Lectures related to Lattices: Theory and Applications

Explores adelic number theory, emphasizing lattices, modules, linear combinations, and Z-linear properties.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

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

Explores compact sets, extreme values, and function theorems on bounded sets.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

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

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.