MaPSS: Maths Postgraduate Seminar Series: Hazel Browne & Edda Koo

Hello all, 

The next MaPSS talk of this semester will be at 17:00 on Mon 23rd of September in
Carslaw 535.  It’s a great opportunity to meet fellow postgrads, listen to an
interesting talk, and of course get some free pizza! 

This time we have two speakers, Hazel Browne and Edda Koo. The title and abstract of 
their talks are attached as follows.

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Speaker: Hazel Browne 

Title: A Generalisation of the McKay Correspondence 

Abstract: "If we needed to make contact with an alien civilization and show them how 
sophisticated our civilization is, perhaps showing them Dynkin diagrams would be the 
best choice!" ~ Etingof et al, Introduction to Representation Theory.
   
The Dynkin diagrams are famous because of their tendency to appear in classification 
problems across disparate areas of mathematics. One example is the McKay Correspondence: 
a natural bijection between conjugacy classes of finite subgroups of SL_2(C) and the 
affine simply-laced Dynkin diagrams.
   
We will begin by explaining this bijection, using some basic Representation Theory. 
Then we’ll introduce a generalisation of the map, and the motivating question of this 
honours project: is the generalised map a bijection? (Unfortunately it isn’t, but there 
are still plenty of interesting things we can say about it!)

I will make sure there are lots of pictures and fun for all the applied mathematicians 
who came to watch Edda’s talk and are stuck watching mine as well :)

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Speaker: Edda Koo

Title: Coherent Structures and Solitary Waves in Geophysical Fluid Flows

Abstract: Coherent structures such as the Great Red Spot in the Jovian atmosphere or 
blocking highs in the atmosphere are prominent features in rapidly rotating fluids. 
Such fluids are described by the so-called quasi-geostrophic equations. We seek to find 
a reduced model description of coherent structures. We first attempt to model them as 
solitary waves and aim to derive the two-dimensional Zakharov-Kuznetsov equation - an 
extension of the one-dimensional Korteweg-de-Vries equation - which supports coherent 
stable lump solitary waves. We do so in a weakly nonlinear analysis of the 
quasi-geostrophic equations in several geophysically relevant scenarios. We will see 
that the QG equations do not allow for reduced solitary wave equations. In a second 
approach we will use collective coordinates to model coherent structures based on exact 
modon solutions of the quasi-geostrophic equations for constant mean flows.


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See you there! 

Details can also be found on the school’s Postgraduate Society website:
http://www.maths.usyd.edu.au/u/MaPS/mapss.2019.html

Cheers,
Wenqi