Lectures related to Monster Group: Representation

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

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

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers level curves and graphs of functions in two and three dimensions.

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

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

Explores Carathéodory's Theorem and its dimension implications for set representation.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers the representation theory of unitary minimal models and the Virasoro algebra.

Covers conformal blocks and their significance in complex structures and moduli spaces.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

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

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Covers commutative groups and their significance in cryptography.

Delves into the representation of SL2Z and the function F, exploring its transformation properties and relation to modular forms.

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

Explores essential chief series in tdlc groups, focusing on closed, normal subgroups and their chief factors.