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Algebra & Geometry Seminar

Speaker: Adrian Zahariuc (University of Windsor)

Title: Interpolation of fat points on K3 and abelian surfaces

Abstract: This talk will be concerned with questions in the style of the Segre-Harbourne-Gimigliano-Hirschowitz (SHGH) Conjecture. I will sketch a proof of the fact that any number of general fat points of any multiplicities impose the expected number of conditions on the primitive linear system of a very general K3 or abelian surfaces of any degree/polarization. The proof relies on the Segal-Wilson formula for the vanishing of the theta function in the KP direction, and thus has a significant (although implicit) transcendental ingredient.

Curves Seminar

Speaker: Julia McClellan

Affiliation: Queen's University

Title: The Robinson-Schensted-Knuth Correspondence

Abstract: Equipped with the necessary tools developed in our previous discussions, we will explore how the row bumping algorithm gives a one-to-one correspondence between matrices of nonnegative integers and pairs of tableaux of the same shape. This is known as the Robinson-Schensted-Knuth correspondence. Through example, we will demonstrate a more “geometric” construction for this correspondence which does not rely on the bumping algorithm, called the matrix-ball construction.

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 (���ϳԹ���Դ).

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.