# John Sylvester

## About Me:

I am a third year PhD student in the MASDOC programme at Warwick (Expected completion Sept. 2017). I am supervised primarily by Agelos Georgakopoulos with David Croydon as my second supervisor.

Before coming to Warwick I was studying MSci mathematics at University College London and my MSci project was in random sorting networks.

I am originally from the town of Guildford and outside of maths I like music, travelling and bouldering.

## Mathematical Interests:

My mathematical interests are in Probability and Combinatorics. In particular I am interested in random graph models, random walks on graphs and extremal combinatorics.

## Papers:

Random walk hitting times and effective resistance in sparsely connected Erdős-Rényi random graphs - arxiv:1612.00731

Connectivity of Erdős-Rényi random graphs - *in preparation*

## Projects:

I did a group project during my Msc year with fellow MASDOC students Adam Bowditch and Qiaochu Chen on long-range first passage percolation. Here is a link to the webpage produced for the project.

## Talks Given:

6th Polish Combinatorial Conference, Będlewo, 19th-23rd September, 2016: *Hitting times and electrical resistances in Erdős–Rényi random graphs.*

Workshop on Random Processes in Discrete Structures, Warwick, England, 30th August - 2nd September 2016:* Hitting times and electrical resistances in Erdős–Rényi random graphs.*

MASDOC Retreat, Wilderhope Manor, Shropshire, 24th May 2016: *Random walk hitting times and electrical resistances in Erdős–Rényi random graphs.*

Postgraduate seminar, Kent, 18th March 2016: *Random walk hitting times and electrical resistances in Erdős–Rényi random graphs.*

*Young researchers in mathematics, Oxford, 17th August 2015: **Paths, hitting times and effective resistance in sparsely connected Erdős–Rényi graphs.*

Probability on graphs and groups, EPFL Switzerland, 4th August 2015: *Paths, hitting times and effective resistance in sparsely connected Erdős–Rényi graphs.*

Random walks and Potential theory workshop, Warwick, 18th May 2015: *Hitting times and effective resistances in sparsely connected Erdős–Rényi random graphs.*

* *Postgraduate seminar, Warwick, 4th February 2015: *The cover cost of a random walk on a random graph.*

## Poster:

Here is a link to a poster I presented at the Simons Conference on Random Graph Processes, University of Texas, Austin TX, 9th-12th May 2016.

## Conferences Attended:

School and Workshop on Random Interacting Systems, University of Bath, England 19th-24th June 2016.

MASDOC Retreat, Wilderhope Manor, Shropshire, England, 23rd-25th May 2016.

Simons Conference on Random Graph Processes, University of Texas, Austin TX, 9th-12th May 2016

Probabilistic Combinatorics: A celebration of the work of Colin McDiarmid, Oxford, UK, 9th-10th April 2016.

UK Easter Probability Meeting, Lancaster, UK, 4th-8th April 2016

British Mathematical Colloquium, Bristol, UK, 21st-24th March 2016

Combinatorics: Challenges and Applications (Noga60), Tel Aviv University, Israel, 17th-21th January 2016,

LMS–EMS mathematical weekend, Uni of Birmingham, 18th–20th September 2015.

Non-Combinatorial Combinatorics, Warwick, 14th-16th September 2015

Young Researchers in Mathematics, Oxford, 17th - 20th August 2015.

Probability on graphs and groups, EPFL Switzerland, 3rd - 7th August 2015.

Regularity and Analytic Methods in Combinatorics, Warwick, 1st-5th July 2015.

*Random walks and Potential theory*, Warwick, 18th-22nd May 2015.

*Random Walks on Random Graphs and Applications*, TU Eindhoven, 14th-16th April 2015.

*Young European Probabilists*, TU Eindhoven, 23rd-27th March 2015.

*Random Graphs, Random Trees and Applications*, Isaac Newton institute, 16th-20th March 2015.

Young Researchers in Mathematics, Warwick, 30th June - 3rd July 2014.

## Other workshops attended

British Council Mexico: Education+ Technology Workshop, Mexico City, 9th-11th March 2016.

- I took part in a workshop ran by the British council to design apps to teach maths to 5/6th grade school children. A prototype of the app our team designed can be found here (in Spanish)

## Teaching:

Term 1, 2014/15: I was one of the teaching assistants for Geometry, a second year maths module at Warwick. During this term I also supervised two groups of second year maths undergraduates at Warwick.

Term 2, 2014/15: I was one of the teaching assistants for Probability A & B, a first year maths/stats module at Warwick.

12th-16th October 2015: I was one of two tutors on a one week residential maths course at Villiers park. The aim of the course was to give a group of around twenty five A-level students a taste of University maths. I planned and delivered six 1-1:30 hour introductory lectures on topics including: Permutations, Martingales, Hyperbolic Geometry, Continued fractions, Ramsey Theory and Overhanging Blocks.

Term 1, 2015/16: I am one of the TA's for Maths of Random Events, a third year stats module at Warwick.

Term 2, 2015/2016: I am one of the TA's for Stochastic Processes, a second year stats module at Warwick.

## Contact:

jasylvesterwarwickacuk

My office is B3.04, Warwick Mathematical Institute, Zeeman building.

Link to Warwick access to MathsSciNet