Gedeon, Proudfoot, and Young first conjectured that the graded Sn -representations H∙(Conf(n,Rd);Q) are strongly equivariantly log concave for even d. Later work of Matherne, Miyata, Proudfoot, and...

We consider problems concerning the largest degrees of irreducible characters of symmetric groups, and the multiplicities of character degrees of symmetric groups. Using evidence from computer experiments, we posit several new conjectures or extensions of previous conjectures, and prove a number of results. One of these is that, if n >= 21, then there are at least eight irreducible characters of S_n, all of which have the same degree, and which have irreducible restriction to A_n. We explore similar questions about unipotent degrees of GL_n(q). We also make some remarks about how the experiments here shed light on posited algorithms for finding the largest irreducible character degree of S_n.

We classify representations of a class of Deligne-Mostow lattices into PGL(3,C). In particular, we show local rigidity for the representations (of Deligne-Mostow lattices with three-fold symmetry and of type one) where the generators we chose are of the same type as the generators of Deligne-Mostow lattices. We also show local rigidity without constraints on the type of generators for six of them and we show the existence of local deformations for a number of representations in three of them. We use formal computations in SAGE and Maple to obtain the results. The code files are available on GitHub.

In a significant advancement for the field of mathematics, Professor Pham Tiep of Rutgers University has solved two fundamental problems that have puzzled

Orbit Meetings take place on Wednesday afternoons three times a year across the Universities of Birmingham, Manchester and Warwick. The meetings focus on topics in group theory and representation…