Harvard CMSA Courses

Generative Modeling via Parabolic Monge-Ampère PDEs

Explore advanced generative modeling using parabolic Monge-Ampère PDEs, connecting optimal transport theory with modern AI techniques for non-log-concave distributions.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Tropical-Topological (Tropological) Sigma Models

Explore tropical geometry's bridge between complex and combinatorial worlds through topological field theory, examining Gromov-Witten invariants via BRST methods and nilpotent structures.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Tameness of Multisummable Series

Explore the tame geometric behavior of multisummable power series and their applications to differential equations, including analysis of the Stirling series and Gamma function.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Finiteness, Connectivity, and the Power of Fibrations in the Calabi-Yau Landscape

Explore finiteness and connectivity properties in Calabi-Yau manifolds through fibration techniques, bridging geometry and physics in string theory applications.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Finiteness and Tameness in Non-Archimedean Geometry

Explore non-archimedean geometry focusing on orders of magnitude, o-minimality analogues, and Pila-Wilkie counting results in tame geometric settings.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Analytic Tameness - Complex Cells

Explore complex cells, a complex analytic version of o-minimality cells, and their applications in quantifying analytic information within complex sets.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Degrees of Hodge Loci

Explore the geometric properties and computational aspects of Hodge loci through advanced mathematical analysis in this specialized geometry and physics seminar.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

O-Minimality - Finiteness and Complexity

Explore o-minimality's mathematical formalism for tame geometry, where sets have finite complexity, with applications to physics and quantitative complexity measures.

• YouTube
• 1 hour 36 minutes
• Self-Paced
• Free Video

The Swampland Program

Discover the Swampland Program's principles distinguishing valid quantum gravity theories from inconsistent ones in this Harvard physics lecture.

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

Tameness and Complexity in Physical Theories

Explore o-minimality applications in quantum field theory and quantum gravity, examining finiteness principles and tameness concepts in physical theories.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

Dualities and the Compactifiability of Moduli Space

Explore string theory dualities and moduli space compactifiability, connecting finite volume conditions to duality existence and semisimple representations in theoretical physics.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video