# Piet Lammers

My name is Piet Lammers, I am a PhD student in the probability group of the University of Cambridge. I am also a Foundation Scholar of Queens’ College.

I am broadly interested in probability theory; my current research focus is on random discrete functions. I have uploaded my first preprint to the arXiv quite recently. This paper discusses the diffusive scaling limit of a random walk on a specific collection of discrete functions. My PhD advisor is James Norris.

This website intends to give an overview of my activities in Cambridge and I hope to regularly update it with new ideas, educational material and publications.

## Weblog

21 August 2017

The dimer model part III: The square lattice on a rectangle

To count the number of tilings of a large graph it is essential to calculate the determinant of a large matrix. This is a hard task in general, but in certain cases some reasoning greatly simplifies the calculations. In this post we show how to do this for... Click to read on.

9 August 2017

The dimer model part II: Kasteleyn theory

A first objective is to count the number of dimer covers of a given finite graph. The set of dimer covers is a complex combinatorial object; there will usually be too many dimer covers to simply calculate them all and count. The Kasteleyn theory simplifies this counting problem. The main ingredient of the theory is... Click to read on.

8 August 2017

The dimer model part I: A first introduction

Consider a chessboard covered by thirty-two domino tiles. Let $G=(V,E)$ be the graph with the squares of the board being the vertices and with edges connecting adjacent squares. Each domino tile is associated with an edge of this graph; write $M\subset E$ for the set of edges associated to domino tiles in our configuration. The set $M$ has the property that... Click to read on.

## Publications

Preprint

Diffusivity of a walk on fracture loops of a discrete torus (pdf, arXiv)

## Supervising

Lent 2017

1A Probability

This course was lectured by James Norris and I supervised this course at Queens’ and Jesus. This is the course web page.

Michaelmas 2016

1B Markov chains

This course was lectured by Geoffrey Grimmett and I supervised this course at Queens’. This is the course web page.

Michaelmas 2016

1B Optimisation

This course was lectured by Felix Fischer and I supervised this course at Queens’. This is the course web page.

## Curriculum vitae

2016 — 2020

University of Cambridge
PhD in Mathematics

2015 — 2016

University of Cambridge
MASt in Mathematics, disctinction

2012 — 2015

University of Utrecht
BSc in Liberal Arts and Sciences, summa cum laude

## Contact details

Room F0.01
Centre for Mathematical Sciences