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Adina Goldberg, University of Waterloo

Categorical Strings for Quantum Things

Heard of quantum graphs or quantum groups? Wondering if this is the same as the "physics" notion of quantum, as in quantum entanglement or quantum channels? When I started my PhD, I was perplexed. Now, some years of marinating in the stew of categorical quantum mechanics has convinced me of its descriptive power for tackling all things quantum. I will show you the string-diagram interface that goes hand-in-hand with dagger (compact/symmetric monoidal) categories, and give examples. Prerequisites: Familiarity with the vague idea of a category, and a willingness to wave your hands a little bit.

MC 5501

Viktor Majewski, Humboldt University Berlin

Resolutions of Spin(7)-Orbifolds

In Joyce’s seminal work, he constructed the first examples of compact manifolds with exceptional holonomy by resolving flat orbifolds. Recently, Joyce and Karigiannis generalised these ideas in the G2 setting to orbifolds with Z2-singular strata. In this talk I will present a generalisation of these ideas to Spin(7) orbifolds and more general isotropy types. I will highlight the main aspects of the construction and the analytical difficulties.

MC 5479

Adina Goldberg, University of Waterloo

Synchronous Quantum Games

We recast nonlocal games using string diagrams, allowing for a natural extension to quantum games (with bipartite question and answer states). We define strategies in this setting and show that synchronous quantum games require synchronized players to win. We give examples of some quantum games on quantum graphs and see that these require quantum homo/isomorphisms to win. (The talk is based on a preprint ``Quantum games and synchronicity'' (https://arxiv.org/abs/2408.15444). This work is inspired by Musto, Reutter, and Verdon's paper ``A compositional approach to quantum functions'', and relies heavily on the reference ``Categories for Quantum Theory'' by Heunen and Vicary for string diagrams in quantum information.)

MC 5417

Matthew Harrison-Trainor, University of Illinois Chicago

Scott analysis of linear orders

The Scott analysis measures the complexity of describing a structure up to isomorphism, and equivalently the complexity of describing its automorphism orbits, and of computing isomorphisms between different copies. I will introduce the Scott analysis in general and talk about the Scott analysis of linear orders in particular. Linear orders have a few special properties which makes their behaviour quite interesting and sometimes different from structures in general.

MC 5479

Cynthia Dai, University of Waterloo

Height Modulis on Toric Stacks

In this talk we will go through Matt’s work on height modulis on weighted projective space, mainly its construction, and then its application. If time permits, I will talk about generalizations of this construction to toric stacks.

MC 5403

Joey Lakerdas-Gayle, University of Waterloo

Symmetrically indivisible and elementarily indivisible structures

A first order structure M is indivisible if for every colouring of M into two colours, there is a monochromatic substructure N of M that is isomorphic to M. We will consider two stronger properties: M is symmetrically indivisible if N can be chosen so that every automorphism of N extends to an automorphism of M; and M is elementarily indivisible if N can be chosen to be an elementary substructure of M. We will discuss Model-Theoretic methods developed by Kojman and Geschke (2008), Hasson, Kojman, and Onshuus (2009), and Meir (2019) to study the relationships between these notions.

MC 5403

Joey Lakerdas-Gayle, University of Waterloo

Fundamentals of Computability Theory 3

We will continue learning about priority constructions, now using the finite injury method, following Robert Soare's textbook.

MC 5403

Paul Cusson, University of Waterloo

The Kodaira embedding theorem and background material

The Kodaira embedding theorem is a crucial result in complex geometry that forms a nice bridge between differential and algebraic geometry, giving a necessary and sufficient condition for a compact complex manifold to be a smooth projective variety, that is, a complex submanifold of a complex projective space. The material and proof will follow the exposition in Griffiths & Harris's classic textbook.

MC 5479

AJ Fong, University of Waterloo

Toric geometry without (most of) the geometry

Toric varieties are great because they lend themselves to combinatorial description and study. I will introduce some of the combinatorial objects involved, leaning heavily on and subsequently specialising to smooth toric surfaces as simple examples. If time permits, I will demonstrate the power of this approach by showing a result on Galois representations of toric surfaces.

MC 5403

Agniva Dasgupta, University of Texas at Dallas

Second Moment of GL(3) L-functions

In this talk, I will discuss our recent result, joint with Wing Hong Leung and Matthew Young, on the second moment of GL(3) L-functions on the critical line. Moments of L-functions on the critical line have been studied for over a hundred years now, and still remains a very active field of research in number theory. The second moment of GL(3) L-functions has proved to be especially difficult, and only in the last couple of years have we seen some progress on this. Building on top of these works, we are able to obtain a strong upper bound for this moment. This allows us to deduce some nice corollaries including an improvement on the error term in the Rankin-Selberg problem, and on certain subconvexity bounds for GL(3) x GL(2) and GL(3) L-functions. As a byproduct of the method of proof, we also obtain an improved estimate for an average of shifted convolution sums of GL(3) Fourier coefficients. 

MC 5479