifying these materials. In this talk, I will offer a brief look at a vast extension to this story, arising from my work with various collaborators over the last three years, that sees complex algebraic geometry — in particular, Riemann surfaces and moduli spaces associated to them — being used to anticipate new models of quantum matter. There will be lots of pictures.
MC 5501
Sun Woo Park, University of Wisconsin-Madison
"On the prime Selmer ranks of cyclic prime twist families of elliptic curves over global function fields"
Fix a prime number $p$. Let $\mathbb{F}_q$ be a finite field of characteristic coprime to 2, 3, and $p$, which also contains the primitive $p$-th root of unity $\mu_p$. Based on the works by Swinnerton-Dyer, Klagsbrun, Mazur, and Rubin, we prove that the probability distribution of the sizes of prime Selmer groups over a family of cyclic prime twists of non-isotrivial elliptic curves over $\mathbb{F}_q(t)$ satisfying a number of mild constraints conforms to the distribution conjectured by Bhargava, Kane, Lenstra, Poonen, and Rains with explicit error bounds. The key tools used in proving these results are the Riemann hypothesis over global function fields, the Erd\"os-Kac theorem, and the geometric ergodicity of Markov chains.
MC 5501