Harvard CMSA Courses

Non-interacting Quantum Field Theory in Riemannian Signature

Explore advanced mathematical concepts in quantum field theory, focusing on Riemannian manifolds and Feynman propagators through microlocal analysis and scattering theory applications.

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

Real-time Observables in Horizon Thermodynamics

Delve into quantum field theory concepts through an exploration of black hole thermodynamics, focusing on quasinormal modes and their relationship with thermal correlators in de Sitter space.

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

Theta Correspondence and Relative Langlands

Delve into advanced mathematical concepts exploring theta correspondence, hyperspherical varieties, and relative Langlands duality through geometric constructions and principal series representations.

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

The Geometric Langlands Conjecture

Delve into advanced mathematical concepts as Sam Raskin explains the proof and main ideas behind the unramified, global geometric Langlands conjecture in this Yale-Harvard collaboration.

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

Local Langlands Correspondence: From Extended Quotients to Affine Hecke Algebras

Delve into the mathematical foundations of Local Langlands correspondence, exploring extended quotients and their connection to affine Hecke algebras in p-adic group representations.

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

Relative Langlands and Endoscopy in Arithmetic Settings

Delve into advanced mathematical concepts exploring spherical varieties, relative trace formulas, and endoscopy in symmetric varieties, with applications to periods of automorphic forms.

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

Finite and p-adic Chern-Simons Type Invariants

Explore arithmetic invariants in Galois covers and étale local systems, examining Dijkgraaf-Witten and Chern-Simons constructions with applications to quantum field theory.

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

Going to the Boundary - Degenerating Marked Curves in Automorphic Moduli Spaces

Delve into advanced mathematical concepts exploring degenerating marked curves and their implications for automorphic moduli spaces, with applications to Langlands duality and Hecke categories.

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

Functional Analysis Over the Integers, L-Functions and Global Hodge Theory

Delve into advanced mathematical concepts exploring functional analysis over integers, unifying Archimedean and non-Archimedean analysis, with applications to L-functions and global Hodge theory.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

The Light We Can See - Extracting Black Holes from Weak Jacobi Forms

Delve into the mathematical connection between modular forms and black hole entropy, exploring how weak Jacobi forms reveal insights about supersymmetric black holes and AdS/CFT correspondence.

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

On the Nonabelian Fourier Kernel and the Lafforgue Transform

Delve into advanced mathematical concepts exploring nonabelian Fourier kernels, Lafforgue transforms, and functional equations of automorphic L-functions, with focus on SL2 cases and Gelfand-Graev formulas.

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

Connections Between Special Values of L-Functions and Scattering Amplitudes

Explore the mathematical connections between L-function special values and scattering amplitudes through differential equations, focusing on recent developments in arithmetic quantum field theory.

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

Modularity for W-algebras, Affine Springer Fibres and Associated Variety

Delve into advanced mathematical concepts exploring modularity for W-algebras, affine Springer fibres, and their relationship with Kac-Moody algebra representations and Cherednik's modular group actions.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Unexpected Unitarity in Supersymmetric Quantum Field Theories

Delve into advanced concepts of Supersymmetric Quantum Field Theories, exploring twisted theories, unitarity restoration, and their applications in the Analytic Langlands program and Symplectic Duality.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Analytic Langlands Correspondence Over C and R

Explore the analytic aspects of geometric Langlands correspondence, focusing on archimedean local fields and recent developments in mathematical physics and quantum field theory.

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