May

23

2022

Persistent homology is a novel tool in data analysis executed by first assigning Vietoris-Rips complexes onto data and then compute the homology. In this talk we explore how finite group actions have the potential to improve existing persistent homology algorithms. We look at an interesting class of Vietoris-Rips complexes called the Regular Cyclic Graphs and see how ideas of group actions can be applied to it.

May

23

2022

The study of integer partitions is a fascinating and far-reaching area of study. Integer partitions with parts that differ by at least $d$, called $d$-distinct partitions, arise in a famous identity of Euler and the first Rogers-Ramanujan identity. The Alder-Andrews Theorem, namely that there are at least as many $d$-distinct partitions of $n$ as partitions of $n$ into parts that are $\pm 1$ modulo $d+3$, was proved in 2011 after more than 50 years of work. In 2020, Kang and Park constructed an extension of Alder's conjecture which relates to the second Rogers-Ramanujan identity.

May

24

2022

A material's interaction with electromagnetic waves can be described by complex permittivity. Moreover, electromagnetic waves can be simulated with the Finite Difference Time Domain method. We will explore how to estimate the effective complex permittivity of a heterogeneous Lorentz Media from a Finite Difference Time Domain simulation.

May

26

2022

We consider the set M_n(Z; H) of n x n matrices with integer elements of size at most H and obtain upper and lower bounds on the number of s-tuples of matrices from M_n(Z; H), satisfying various multiplicative relations, including multiplicative dependence, commutativity and bounded generation of a subgroup of GL_n(Q). These problems generalise those studied in the scalar case n=1 by F. Pappalardi, M. Sha, I. E. Shparlinski and C. L. Stewart (2018) with an obvious distinction due to the non-commutativity of matrices.

May

27

2022