Harvard CMSA Courses

Dynamical Mean-Field Analysis of Adaptive Langevin Diffusions

Explore dynamical mean-field theory applied to adaptive Langevin diffusions in high-dimensional Bayesian linear regression with evolving priors and posterior sampling convergence.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Probably Approximately Correct Labels

Discover how to create cost-effective labeled datasets by combining expert annotations with AI predictions, ensuring high-quality results with rigorous mathematical guarantees.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Global Minimizers of Sigmoid Contrastive Loss

Explore theoretical foundations of sigmoid contrastive loss in SigLIP models, understanding (m,b)-Constellations and their role in representation learning and retrieval tasks.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Kernel Learning on Manifolds

Explore L_2 risk bounds for minimum norm interpolation using trace class elliptic kernels on Riemannian manifolds, revealing spectral cutoff relationships between samples and dimensions.

• YouTube
• 48 minutes
• On-Demand
• Free Video

An AI Approach to a Conjecture of Erdős

Explore how machine learning tackles Erdős' conjecture on tree independence sequences, uncovering thousands of counterexamples using PatternBoost architecture.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Predicting Euler Factors of Elliptic Curves

Discover how machine learning models predict Euler factors of elliptic curves with surprising accuracy from limited data in this advanced mathematical research presentation.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Machine Learning Mutation-Acyclicity of Quivers

Explore machine learning approaches to determining mutation-acyclicity properties in quiver theory through advanced mathematical techniques.

• YouTube
• 57 minutes
• On-Demand
• Free Video

Recent Developments in Automated Conjecturing

Explore how machines generate mathematical conjectures using optimization, enumeration, and AI, from graph theory to string theory with automated verification in Lean 4.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

RCD Structures on Singular Kähler Varieties

Explore RCD structures on 3D projective varieties with klt singularities, connecting algebraic geometry with Ricci curvature bounds and Nash entropy.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Dimension Reduction and Adiabatic Limits of Generalized ASD Instantons

Explore dimension reduction techniques for generalized anti-self-dual instantons over product manifolds, including G2 and Spin(7) cases with adiabatic limit analysis.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Can Transformers Reason Logically? A Study in SAT-Solving

Explore how Transformer models perform Boolean reasoning and solve 3-SAT problems, examining their capabilities, limitations, and potential solutions through Chain-of-Thought methodology and DPLL algorithms.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

The Einstein-Vlasov System in a Large Data Regime

Delve into advanced mathematical analysis of Einstein-Vlasov systems, exploring large data regimes, stability of Minkowski spacetime, and novel estimation techniques for Vlasov matter in relativistic contexts.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Quantum Cellular Automata - Understanding Evolution in Lattice Systems

Explore quantum cellular automata systems, focusing on lattice translations, topological phases, and locally generated subalgebras in discrete time evolution models.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Ranks of Elliptic Curves - A Survey of Rational Points and Group Structure

Explore the fundamental concepts of elliptic curves, their rational points, and group structures through an advanced mathematical examination of Mordell's theorem and contemporary research.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Frontier of Formal Theorem Proving with Large Language Models - DeepSeek-Prover Series

Explore the latest developments in automated theorem proving using LLMs, focusing on DeepSeek-Prover's innovative approaches to mathematical reasoning and formal verification systems.

• YouTube
• 53 minutes
• On-Demand
• Free Video