Spectral Analysis: Hyperbolic Surfaces

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Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.

Explores quantum entanglement, Bell inequalities, and self-testing in quantum systems.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.