Mathematics
Te Tari Pāngarau me te Tatauranga
Department of Mathematics & Statistics

Upcoming seminars in Mathematics

Research seminars
Seminars in Statistics
Project presentations

Honours and PGDip students

Department of Mathematics and Statistics

Date: Friday 25 May 2018
Time: 2:00 p.m.
Place: Room MA241, 2nd floor, Science III building

STATISTICS

Qing Ruan : Bootstrap selection in kernel density estimation with edge correction

Willie Huang : Autoregressive hidden Markov model - an application to tremor data

MATHEMATICS

Tom Blennerhassett : Modelling groundwater flow using Finite Elements in FEniCS

Peixiong Kang : Numerical solution of the geodesic equation in cosmological spacetimes with acausal regions

Lydia Turley : Modelling character evolution using the Ornstein Uhlenbeck process

Ben Wilks : Analytic continuation of the scattering function in water waves

Shonaugh Wright : Hilbert spaces and orthogonality

Jay Bhana : Visualising black holes using MATLAB

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Kohnert polynomials

Dominic Searles

Department of Mathematics and Statistics

Date: Tuesday 29 May 2018
Time: 11:00 a.m.
Place: Room MA241, 2nd floor, Science III building

In 1990, Kohnert introduced an algorithmic operation on box diagrams in the positive quadrant. Kohnert proved that when the diagrams are left-justified, a weighted sum over such diagrams yielded a formula for the key polynomials, important in representation theory. He also conjectured that applying the same algorithm to another specific class of box diagrams, the Rothe diagrams of permutations, gave a formula for the geometrically-important Schubert polynomials.

In joint work with Assaf, we consider the application of Kohnert's algorithm to arbitrary box diagrams in the positive quadrant; we call the resulting polynomials Kohnert polynomials. We establish some structural results about Kohnert polynomials, including that their stable limits are quasisymmetric. Certain choices of box diagrams yield bases of the polynomial ring in a natural way; as an application, we use these results to introduce a new basis of polynomials whose stable limit is a new basis of quasisymmetric functions that contains the Schur functions. Some further conjectures regarding Kohnert polynomials will be presented.

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