Week starting Monday 15 October 2018
A useful approach for studying representations of reductive groups over finite or local fields is to use parabolic induction and restriction that allow one to relate representations of different groups. The idea is to divide the theory into two complementary parts: decomposition of induced representations (using Weyl group combinatorics) and construction of the non-induced ones (which reflect the arithmetic of the field). In this talk I will describe new variants of parabolic induction and restriction which are suitable for groups over the p-adic integers. This is based on a joint work with T. Crisp and E. Meir.
Join us for a live webinar to learn more about the Master of Mathematical Sciences (Advanced). This webinar will include information about the course structure and career outcomes. Most importantly you will be able to ask any questions about studying at Australia's number one university
About the program
The Master of Mathematical Sciences (Advanced) enables you to upgrade your expertise in the mathematical sciences, either as a route to further study of mathematical sciences, or to upgrade your quantitative skills in areas that are rapidly becoming more reliant on advanced techniques from the mathematical sciences, such as the biological and computational sciences.
This course is only offered as an Advanced program and focusses on completing a substantial research project and dissertation, which constitutes appropriate research training for a PhD.
Professor John Urbas
John Urbas is an Professor at the Mathematical Sciences Institute. His research interests lie in partial differential equations and algebraic and differential geometry. He was the recipient of the Australian Mathematical Society Medal for his work on the positive resolution of the long-outstanding problem of global reglarity of the natural boundary value problem for the Monge-Ampere equation.
Modern algebraic-geometrical spectral theory of periodic operators is central for the construction of exact periodic solutions of a wide class of nonlinear models known as soliton systems. These solutions are expressed in terms of Riemann theta functions. The interaction between algebraic geometry and the soliton equations turns out to be beneficial for both sides. The famous Novikovs conjecture on the characterization of Jacobians of algebraic curves (more than 130 years old Riemann-Shottky problem) via solutions of the Kadomtsev-Petviashvili equation was proved by Shiota in 1986. Much stronger characterization was obtained by the author who proved Welters' trisecant conjecture.
In the talk we present these results and the solutions of another classical problem on characterization of Prym varieties via the theory of 2D Shrodinger operators integrable on one energy value. We then discuss another class of applications of the spectral theory that include a new approach to the construction of exact solutions to sigma-models. The latter is a joint work with A. Ilina and N. Nekrasov.
Do you want to explore career opportunities in the mathematical sciences? are you interested in furthering your mathematical studies with Honours, Masters or a PhD?
We have secured participation from the Ribit (CSIRO/ Data61), McKinsley & Company, Inc, Department of Defence, Australian Bureau of Statistics, Palantir Technologies, amongst others.
Timetable: (subject to change)
1pm Event start time
1.10pm Mathematical Sciences Institute
1.20pm McKinsley & Company, Inc
1.30pm Department of Defence, Defence Science & Technology Group
1.50pm Department of Defence, Australian Signals Directorate
2pm Stalls open
2.30pm Lucky draw prize
3pm Event close
There will be games to play, prizes to win, free goodies and much more.
No registration required.