Ian Letter

About Me


I am a DPhil student in the Department of Statistics at the University of Oxford. My supervisors are Alison Etheridge and Julien Berestycki.

My current research focuses in understanding how constraints affect certain models of population genetics in spatial continuum.

Email: ian.restuccia@stats.ox.ac.uk

Last updated 17 of March, 2021.

Short (Academic) Biography

I completed my undergraduate of Engineering in Mathematics and Master's in Applied Mathematics at Universidad de Chile, 2012-2018, graduating with a first class Distinction in both of my titles. I specialized in Probability and its application to other problems, in particular population genetics. I have also been interested and work in problems related to computer science.

In July 2016 I started working with Jorge Pérez in my first research problem. It was a problem focused on modeling and understanding communications interfaces in computer science. From this work came my first paper A Formal Framework for Comparing Linked Data Fragments, that was presented in the ISWC 2017 and won the Best Research paper award.

In October 2016 I started my master thesis with Servet Martínez. The goal was to use probabilistic techniques to understand recombination in population dynamics in continuous time.I presented my thesis and graduated in January 2018, but continued working in this problem until September 2018.

In September 2018 I moved to Oxford to start my DPhil in Statistics (although I did not know Statistics at that time). From 2020 I am a Non-stipendiary lecturer in St.Hilda's college.

My PhD project focus on understanding how constraints affect certain models of population genetics in the spatial continuum. The models themselves translate into nice mathematical objects, like interacting particle systems, branching processes or measure valued processes. My goal is understanding how those models can incorporate external factors and how their behavior changed by the addition of said externalities.

In general I have a keen interest in models of population genetics and how can we use them to understand patterns and make predictions of real populations. This have lead me to learn techniques from Stochastic Analysis, Branching processes, Partial Differential equations and Stochastic Partial Differential equations. Although I not working in anything related to graph theory and its connection with probability I am really interested in that and would love to work on that in the future. The same applies for models related to the KPZ-fixed point.


  • Olaf Hartig, Ian Letter, Jorge Pérez, 2017, A Formal Framework for Comparing Linked Data Fragments, International Semantic Web Conference 2017, original draft.
  • Olaf Hartig, Ian Letter, Jorge Pérez, 2018, A Model of Distributed Query Computation in Client-Server Scenarios on the Semantic Web., IJCAI 2018, preprint.
  • Ian Letter, Servet Martínez, 2018, A probabilistic analysis of a continuous-time evolution in recombination, arXiv.
  • Frederic Alberti, Ellen Baake, Ian Letter, Servet Martínez, 2020, Solving the migration-recombination equation from a genealogical point of view, arXiv, accepted in Journal of Mathematical Biology.
  • Adam Smith, Sarah Penington, Ian Letter, Daniel Wilson, George Constable, 2021, Genetic diversity in facultatively sexual populations and its implications for the origins of self-incompatibility in algae and fungi, biorXiv, submitted.


Universidad de Chile, class tutor:
  • Multivariate Calculus (2-2013, 1-2014, 2-2016).
  • Ordinary differential equations (1-2014).
  • Probability and Statistics (1-2015, 2-2017, 1-2018).
  • Discrete Mathematics (1-2015, 2-2015, 2-2017).
  • Probability for Mathematicians (1-2016, 1-2017).
  • Markov processes (1-2016).
  • Computation theory (2-2016).
  • Evolution models (1-2017).
  • Stochastic Calculus (2-2017).
  • Stochastic Models for Engineering Systems (2-2017).
  • General topology (1-2018).
  • Dos Relojes, a initiative to help student study by open problem solving. (2017 and 1-2018).
  • Functional analysis (1-2021, remotely.).
Universidad Adolfo Ibañez, class tutor:
  • Stochastic models. (1-2017).
Oxford University, TA and tutor:
  • Applied Probability (T.A.: HT-2019, HT-2020, tutor: HT-2020, HT-2021).
  • Stochastic Models in Population genetics. (tutor: MT-2020, MT-2021).
  • Part A Probability (at St. Edmund's Hall) (tutor: MT-2020).
  • Non-stipendiary lecture in St.Hilda's college (Prelims and Part A: Probability, Statistics. Optional In Graph Theory). (tutor: 2020-2021).


  • Un contexto formal para comparar interfaces de comunicación, October, ENIM (Encuentro Nacional de Ingeniería Matemática), Universidad de Chile, 2017, slides (in Spanish).
  • An Introduction to local times and some applications, May, Oxford Junior Probability seminar, 2019.
  • On blocking phenomena of the Allen-Cahn equation using branching Brownian motion and curvature flow, November, Bielefeld Probability seminar, 2019.
  • On blocking phenomena of the Allen-Cahn equation using branching Brownian motion and curvature flow, April, Statistics department weekly meetings, 2020, slides.
  • Introducción a procesos tipo Lookdown y aplicación a determinar lineas ancestrales en poblaciones, February, ALMA Joven, 2021, slides (in Spanish).

Events attended

  • Meeting of SOMACHI, Chilean mathematical society, Talca, 2017.
  • APTS, First and second sessions of Academy for PhD Training in Statistics, Cambridge University and Southampton University, 2018/2019.
  • Probability meets biology, Bath University, 2019.
  • PIMS, School in Probability, Vancouver, 2020 (Canceled because the fire nation attacked, attended the online version instead).
  • ALMA Joven, Online, 2021.

Other work and events

  • Did an internship in the Department of Industrial Engineering of the Universidad de Chile working on a code to help control evasion on the public transport system, January, 2018.
  • Part of the organizer of the Statistics department weekly board games, from 2019 to 2021.
  • Organized a Reading group for the Probability group in the Statistics Department centered in models for population genetics, April to June, 2020.
  • Outreach event on PhD experiences for the CEIMAT of Universidad de Chile, 25 of November, 2020.
  • Scientific outreach podcast Matemáticas: logaritmos, algoritmos y otras palabras complicadas, from La voz del Welen, 30 of November, 2020.
  • ¿Qué hace un matemático? Computadores que hablan, perritos bailando y pájaros volando, Outreach talk for Colegio Pedro de Valdivia, March 2021, slides (in Spanish).
  • Mentor in the mentor and mentee program for new students in engenieer in mathematics, organized by CEIMAT, Universidad de Chile.

Awards and founding

  • CMM Scholarship for my master thesis, 2017.
  • Becas Chile, Doctorado en el extranjero scholarship for my PhD work, 2018 to 2022.

I helped to organize a seminar in the Probability group in the statistics department. This was conceive as a way to generate the feeling of community during the coronavirus pandemic. I was the main organizer during 2020. Since Febraury 2021 the title of organizer is property of Adrian Martini. I do still mantain the website where you can find the name of the talks and most of the sildes.