In order to study a random process, it is easier to set it up on a "small" region and then gradually "stretch it out" until it covers the whole of space. This is called the thermodynamic limit. On the other hand, discrete processes (those with small "jumps" at constant intervals) are easier to study than "continuous" processes. We therefore begin with a discrete field defined on a "grid" and gradually "shrink" the grid (or "zoom out") until it looks like a continuous process on smooth space, with no "jumps". This is called a scaling limit. A crucial question is: how do these two limits interact? My project revolves around this question.
|2019-2020 (Current)||MASt in Matematical Sciences||University of Warwick|
|2015-2019||BSc (Hons) in Philosophy and Mathematics with Specialism in Foundations and Logic||University of Warwick|
|2019-2020||TA for MA260 Norms, Metrics and Topologies||Wednesdays 12-1 B3.03|
|2019-2020||Supervisions||Small Group Teaching (11 students)|
MA260 Support Classes
Here is some material I discussed during the Support Class for Norms, Metrics and Topologies:
DISCLAIMER: This material is my own and I take full responsibility for its content and any mistakes it may contain. It has not been revised by the lecturers or any other member of the department.
- Week 3 [22/01/20]: Uniform Continuity Handout
Notes and slides
- Introductory notes on Complex Analysis (aimed at second year undergraduates with a bit of multivariable calculus)
- All functions are continuous! A provocative introduction to constructive analysis (Slides, no animations)