Lectures related to Coherent duality

Covers the application of Serre Duality in the general case, focusing on line bundles and core concepts.

Explores the applications of Serre duality in Enriques-Severi-Zariski lemma, foliations, and Riemann-Roch theorem.

Covers the concept of quasi-coherence in algebraic geometry, discussing the lifting of functions, sections of sheaves, and push forwards of coherent sheaves.

Coherent Sheaves: Locally Ringed Space

Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.

Duality in Linear Programming

Explores the concept of duality in linear programming, discussing the relationship between primal and dual problems.

Local Global Duality

Explores local-global duality in lattices and joint equidistribution of CM points.

Cup and Cap Product: Poincaré Duality

Explains the cup and cap product in algebraic topology and their relation to homology groups.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Duality Principle: Radon Measures and Homeomorphisms

Explores the Duality Principle for Radon measures and its applications.

Primal-dual Optimization: Fundamentals

Explores primal-dual optimization, minimax problems, and gradient descent-ascent methods for optimization algorithms.

Linear Programming Duality

Explores Linear Programming Duality, covering weak duality, strong duality, Lagrange multipliers interpretation, and optimization constraints.

Support Vector Regression: Recap and Convex Optimization

Covers the recap of Support Vector Regression with a focus on convex optimization and its equivalence to Gaussian Process Regression.

Cohomology of Quasi-Coherent on Affine Schemes

Covers the cohomology of quasi-coherent sheaves on affine schemes.

Optimal Decision Analysis

Explores strong duality, complementary slackness, economic interpretation, and stochastic problem scenarios in linear programming.

Linear Programming Duality

Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.

Duality: Duality in Linear Optimization

Covers the concept of linear optimization and the duality relationship between primal and dual problems.

Quadratic Lattices: Properties and Equidistribution

Covers non-degenerate quadratic lattices, local representability, equidistribution, and the Siegel theorem.

Primal-dual optimization: Theory and Computation

Explores primal-dual optimization, conjugation of functions, strong duality, and quadratic penalty methods in data mathematics.

Vector Bundles & Locally Free Sheaves

Covers vector bundles, locally free sheaves, depth, Serre twisting sheaf, and graded modules in algebraic geometry.

Optimization Duality: Theory and Algorithms

Explores optimization duality, weak and strong duality, practical optimization algorithms, and challenges in nonconvex-concave problems.