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Algebra & Geometry Seminar

Speaker: Kirill Zaynullin (University of Ottawa)

Title: Twisted coproduct on the equivariant cohomology and its applications

Abstract: 
We introduce the twisted coproduct structure on the equivariant cohomology of complete flag variety and discuss its various applications and generalizations (cohomology of a group, Peterson subalgebra, finite real reflection groups). This is based on recent joint projects with Martina Lanini, Rui Xiong and Changlong Zhong.

Department Colloquium

Speaker: Maria Teresa Chiri (Queen's University)

Title: Conservation laws with flux discontinuous in the conserved quantity

Abstract:
We investigate a class of conservation laws where the flux function is discontinuous with respect to the conserved quantity, motivated by applications such as conveyor belt systems and traffic flow models. This discontinuity gives rise to solutions associated with multivalued fluxes, which we interpret as pairs consisting of a conserved quantity and its corresponding flux. These solutions can be obtained as limits of conservation laws with regularized fluxes, whose approximations exhibit shocks with arbitrarily large slopes. As a consequence, the fundamental property of finite speed of propagation no longer holds, and information may propagate instantaneously. In this talk, we introduce a suitable notion of entropy solution for the associated boundary value problem, establish existence via front-tracking techniques, and prove Kruzhkov-type stability estimates.

This is joint work with Fabio Ancona (University of Padua) and Ben van Eeden (ºÚÁϳԹÏ×ÊÔ´).

Dynamics, Geometry and Groups Seminar

Speaker: Abdul Zalloum (Queen's University)

Title: Constructing Isometric Actions on Metric Spaces from Walls

Abstract:
A guiding principle in geometric group theory is that one can learn about groups via their isometric actions on metric spaces. This approach is exceptionally successful when the underlying metric spaces satisfy certain non-positive curvature conditions. The following theorem is a simple example of the above phenomenon "a group is free if and only if it admits a free action on some tree". In this theorem, the geometric property of the tree having no loops, implied the algebraic property of the group being free and vice versa; this is a theme in geometric group theory. The goal of the talk is to discuss a procedure that takes as an input an arbitrary set S, a collection W of bi-partitions on S (thought of as "walls") and, depending on the combinatorics of W, it produces a range of metric spaces of non-positive curvature. The procedure is canonical in the sense that if G is any group acting on the set S preserving the collection of walls W, then it will act by isometries on the resulting metric spaces. I will also discuss some applications. This work is joint with Petyt.

Curves Seminar

Speaker: Dylan Gawlak

Affiliation: Queen's University

Title: Column words

Abstract: In this talk, we finish up  our discussion of chapter 2. We introduce two important partial orders on diagrams. Namely the lexicographic and dominance ordering. We will then discuss column words, which are a dual way writing down a word from a tableau or skew tableau. We will show that the column word of a diagram is Knuth-equivalent to the row word of the diagram.

Speaker: Luke Steverango

Title: The Plactic Monoid and Schur Polynomials

Abstract: In this talk we will continue with our investigation of the relationship between Young tableaux and words by specifically looking at how the sliding rule for skew tableaux works with elementary Knuth transformations. We will then define the plactic monoid, the tableaux ring, and continue on to Schur polynomials.

Algebra & Geometry Seminar

Speaker: Alexandre (Sasha) Zotine (McMaster University)

Title: Dynamics of Projectivized Toric Vector Bundles

Abstract:
Understanding the dynamics (self-maps) of a variety can often reveal information about its geometry. For example, the only curves with non-trivial surjective endomorphisms are of genus zero or one. In this talk, I will discuss the dynamics of projectivized vector bundles, where a similar classifying phenomenon seems to arise: the existence of non-trivial surjective endomorphisms suggests that the bundle splits into a direct sum of line bundles. This is joint work with Javier González Anaya and Brett Nasserden.

Dynamics, Geometry and Groups Seminar

Speaker: David Miyamoto (Queen's University)

Title: The smooth structure of a Lie group and its quotients

Abstract:
Given a Lie group G and a closed normal subgroup H, the quotient G/H is a Lie group with Lie algebra Lie(G)/Lie(H). When H is not closed (e.g. H could be dense), then G/H is no longer a manifold, and its quotient topology could even be trivial. I will discuss how, by instead viewing G/H as a diffeological space, we may always treat this quotient group as a smooth group with the expected Lie algebra. Specifically: G/H is a quasifold group, meaning it is locally modeled by quotients of R^n by countable affine actions (joint with Yi Lin), and it is elastic, meaning we have a Lie functor for which Lie(G/H) = Lie(G)/Lie(H) (invoking results of Christian Blohmann). Time permitting, I will indicate how this generalizes to the case of infinite-dimensional Banach Lie groups.