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Seminars in Combinatorics and Optimization
Algebraic and enumerative combinatorics seminar-Stephan Pfannerer-Mittas
Title:Descents for Border Strip Tableaux
Speaker | Stephan Pfannerer-Mittas |
Affiliation | University of Waterloo |
Location | MC 5479 |
Abstract: Lusztig's fake degree is the generating polynomial for the major index of standard Young tableaux of a given shape. Results of Springer and James & Kerber imply that, mysteriously, its evaluation at a d-th primitive root of unity yields the number of border strip tableaux with all strips of size d, up to sign. This is essentially the special case of the Murnaghan-Nakayama rule for rectangular partitions as cycle type. We refine this result to standard Young tableaux and border strip tableaux with a given number of descents. To do so, we introduce a new descent statistic for border strip tableaux, extending the classical definition for standard Young tableaux.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,
Tutte colloquium-R. Tyrell Rockafellar
Title: Problem Decomposition in Optimization: Algorithmic Advances Beyond ADMM
Speaker: | R. Tyrell Rockafellar |
Affiliation: | The University of Washington |
Location: | Main Hall, Federation Hall |
Abstract:
Decomposition schemes like those coming from ADMM typically start by posing a separable-type problem in the Fenchel duality format. They then pass to an augmented Lagrangian, which however can interfere with the separability and cause a slow-down. Progressive decoupling offers a more flexible approach which can utilize augmented Lagrangians while maintaining decomposability. Based on a variable metric extension of the proximal point algorithm that's applied in a twisted sort of way, progressive decoupling benefits from stopping criteria which can guarantee convergence despite inexact minimization in each iteration. The convergence is generically at a linear rate, and for convex problems, is global. But the method also works for nonconvex problems when initiated close enough to a point that satisfies a natural extension of the strong sufficient condition for local optimality known from nonlinear programming.
This talk is held as part of the 26th Annual Midwest Optimization Meeting (“MOM26”).
Algebraic and enumerative combinatorics seminar-Colleen Robichaux
Title:Complexity of structure constants
Speaker | Colleen Robichaux |
Affiliation | UCLA |
Location | MC 5479 |
Abstract: In algebraic combinatorics many families of polynomials have non-negative integral structure constants. Several open problems seek to provide manifestly positive combinatorial formulas for these coefficients. In part one of this talk, we prove the existence of signed combinatorial formulas for many families of structure constants. In the second part, we narrow our discussion towards Schubert structure constants. We discuss their complexity and explore potential implications. This is joint work with Igor Pak.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,