Lectures related to Generalized flag variety

Explores isotypic decomposition in finitely generated C-algebras and its implications, including G-stable ideals and linear projections.

Covers invariants and dimensions of projective varieties, emphasizing their importance.

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Explores automorphisms of projective varieties, discussing isomorphism between complements and key observations on dimensions and examples.

Covers the study of projective varieties and their relation to compact manifolds.

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Covers adjunctions, projective varieties, regularity, and valuative criteria in algebraic geometry.

Covers fixed points, orbits, and stabilizers in G-varieties, including properties of closed subgroups and faithful actions.

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

Introduces the regular representation, a key tool for studying group actions on varieties.

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

Explores integration theory over real numbers and Berkovich spaces, revealing intriguing asymmetries and unsolved conjectures.

Explores the embedding of chi-varieties into vector spaces with linear actions.

Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.

Covers the Shor Code, stabilizer matrices, encoding techniques, and error correction concepts.

Covers the construction of the connected sum of two tori in 10 minutes.

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Explores homogeneous ideals, regular rings, N-graded rings, and closed sets in projective geometry.

Covers the basics of probability theory, including probability spaces, random variables, and measures.