Lectures related to Discrete group

Spectral Analysis: Hyperbolic Surfaces

Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.

Proper Actions and Quotients

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

Dynamics on Homogeneous Spaces and Number Theory

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

Conformal Field Theory Basics

Covers the basics of Conformal Field Theory, focusing on Large N CFTs and correlation functions.

Spectrum of Hyperbolic Surfaces

Explores the spectrum of hyperbolic surfaces, focusing on Fuchsian groups and their actions.

Minkowski's Theorems: Lattices and Volumes

Explores Minkowski's theorems on lattices, volumes, and set comparisons.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Lattices: Properties and Theta Functions

Explores lattices in Rd, Gram matrices, theta functions, and modular properties.

Quantum Field Theory II: Cross Section & Lifetime

Covers cross section, lifetime, quantum fluid, asymptotic states, discrete symmetries, and normal ordering in quantum field theory.

Open Mapping Theorem

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

Lattice Theory: Minkowski's Theorems

Delves into lattice theory, emphasizing Minkowski's theorems and their implications on lattice structures.

Image manipulations: Affine transforms and Interpolation

Covers affine transforms, rotation, shear, and bilinear interpolation for image manipulations.

Lattices: Theory and Applications

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Number Fields: Embeddings and Ideal Classes

Covers the embeddings of number fields and ideal classes with proofs and examples.

Hermite Normal Form: Computation & Properties

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Advanced Numerical Analysis: Space Discretization

Explores advanced space discretization techniques in numerical analysis for solving differential systems efficiently and accurately.

Policy Gradient Methods in Reinforcement Learning

Covers policy gradient methods in reinforcement learning, focusing on optimization techniques and practical applications like the cartpole problem.

Thermodynamical Formalism and Martin Boundary

Explores SFT, top mixing, Hölder functions, and equilibrium in geodesic flows.

Homotopy Lifting

Explains homotopy lifting, paths, proofs, constant paths, discrete spaces, and monomorphisms.

Adelic Number Theory

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