Public explanation
Talks and presentations
Research talks and course presentations across mathematics, computer vision, information theory, and language models.
I use presentations to test whether an idea has become clear enough to explain. These talks range from mathematical concentration phenomena to computer vision and language-model reasoning.
Honor thesis presentation in Department of Mathematics of Washington University in St. Louis
Senior Honors Thesis Presentation: Measure concentration in complex projective space and quantum entanglement
Eads Hall, Room 115, Washington University in St. Louis
We explain, after Patrick Hayden, how concentration inequalities can be used in quantum theory to show that random quantum states associated to high-dimensional bipartite systems are highly entangled with high probability. A geometric interpretation of the concentration phenomenon can be given in terms of Michael Gromov's notion of the observable diameter of families of measure-metric (MM) spaces. We use Hayden's result to obtain estimates for the observable diameter of complex projective spaces.
CSE 5519 Advances in Computer Vision
GeoNet: Unsupervised learning of Monocular depth
Washington University in St. Louis
An introduction to GeoNet: Unsupervised learning of Monocular depth. GeoNet is a deep learning model that learns to predict depth from a single image.
Freiwald research program Summer 2025
Non-commutative probability theory and its applications
Washington University in St. Louis
An introduction to non-commutative probability theory and its applications.
Freiwald research program Summer 2025
Concentration of measure effect on quantum communication
Washington University in St. Louis
Given a bipartite system $A\otimes B$, assume $\dim(B)\geq \dim(A)\geq 3$, as the dimension of the smaller system $A$ increases, with a very high probability, a random pure state $\sigma=|\psi\rangle\langle\psi|$ selected from $A\otimes B$ is almost as good as the maximally entangled state.
Lectures on Honor Seminar for Mathematics
Introduction to Information theory and Shannon entropy
Washington University in St. Louis
An introduction to information theory and Shannon entropy.
Lecture 5 CSE 561 Fall 2024
Language Model Reasoning via Chain of Thought
Washington University in St. Louis
An introduction to language model reasoning via chain of thought.