Community & teaching
Mentorship & Seminars
Seminars and mentorship programs I have helped organize at UC Berkeley.
Student Probability Seminar
The UC Berkeley Student Probability Seminar is a venue for graduate students in mathematics, statistics, and neighboring departments to study topics in modern probability theory. In Fall 2023, I organized the seminar with Daniel Raban around Sourav Chatterjee's Superconcentration and Related Topics.
Introductory talk — Vilas Winstein
Superconcentration, chaos, and multiple valleys across a collection of running examples.
Markov semigroups and Poincaré inequalities — Adam Jaffe
Two fundamental tools for the semester, with applications to Gaussian polymers.
Superconcentration and chaos — Vilas Winstein
The equivalence of the two phenomena in a general Markov-process framework.
Chaos implies the multiple valley property — Ella Hiesmayr
A detailed treatment for the Gaussian polymer model.
Talagrand's method — Zoe McDonald
The L¹–L² method as a sharpening of the Poincaré inequality.
Two examples of superconcentration — Mriganka Basu Roy Chowdhury
First-passage percolation and the Sherrington–Kirkpatrick model.
The spectral method for proving superconcentration — Zachary McNulty
Chapter 6: spectral decomposition of the Ornstein–Uhlenbeck semigroup, an improved Poincaré inequality, and superconcentration in the Sherrington–Kirkpatrick model.
Extremal fields — Daniel Raban
Chapter 8: superconcentration and extremality, with applications to spin glasses and the discrete Gaussian free field.
Further applications of hypercontractivity — Zachary McNulty
Chapter 9: largest-eigenvalue superconcentration, low-correlation fields, subfields, and Gaussian fields on tori and Euclidean spaces.
Dimensions of level sets — Victor Ginsburg
Chapter 12: level sets of extremal fields and their induced dimensions.
Other semesters
- Fall 2025: arXiv seminar
- Spring 2025: stochastic calculus and arXiv seminar
- Fall 2024: approximation, inference, and sampling of Gibbs measures
- Spring 2024: topics in discrete probability
- Spring 2023: Stein's method
- Fall 2022: Large deviations for random graphs
- Spring 2022: The Gaussian free field
- Fall 2021: Markov chain mixing times
- Spring 2021: Random matrix theory
- Fall 2020: Random cluster model
- Spring 2020: Percolation and SLE
- Fall 2019: Optimal transport
Directed Reading Program
Spring 2025 — Foundations of Data Science
I mentored a second Directed Reading Program focused on high-dimensional data analysis. We followed Blum, Hopcroft, and Kannan's Foundations of Data Science, spending roughly two to three weeks on each chapter.
High-dimensional space — Chapter 2
Concentration and geometry in high dimensions, properties of the unit ball, high-dimensional Gaussians, random projections, and the Johnson–Lindenstrauss lemma.
Best-fit subspaces and singular value decomposition — Chapter 3
Singular vectors and SVD, optimal low-rank approximation, the power method, principal component analysis, and applications to clustering and ranking.
Random walks and Markov chains — Chapter 4
Stationary distributions, Markov chain Monte Carlo, Metropolis–Hastings and Gibbs sampling, conductance and convergence, electrical networks, and PageRank.
Machine learning — Chapter 5
The perceptron and kernel methods, generalization and overfitting, regularization, online learning, support-vector machines, VC dimension, boosting, and stochastic gradient descent.
Fall 2023 — Time Series Analysis by State Space Methods
In Fall 2023, I mentored a student through Berkeley Mathematics' Directed Reading Program. We studied Durbin and Koopman's Time Series Analysis by State Space Methods, moving from the local-level model to general linear Gaussian state-space models.
Filtering and smoothing in the local-level model
Kalman filtering from conditional multivariate normal distributions, Bayesian interpretation, and state-space smoothing.
Missing observations, initialization, and parameter estimation
Forecasting with missing data, diffuse priors, and maximum-likelihood estimation of variance parameters.
The general linear model
A framework encompassing local-level, ARMA/ARIMA, exponential smoothing, seasonal, and trend models.
Initialization of the filter and smoother — Chapter 5
Exact initialization of Kalman filtering and smoothing recursions when components of the initial state are known, diffuse, or treated as unknown constants.
Maximum-likelihood estimation of parameters — Chapter 7
Likelihood evaluation through the Kalman filter, parameter estimation under diffuse initial conditions, goodness of fit, and diagnostic checking.
Illustrations of the linear model — Chapter 8
Applications of linear state-space methods to structural time series, ARMA models, spline smoothing, and dynamic factor analysis.
Special cases of nonlinear and non-Gaussian models — Chapter 9
Exponential-family and heavy-tailed models, stochastic volatility and other financial models, and broader nonlinear state-space formulations.