Harvard CMSA Courses

Some Thoughts About the Kapustin-Kitaev Cobordism Conjecture

Explore advanced mathematical physics connecting gapped quantum phases to bordism theory, investigating the Kapustin-Kitaev conjecture through category theory and topological methods.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Generalized Kitaev Pairings and Higher Berry Curvature in Coarse Geometry

Explore advanced mathematical concepts connecting Kitaev pairings with coarse geometry, extending topological invariants to higher dimensions and Berry curvature theory.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Quantizing Homotopy Types

Explore advanced topological quantum field theory through Kontsevich's quantization of finite homotopy types and its enhancement to fully extended TQFTs in iterated algebras.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Moduli Spaces of Projective 3D TQFTs

Explore moduli spaces of 3D topological quantum field theories and their connection to gapped quantum systems through homotopy theory and ribbon category automorphisms.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

On Some New Irrationality Results

Explore new techniques from mirror symmetry and quantum cohomology to prove irrationality of 4-dimensional unirational varieties using Hodge atoms theory.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

From Geometric to Classical Langlands

Explore the geometric Langlands equivalence and its implications for automorphic functions, including connections to Ramanujan and Arthur multiplicity conjectures.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Analytic Properties of Automorphic Functions as Seen from Algebraic Geometry

Explore how geometric Langlands equivalence reveals automorphic functions through algebraic geometry, connecting to Ramanujan and Arthur multiplicity conjectures.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Discretization and Distribution Learning in Diffusion Models

Explore discretization techniques and distribution learning in diffusion models, covering randomized midpoints, score matching, and applications to parameter estimation and density learning.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

The Value of Side Information in Unlabeled Data

Discover how side information in unlabeled data improves machine learning models through iterative pseudo-labeling and error decorrelation analysis.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Negative Stepsizes Make Gradient-Descent-Ascent Converge

Discover how negative stepsizes enable Gradient-Descent-Ascent convergence on min-max problems through innovative time-varying, asymmetric stepsize schedules and slingshot dynamics.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Self-play LLM Theorem Provers with Iterative Conjecturing and Proving

Explore self-play reinforcement learning for theorem proving where LLMs act as both conjecturers and provers, achieving state-of-the-art results on mathematical benchmarks.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Leveraging Synthetic Data in Statistical Inference

Discover how to safely combine synthetic and real data to enhance statistical inference power while maintaining error bounds without distributional assumptions on synthetic data quality.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

To Intrinsic Dimension and Beyond - Efficient Sampling in Diffusion Models

Explore theoretical foundations of diffusion models, focusing on how DDPM achieves efficient sampling by exploiting intrinsic data dimensionality and mixture structures.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

The Hidden Width of Deep ResNets

Explore mathematical frameworks analyzing deep ResNet training dynamics, revealing how infinite-depth networks behave as infinitely wide and optimal Transformer scaling laws.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Elements of Interactive Decision Making

Explore interactive decision making frameworks covering multi-armed bandits, contextual bandits, and reinforcement learning with statistical learning theory and algorithmic primitives.

• YouTube
• 58 minutes
• Self-Paced
• Free Video