Lectures related to Gauge Theories: Chiral Transformations and Path Integrals

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores renormalization, scaling, critical points, exponents, and phase transitions in conformal field theory and quantum gravity.

Compactified Imaginary Liouville Theory: Scaling Limits and Challenges

Covers compactified imaginary Liouville theory and the scaling limits of loop models, addressing mathematical challenges and future research directions.

Statistical Models: Unitary Conformal Field Theories

Covers the connection between statistical models and unitary conformal field theories, focusing on critical points and the role of local fields.

Easing Model Conformal Theory: Scaling Limits and Correlations

Covers the Easing model conformal theory, focusing on scaling limits and correlation functions.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Local Fields and Correlations in Ising Models

Covers local fields and correlations in Ising models and conformal field theory.

Conformal Blocks: Functions on Moduli Spaces

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

Renormalization Group in Field Theory

Explores the Renormalization Group in field theory, discussing scaling functions, critical exponents, and Gaussian fixed points.

Advanced Quantum Field Theory

Covers advanced topics in Quantum Field Theory, including representations of the Poincare group and the construction of unitary irreps.

Currents in the O(n) Model: Conformal Field Theory Insights

Covers the O(n) model on the hexagonal lattice and its currents.

Understanding Chaos in Quantum Field Theories

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Comparison Series and Integrals

Explores the relationship between series and integrals, highlighting convergence criteria and function examples.

Dotsenko-Fateev Approach: Correlation Functions in Quantum Field Theory

Covers the Dotsenko-Fateev approach to computing correlation functions in quantum field theory.

Renormalization Program: Fixed Points and Couplings

Explores fixed points and couplings in the renormalization program, revealing how complex low-energy phenomena arise from simple dynamics.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Integration of CnR Class Functions

Explains the integration of Taylor series for CnR class functions.

Trans-series in Quantum Field Theory: SVZ Approach and Applications

Discusses the SVZ sum rules and their application in quantum field theory, focusing on trans-series and non-perturbative corrections.

Riemann Sphere: Correlations and Conditions

Covers the Riemann sphere, focusing on its conditions and correlation functions in mathematical and physical contexts.

Scaling & Renormalization in Statistical Mechanics

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.