Lectures related to Moduli stack of elliptic curves

Conformal Blocks: Functions on Moduli Spaces

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

Isogeny Graphs: Eigenvalues and Cryptography

Explores isogeny graphs of supersingular elliptic curves, showing optimal mixing times for random walks and applications to cryptography.

Introduction to Elliptic Curves

Covers the basics of elliptic curves, their significance in cryptography, and their applications in public key cryptography.

Symmetric Product Orbifolds & Holography

Explores Symmetric Product Orbifolds and their relation to Holography in AdS/CFT duality, covering AdS3 Gravity, primary operators, and BPS states.

Elliptic Curves: Theory and Applications

Covers the theory and applications of elliptic curves in cryptography and number theory.

Elliptic Curves: Singular Points and Group Law

Explores singular points, the group law, and the ambiguity in defining the sum of a point with itself on elliptic curves.

Homomorphic Encryption: Applications and Implementations

Explores homomorphic encryption, its applications, challenges, and comparisons with Trusted Execution Environments, as well as the use of aggregated keys for secure data sharing.

Modular Curves: Genus and Mapping Theorems

Explores holomorphic maps, ramification points, and the genus of a modular curve.

Covering Systems: Intellectual Property and Innovation

Covers covering systems in mathematics and the significance of intellectual property in innovation.

Modular Lambda Function: Properties and Applications

Explores the modular lambda function, its properties, and applications in modular forms.

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Viscoelasticity: Principles and Applications

Explores viscoelasticity in polymer materials, emphasizing time-dependent behavior and transitions in properties, and discusses Dynamic Mechanical Analysis.

Discrete Log Problem: Index Calculus

Explores the discrete log problem and index calculus method in cryptography.

Homomorphic Encryption: Applications and Operations

Explores legal aspects, security, and privacy in homomorphic encryption, covering elliptic curves, encoding, and practical applications.

Elliptical Curves and Surfaces

Explores elliptical curves, surfaces, and spatial constructions, emphasizing resolution techniques and parallelism.

Incidence Geometry & Elliptic Curves

Explores the Cayley-Bacharach theorem in incidence geometry and introduces elliptic curves with a commutative law.

Advanced Analysis II: Length of Continuously Differentiable Paths

Explores the length of continuously differentiable paths using integrals and parametrizations.

Affine Algebraic Sets

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.

Elliptic Curves and Lattices

Explores Elliptic Curve Discrete Logarithm Problem, lattice-based cryptography, and cryptographic schemes like ECDSA.

Homomorphic Encryption: Basics and Applications

Covers homomorphic encryption using elliptic curves and its applications in decentralized systems.