# Weekly bulletin

## Week starting Monday 19 March 2018

### Monday 19 March - Computational Mathematics Seminar

Start time: 4pm
Location: John Dedman Building 27 Room G35
Presenter(s): Mr Joseph O’Leary, School of Information Technology and Mathematical Sciences, University of South Australia and SERC Limited, AITC2 Mount Stromlo Observatory
Abstract:

The consequences and predictions of the theory of relativity are both far-reaching and non-intuitive; for example clock rates are measured differently by observers in relative motion and in varying gravitational fields. Furthermore, it predicts the universe is heavily populated with strange and exotic objects known as black holes and that light from objects will bend in the presence of massive bodies.

The incorporation of General Relativity (GR) is paramount in fields such as geodesy and astronomy where highly precise measurements are required. Current accuracy levels in geodesy and astronomy require that reference frames, planetary and satellite orbits and signal propagation be treated within the regime of GR.

In this talk, we present an overview of the history of GR and areas of interest being investigated as part of a PhD project. Finally, we address why the incorporation of GR is critical in present and future geodetic and astronomical techniques.

### Tuesday 20 March - Algebra and Topology Seminar

Start time: 3.30pm
Location: John Dedman Building 27, Room G35.
Presenter(s): Noah Snyder (Indiana)
Abstract:

For generic $q$, Kuperberg's $G_2$ spider agrees with the category of representations of the quantum group.  What happens when $q$ is a root of unity?  Except for a few small roots of unity, it turns out that the spider agrees with the category of tilting modules for $G_2$, and as a consequence the semisimplified spider agrees with the semisimple quantum group fusion category.  As a corollary of this result together with the trivalent categories classification, we can prove a Kazhdan-Wenzl-style recognition theorem for $G_2$.  This is joint work with Victor Ostrik.

### Friday 23 March - Quantum mathematics meeting

Start time: 3pm
Location: John Dedman Building 27, Room JD1177 (meeting room)
Presenter(s): César Fernando Venegas Ramírez (Universidad de los Andes)
Abstract:

This talk is based on a joint work done with César Galindo at Universidad de los Andes from Colombia. The purpose of this talk is to present some results on  minimal modular extensions of braided fusion categories doing emphases in minimal modular extensions of super-Tannakian fusion categories. We define actions of finite super-groups on fermionic fusion categories and spin-braided fusion categories. Similar to the case of groups, our motivation came from the study of fusion categories containing the representation category of a super-group. We develop many analog results to the Tannakian case, including cohomological obstructions, relation with braided $G$-crossed categories and minimal modular extensions.  We apply the general results to the construction and classification of minimal modular extensions of super-groups and braided fusion categories. In particular, we exhibit some examples of braided fusion categories without minimal modular extensions.

Updated:  25 March 2018/Responsible Officer:  Director/Page Contact:  School Manager