Abstract:
Given a finite group G we discuss how to determine from its character table whether a Sylow 3-subgroups of G has a minimal generating set of size 2. The algorithm to make this determination involves studying the Galois action on the characters of G, and the result provides evidence for the Alperin–McKay–Navarro conjecture.
Abstract:
The relational complexity of a permutation group G on a set Ω is a statistic measuring the minimal "complexity" of certain combinatorial/model-theoretic objects (homogeneous relational structures defined on Ω) with automorphism group G. Equivalently, the relational complexity of G is a measure of the way in which the orbits of G on k-tuples of points of Ω, for various k, determine the original action of G on Ω.
This talk, which will explore relational complexity from both of the above perspectives, will feature new results, joint with Veronica Kelsey and Colva Roney-Dougal, on the relational complexity of almost simple linear groups, and on the minimal number of relations of a homogeneous relational structure with a given automorphism group.
Abstract:
Every tensor $t$ naturally determines a Lie algebra of derivations, $Der(t)$, together with an associated space of tensors obtained by “tensoring” over $Der(t)$. This Lie algebra is universal among algebras generated by tensor operators. In this talk, we will survey the construction and universality of $Der(t)$, and present applications in tensor isomorphism testing and clustering. This is ongoing work with James Wilson.
Abstract:
Vertex operator algebras (VOAs) and their super analogues are algebraic objects that connect representation theory to physical theories like two-dimensional (super) conformal field theories. In this talk, we will define vertex operator (super) algebras and give some examples, including the singlet and the super singlet VOAs. While representation categories of the singlet VOAs have been thoroughly studied, less is known about the module categories of the super singlet. We'll discuss some open questions in the area and their relevance to VOA theory. This talk is based on an ongoing project with T. Creutzig, F. Orosz Hunziker, Y. Wang and J. Yang.
Abstract:
We propose a new method using the derivation algebra of the adjacency tensor. Current methods utilize the spectral theory of adjacency tensors to study hypergraphs. Our methods give insight into the internal structures of a hypergraphs which is often not discernable using combinatorial methods. They also lead to theorems on uniqueness of the decompositions found.