**Sam Thomas // Personal Homepage**

**Here you can find my publications and slides from my talks, among other things.**

I appreciate there's not much on here yet, but hey, I'm only a year into my PhD!

I'm doing my PhD with Dr Perla Sousi. Currently, we are looking at the mixing time of a random walk on dynamical percolation where the underlying graph is the complete graph. For the moment, we are looking at the annealed mixing time of the walk: we consider the worst-case initial environment and starting location for the walk, then look at the TV distance of the walk from uniform while averaging over the environment.

My email address is s.m.thomas@statslab.cam.ac.uk.

**Publications**

- Mixing Time for Random Walk on Dynamical Erdos-Renyi (with P. Sousi) -- in final stages of preparation
- A paper rigorously showing hysteresis in a model of a fully connnected stochastic network with alterantive routing -- in progress
- Cutoff in Random Cayley Graphs (with J. Hermon) -- in progress

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**Invited Talks**

- Young European Probabilists (YEP), Eindhoven, Sept. 2017

- For a set of slides, click here

- Cambridge Analysts' Knowledge Exchange (CAKE), Cambridge, Nov. 2017
- For a set of slides, click here

- University of Warwick Combinatorics Seminar, Warwick, Feb. 2018
- For a set of slides, click here

**Teaching**

I have done supervisions (primarily for my college, St John's) and examples classes for various courses, as listed below.

- Part III
- 2017/18, Percolation and Random Walks on Random Graphs

- Part IB
- Part IA
- 2017/18, Analysis I
- 2016/17, Analysis I

**Education**

- 2017--current: PhD, University of Cambridge
- 2015--2016: Part III, University of Cambridge
- 2012--2015: BA, University of Cambridge