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

## Upcoming seminars in Mathematics

Research seminars
Seminars in Statistics

### Russell Higgs

School of Mathematics and Statistics, University College Dublin

Date: Tuesday 5 March 2019
Time: 11:00 a.m.
Place: Room 241, 2nd floor, Science III building

This will be a survey talk discussing three open conjectures concerning the degrees of irreducible projective representations of finite groups. First a review of ordinary representations will be given with illustrative examples, before considering projective representations. A projective representation of a finite group $G$ with 2-cocycle $\alpha$ is a function $P:G \rightarrow GL(n, \mathbb{C})$ such that $P(x)P(y) = \alpha(x, y)P(xy)$ for all $x, y\in G$, where $\alpha(x, y)\in \mathbb{C}^*.$ One of the conjectures is can one conclude that $G$ is solvable given that the degrees of all its irreducible projective representations are equal.}

190214131235
Pattern formation in reaction-diffusion systems on time-evolving domains

### Robert van Gorder

Department of Mathematics and Statistics, University of Otago

Date: Tuesday 12 March 2019
Time: 11:00 a.m.
Place: Room 241, 2nd floor, Science III building

The study of instabilities leading to spatial patterning for reaction-diffusion systems defined on growing or otherwise time-evolving domains is complicated, since there is a strong dependence of spatially homogeneous base states on time and the resulting structure of the linearized perturbations used to determine the onset of stability is inherently non-autonomous. We obtain fairly general conditions for the onset and persistence of diffusion driven instabilities in reaction-diffusion systems on manifolds which evolve in time, in terms of the time-evolution of the Laplace-Beltrami spectrum for the domain and the growth rate functions, which result in sufficient conditions for diffusive instabilities phrased in terms of differential inequalities.

These conditions generalize a variety of results known in the literature, such as the algebraic inequalities commonly used as sufficient criteria for the Turing instability on static domains, and approximate or asymptotic results valid for specific types of growth, or for specific domains.

190214131405
Folding, surprise and playing games: deep learning at the CS department

### Lech Szymanski

Department of Computer Science, University of Otago

Date: Tuesday 19 March 2019
Time: 11:00 a.m.
Place: Room 241, 2nd floor, Science III building

This talk will give an overview of the research done by the deep learning group at the Department of Computer Science. Specifically, I will talk about the work in three different areas: theoretical analysis of deep architectures using folding transformations, reinforcement learning with surprise, and teaching a deep network to play Atari games without catastrophic forgetting.

190214131558
Projective Characters of Metacyclic p-Groups

### Conor Finnegan

University College Dublin

Date: Tuesday 26 March 2019
Time: 11:00 a.m.
Place: Room 241, 2nd floor, Science III building

The projective characters of a group provide us with important information regarding the structure and properties of the group. The purpose of this research was to find the projective character tables of metacyclic p-groups. This aim was achieved for metacyclic p-groups of positive type, but not in the negative type case. In this talk, I will give an introductory overview of some of the fundamental methods and results in projective representation theory. I will then discuss the application of these methods to metacyclic p-groups of positive type, using the previously understood abelian case as an example.

190318153651