Mary Letey

Mary Letey

PhD Student in Applied Mathematics

Harvard University

Hello There!

I’m Mary, currently a PhD student in theoretical machine learning supervised by Professor Cengiz Pehlevan.

I enjoy learning about and working in a wide range of Applied Maths areas, from early-universe cosmology to machine learning and ML4Physics. I’m excited to develop techniques for understanding how neural network properties emerge through complex interactions of operations, and the role that structure in data plays in such theories.

I am always happy to discuss cool maths and related topics, please reach out if you’re interested!

Education
  • PhD in Applied Mathematics, 2023 - Present

    Harvard University, School of Engineering and Applied Sciences

  • MSc in Theoretical Physics, 2022 - 2023

    Perimeter Institute for Theoretical Physics

  • BA in Mathematics, 2018 - 2022

    University of Cambridge, St Johns College

Recent Posts

Variational Inference and Diffusion
A physics-vibes post on variational inference through the lense of denoising diffusion on structured probabilistic models.
Variational Inference and Diffusion

Projects

In-Context Learning in Transformers

Work underway … expect more soon!

Supervisor: Professor Cengiz Pehlevan.

In-Context Learning in Transformers
Poincare Symmetric Spacetime Lattices

Towards the goal of constructing discretisations of spacetime models that preserve as large of a discrete subgroup of Poincare symmetry as possible, we investigate lattices in maximally-symmetric relativistic geometries (i.e. Minkowski, de Sitter, and Anti-de Sitter spaces), and explore their properties and symmetry groups.

Supervisors: Professor Latham Boyle, Professor Jasper van Wezel.

Colleagues: Lizzy Rieth, Dr Felix Flicker.

Poincare Symmetric Spacetime Lattices
Reflection Groups in Lorentzian Spaces

Master’s Thesis. Towards constructing a mathematical framework to generalise the use of reflection groups in classifying discrete symmetries of Lorentzian spaces. We present a generalisation of the notion of crystallographic symmetry, an important property in the classical study of lattices and reflection groups, and then demonstrate substantial differences between reflection groups in Euclidean spaces vs Lorentzian spaces.

Supervisor: Professor Latham Boyle.

Reflection Groups in Lorentzian Spaces
Scattering Amplitudes and Colour Ordering

Investigating tree-level scattering amplitudes for gluons in Yang-Mills. By utilising colour decomposition, we consider partial amplitude formulas in the case of 3 negative-helicity gluons; in particular, we study their singularity structure using projective geometry.

Supervisor: Professor Freddy Cachazo.

Colleagues: Dawit Belayneh, Raquel Izquierdo Garcia, James Munday.

Scattering Amplitudes and Colour Ordering
Learning Quantum Wavefunctions with RNNs

Extending recent work pioneered at PiQuIL in approximating the groundstate wavefunction of a quantum lattice system using Recurrent Neural Networks: Investigated the affect of error and noisiness of the quantum data on the accuracy of the wavefunction and other physical quantities.

Supervisors: Professor Roger Melko, Schuyler Moss.

Learning Quantum Wavefunctions with RNNs
Quantum Initial Conditions for Inflation with Curvature

To generalise results in cosmological inflation to include non-flat universes and non-eternal inflation, a novel comoving curvature perturbation variable is proposed and analysed. Novel initial conditions are proposed by setting the vacuum using the renormalised stress energy tensor.

Supervisor: Dr Will Handley.

Quantum Initial Conditions for Inflation with Curvature
Using Media Data and Machine Learning to Predict Stock Fluctuations

Examining the extent that text data (such as financial reports, news articles, and search mentions) can predict the closing stock price of given companies. Text data was analysed using topic modeling to extract relevant features and recurrent neural networks to model time-dependence in the data sets.

Supervisor: Dr Chris Ketelsen.

Colleagues: Morgan Allen, Colton Williams, Aniq Shahid.

Using Media Data and Machine Learning to Predict Stock Fluctuations