Lectures related to Complex geometry

Conservation Laws: General Framework

Covers the fundamental conservation laws and properties of space and time beyond mechanics.

Conformal Blocks: Functions on Moduli Spaces

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

Interpolation Spaces

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Geometric Projects Review

Reviews geometric projects, exploring varying panel sizes and complex geometries.

Additive Manufacturing: Generalities

Explores the generalities of additive manufacturing processes, including benefits, disadvantages, and historical milestones.

Optical forces: Fundamentals and Applications

Explores optical forces and their coupling with mechanical degrees of freedom, covering radiation pressure, optical tweezers, forces in deformable cavities, and complex geometries.

Signal Representation

Discusses signal representation, focusing on mathematical expressions and inequalities in signal processing.

Complex Manifolds: GAGA Principle

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

P-adic integration: Rationality and Igusa zeta function

Explores p-adic integration, Igusa zeta function rationality, and monodromy conjectures.

Algebraic Geometry: Forms and Maps

Covers the concept of forms in algebraic geometry and the implications of constructing Bloch(A) from glued copies of A.

Shells I: Mechanics of Slender Structure

Covers thin pressure vessels, differential geometry of surfaces, and plate buckling theories.

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Position Space Approach: Analyzing Banana Feynman Diagrams

Presents the position space approach to banana Feynman diagrams and their differential equations.

Modern Algebraic Geometry

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Finite Element Modeling: Introduction

Introduces finite element modeling for numerical solutions to complex problems.

Asymptotic Gridshells

Explores asymptotic gridshells, challenges in designing complex curved surfaces.

Integration Techniques: Parts and Simple Elements

Covers integration by parts and decomposition into simple elements, providing step-by-step explanations and examples.

Tangent Spaces in Algebraic Geometry

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Weil Conjectures: Rationality and Function Equation

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.