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Week starting Monday 19 November 2018
20 November - Homological Algebra Reading Group
In this talk Adele, will tell us about some results for H_{1} and H^{1} for Lie algebras.
21 November - Homological Algebra Reading Group
In this talk, Bregje will tell us about the Hochschild-Serre spectral sequence.
22 November - Homological Algebra Reading Group
In this talk, Kie Seng will tell us about the correspondence between H^{2} of a Lie algebra with coefficients in some module M and the set of extensions of the Lie algebra by M.
23 November - Special year 2018: Analysis
This mini course will introduce a method in parabolic stochastic PDE, based on techniques and concepts from harmonic analysis and operator theory. The method was developed in 2012 by van Neerven, Veraar, Weis, and has been rapidly gaining popularity.
This minicourse precedes the Workshop in Stochastic Analysis, to be held from the 26 - 30 November 2018.
Prerequisites for the course will be some functional analysis (including Hahn-Banach theorem, and weak topologies in Banach spaces), and knowledge of probability (including Ito integral). The course will be taught by Pierre Portal (an early adopter of the method).
To make the most of the mini-course, and understand at least the first 1/3 of each talk at the workshop, you need to be fairly familiar with the material contained in (the first half of) books such as:
- Steele Stochastic Calculus https://www.springer.com/gp/book/9781441928627
- Stein-Shakarchi Functional Analysis https://www.amazon.com/Functional-Analysis-Introduction-Princeton-Lectures/dp/0691113874
- Evans PDE https://bookstore.ams.org/gsm-19-r
- Knowledge of operator theory (as in Engel Nagel https://www.springer.com/gp/book/9780387984636) would be very helpful, but will not be assumed for the mini-course.
Advanced knowledge at the level of books such as
- Karatzas-Shreve Brownian motion and stochastic calculus https://www.springer.com/gp/book/9780387976556
- Gilbarg Trudinger Elliptic PDE https://www.springer.com/gp/book/9783540411604
- Stein Harmonic Analysis https://press.princeton.edu/titles/5390.html
- Hytonen, van Neerven, Veraar, Weis Analysis in Banach spaces
- https://www.springer.com/la/book/9783319698076
would guarantee that you can completely follow the mini-course, and almost all of the workshop talks.
Schedule
| Friday 23 November | |
|---|---|
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9 - 9:30am Arrival tea & coffee 10 - 12pm PDE and SPDE as ODE and SDE in Banach spaces 2 - 4pm Stochastic integration in Banach spaces |
| Saturday 24 November | |
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9 - 9:30am Arrival tea & coffee 10 - 12pm Van Neerven-Veraar-Weis maximal regularity theorem for abstract parabolic SPDE 2 - 4pm Applications to concrete SPDE, inc. stochastic Navier-Stokes equations |
Funding:
The event is part of the AMSI funded Special Year in Analysis. Consequently, students from AMSI institutions can apply for AMSI travel support through their institution.
Organiser:
Pierre Portal (Analysis & Geometry, MSI, Australian National University)
