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This seminar covers a wide range of topics in Lie theory including (but not limited to) groups of Lie type, Lie algebras, Coxeter groups and their Hecke algebras, algebraic groups, and quantum groups, with emphasis on combinatorial and representation theoretic properties. Further information about upcoming seminars and people in the math department can be found at the CU Math Department Home Page.
Tue, Sep. 30 2:30pm (MATH 3…
Chindu Mohanakumar (University of Colorado Boulder)
X
The goal of this talk is to give an intuitive idea of coherent orientations and why they provide a useful invariant for symplectic manifolds. I will start from the definition of a symplectic manifold, and motivate the study of J-holomorphic curves in Symplectic Geometry. From there, I will give a loose idea of Floer theory and how it relates to Morse theory, and use this relation to motivate coherent orientations.
Coherent orientations of J-holomorphic curves in Symplectic Topology
Tue, Oct. 7 2:30pm (MATH 3…
Richard Green (CU)
X
Every permutation is associated to a classical combinatorial object called a Rothe diagram, where the number of points in the diagram is equal to the number of inversions in the permutation. In this talk, we generalize this notion by associating a Rothe diagram to a set of positive orthogonal roots for a finite simply-laced Weyl group. This construction turns out to have many applications to algebraic combinatorics and to the theory of invariant polynomials.
This is based on joint work with Tianyuan Xu (University of Richmond).
Orthogonal roots and generalized Rothe diagrams
Tue, Oct. 14 2:30pm (MATH 3…
Richard Green (CU)
X
We explore further applications of the generalized Rothe diagrams associated to sets of orthogonal positive roots of simply laced root systems. We will discuss examples arising from labelled Fano planes and from the representation theory of simple Lie algebras.
This talk is based on joint work with Tianyuan Xu (University of Richmond), and is a continuation of last week's talk.
Orthogonal roots and generalized Rothe diagrams, part 2
We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli space of stable genus zero curves with n marked points. In this talk, we give an explicit combinatorial bijection between these two sets of trees using an insertion algorithm, and also classify the words that appear on the slide trees of caterpillar shape via pattern avoidance conditions.
Insertion algorithms and pattern avoidance on trees coming from the moduli space of curves
Coherent orientations of J-holomorphic curves in Symplectic Topology