Representation of SL2Z

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Explores the significance of the Jacobi identity in Lie algebra and its impact on linear vector spaces.

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Covers the Fourier expansion of modular forms and the Rankin-Selberg method.

Covers the unit tangent bundle of hyperbolic spaces and geodesic flows.

Covers dimension formulas for modular forms and related proofs using Riemann-Roch corollaries.

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Explores Lie groups, scalar fields, and vector spaces transformations.

Explains the representation of Lorentz fields and the concept of gravitons and gravitinos.

Explores meromorphic differentials on Riemann surfaces and modular forms on congruence subgroups.

Explores extremal lattices, emphasizing bounds on shortest vectors and unique modular forms.