I study random trees and quantum information as a BLUE scholar at McGill University.
My research interests include probability theory, random discrete structures, reinforcement learning theory and quantum information theory.
Over my time at McGill, I've had the pleasure of working with great people from organizations such as SUMS, McGill NeuroTech and the McGill Classical Music Club.
When I'm not scribbling mathematical nonsense, you can find me reading Dostoevsky, creating my next oddly specific Spotify playlist or playing piano and cursing Rachmaninov's handspan.
Papers
Reports
Projects
Course Notes
- Brandenberger, A. M., Devroye, L. and Reddad, T. The Horton-Strahler number of conditioned Galton-Watson trees. arXiv:2010.08613 [math.PR] (2020). Submitted October 2020.
- Brandenberger, A. M., Devroye, L. and Goh, M. K. Root estimation in Galton-Watson trees. arXiv:2007.05681 [math.PR] (2020). Submitted July 2020.
- Shi, R., Legrand, C. and Brandenberger, A. Toddlers track hierarchical structure dependence. Language Acquisition 27, 397–409 (2020).
- Xiong, M., Hotter, R., Nadin, D., Patel, J., Tartakovsky, S., Wang, Y., Patel, H., Axon, C., Bosiljevac, H., Brandenberger, A. et. al. A low-cost, semi-autonomous wheelchair controlled by motor imagery and jaw muscle activation. In 2019 IEEE International Conference on Systems, Man and Cybernetics (SMC), 2180–2185 (2019).
For an up to date list, see my Google Scholar.
- Brandenberger, A. On the thermodynamic meaning of negative entropy. Survey paper written for COMP 480: Independent Studies in Computer Science, 18p (2020).
- Brandenberger, A. and McCracken, G. Extending fluctuation dissipation relations to policy gradient methods in reinforcement learning. Project report for COMP 599: Mathematical Foundations of Machine Learning, 14p (2019).
- Alama-Bronsard, Y. and Brandenberger, A. On the study of the topology, geometry, and second order properties of the loss surface of deep neural networks. Project report for COMP 598: Mathematical Foundations of Machine Learning (Statistical Learning Theory), 12p (2018).
- Lie for Me, built in January 2021 with Diego and Gabriela. An animation of the orbits of Lie groups.
- In the Stars, built in January 2021 with Simon and Jacob for Hack the North. Letting the stars answer your burning questions, using GPT-3 and the live feed of a radio telescope.
- Donut Electrodynamics, built in November 2020 with Diego, Shereen, Maia and Gabriela. Simulating electrodynamics on a flat torus. Won 1st place at the McGill Physics Hackathon!
- Random Trees, built in summer 2020 with Diego Lopez. Animating the free tree structures of randomly generated Galton-Watson trees of various offspring distributions.
- Fractal Graphics, building in progress with Diego Lopez. 3D mirror fractal rendered using a recusive ray tracing engine coded from scratch.
- MILO: the brain-controlled wheelchair, built in winter 2019 with McGill NeuroTech. "Students from different backgrounds — including biology, computer science, hardware engineering, data collection, and machine learning — got together on their free-time to start a project to challenge themselves and improve the world around them. By gathering EEG bio-signals from the brain, they were able to process the data in order to direct the wheelchair forward, left, right, and stop. Over the course of the development, the students were able to create a wheelchair without using motor controls – just the control of the user’s mind – further improved with impressive semi-autonomous enhancements."
For more samples of code written at 2am, see my GitHub.
- COMP 252: Honours Algorithms and Data Structures. Algorithm Complexity Analysis and Divide and Conquer, written with Anton Malakhveitchouk (Prof. Luc Devroye, winter 2018). Dynamic Programming (Prof. Luc Devroye, winter 2019).
- MATH 240: Discrete Structures. Full course notes, written with Binyuan Sun (Prof. Benjamin Seamone, winter 2018).
- MATH 247: Honours Applied Linear Algebra. Full course notes, written with Daniela Breitman (Prof. Axel Hundemer, winter 2018).
- MATH 323: Probability Theory. Full course notes (Prof. David Stephens, fall 2018).
Drop a star on the GitHub repo if you found these notes useful