Harvard CMSA Courses

Resurgence, Number Theory, and Quantum Mirror Curves

Delve into resurgence theory's application in quantum physics, exploring how non-perturbative data reveals number-theoretic properties in quantum mirror curves and toric Calabi-Yau threefolds.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Integrability in Discrete Random Matrix Theory

Explore integrability in discrete random matrix theory, covering probabilistic results, Hall-Littlewood polynomial formulas, and new formulas for Hermitian and antisymmetric p-adic matrices with formal Hall-Littlewood processes.

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

Unveiling the Classical Integrable Structure of Weak Noise Theory of KPZ Class

Delve into the classical integrable structure of weak noise theory in KPZ class, exploring the matrix Log-Gamma polymer and q-TASEP with Alexandre Krajenbrink.

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

Cosmology and Cosmological Polytopes I

Explore the intersection of cosmology and mathematical polytopes in this advanced physics lecture by renowned theoretical physicist Nima Arkani-Hamed.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Datasets for Math: From AIMO Competitions to Math Copilots for Research

Explore the evolution of mathematical datasets from AIMO competitions to research copilots, examining limitations, proposing structural shifts, and discussing how LLMs are redefining mathematical evaluation.

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

Tropicalized Quantum Field Theory

Discover a revolutionary approach to quantum field theory computations using tropicalization, enabling polynomial-time algorithms for previously intractable perturbative calculations.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

The Poincaré Conjecture and Mathematical Discovery

Explore the Poincaré Conjecture through topology and differential equations, examining its proof by Hamilton and Perelman and broader impact on mathematical discovery.

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

Understanding Optimization in Deep Learning with Central Flows

Explore how central flows reveal the hidden dynamics of deep learning optimization, explaining why gradient descent succeeds even when loss increases and how adaptive optimizers navigate complex landscapes.

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

Non-Perturbative Aspects of Self-Dual Gauge Theory

Explore non-perturbative effects in self-dual gauge theory, including beta-function computations via Grothendieck-Riemann-Roch and holographic methods, plus novel QCD calculations.

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

Graph Integrals on Kähler Manifolds

Explore convergence of graph integrals on analytic Kähler manifolds and their applications to constructing geometric invariants of Calabi-Yau metrics in holomorphic quantum field theory.

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

Symmetries and Moduli Spaces - Baby Steps beyond Calabi-Yau

Explore the interplay between symmetries and moduli spaces in string compactifications, moving beyond Calabi-Yau to G_2 and Spin(7) cases with worldsheet anomalies and non-invertible symmetries.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Special Kähler Geometry and Collapsing

Explore special Kähler geometry's role in supersymmetric gauge theories and mirror symmetry, focusing on hyperkähler manifolds with algebraic integrable systems and metric collapse.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Discovering Data Structures - Nearest Neighbor Search and Beyond

Explore how deep learning can discover and optimize data structures, focusing on nearest neighbor search algorithms and their applications in neural networks for sophisticated tasks.

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

Symmetry Operators and Gravity in Quantum Theory

Delve into advanced theoretical physics concepts examining the relationship between symmetry operators and gravity, focusing on topological operators and the challenges of conserved charges in gravitational theory.

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

Some Aspects of Symmetry Descent in Quantum Field Theories

Delve into the relationship between Quantum Field Theories and string geometry through SymTFTs, exploring symmetry structures and their geometric engineering applications.

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