Lectures related to Extremal Lattices

Explores modular forms, discussing pullback maps, meromorphic differentials, and the Riemann-Roch theorem.

Explores the Logarithmic Law, geodesic flows, hyperbolic surfaces, and rare events in probability.

Explores isogenic graphs, spectral properties, and mathematical applications in modular forms and cryptography.

Introduces crystallography basics, covering unit cells, lattices, and reciprocal lattice concepts.

Explores crystal structure, real and reciprocal lattice, and Miller indices in the context of wave-particle duality and Schrodinger equation.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.

Covers commutative groups and their significance in cryptography.