5 papers
Large products of double cosets for symmetric subgroups
Brendan Pawlowski
We consider the problem of classifying pairs such that where is a simple compact connected Lie group and is a symmetric subgroup. We give a nece…
Real 3-qubit gate decompositions via triality
Brendan Pawlowski
We show that any unimodular real 3-qubit gate can be expressed as the product of at most 14 CNOT gates plus single-qubit gates, improving on the bound of 16 CNOTs due to Wei and Di…
Ideal transition systems
Eric Marberg, Brendan Pawlowski
We study an inductive method of computing initial ideals and Gröbner bases for families of ideals in a polynomial ring. This method starts from a given set of pairs where…
Introduction to the Cohomology of the Flag Variety
Sara C. Billey, Yibo Gao, Brendan Pawlowski
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumer…
Chromatic symmetric functions via the group algebra of
Brendan Pawlowski
We prove some Schur positivity results for the chromatic symmetric function of a (hyper)graph , using connections to the group algebra of the symmetric group. The first su…