ICTP PWF: Physics for Bangladesh Online Summer Internship

Topic 1: Representation Theory of Quivers / Hecke Algebras

Prerequisites: Linear Algebra, Representation Theory of Groups, Basic Category Theory.

Topic 2: Symmetric Groups and Young Diagram Combinatorics

Prerequisites: Linear Algebra, Representation Theory of Groups, Basic Category Theory.

Topic 1: Hawking-Penrose Singularity Theorems

A project aimed at a mathematically rigorous understanding of the classic Hawking-Penrose singularity theorem, with possible extensions to more modern singularity theorems.

Prerequisites: A solid foundation in general relativity. Background in Lorentzian geometry is useful and can also be built through the project.

Reference: Ettore Minguzzi, Lorentzian causality theory, Living Reviews in Relativity 22, 3 (2019).

Topic 2: Cauchy Problems for Einstein Equations

A reading and problem-based project on the local and global Cauchy problem in general relativity, including the results of Choquet-Bruhat and Geroch from a modern viewpoint.

Prerequisites: A solid foundation in general relativity. Interest in analytic computation and mathematical analysis. Background in partial differential equations is useful and can also be built through the project.

Reference: Hans Ringström, The Cauchy Problem in General Relativity, EMS Press (2009).

Topic 1: Hodge Theory on Compact Manifold

Prerequisites: Linear Algebra, Smooth Manifold Theory, Real Analysis, and recommended background in basic cohomology theory.

Topic 2: Symplectic Geometry (Finite-dimensional Versions)

The stated goal was to complete Ana Cannas da Silva’s Lectures on Symplectic Geometry within two months and prepare students for more advanced or infinite-dimensional treatments.

Prerequisites: Linear Algebra and Smooth Manifold Theory, with comfort using Axler’s Linear Algebra Done Right and Tu’s An Introduction to Manifolds.

Reference: Ana Cannas da Silva, Lectures on Symplectic Geometry.

Topic 1: Supernova Types and Their Distribution Across the Universe

Prerequisites: Basic astronomy, calculus, and programming experience in Python or Fortran/C/C++.

Topic 2: Possibility of Life Around M Dwarf Planets and Their Moons

Prerequisites: Basic astronomy, calculus, and programming experience in Python or Fortran/C/C++.

Topic 1: Dynamics of the Local Group Galaxies

Prerequisites: Classical Mechanics, Scientific Computing in Python, Linear Algebra, Probability, and Statistics.

Topic 1: Galaxy Clusters from Large Sky Surveys

Prerequisites: Standard undergraduate physics courses, familiarity with Python programming, and any astronomy background is helpful.

Topic 2: Galaxies in Different Cosmic Environments

Prerequisites: Standard undergraduate physics courses, familiarity with Python programming, and any astronomy background is helpful.

Topic 1: Extragalactic Astronomy Using the James Webb Space Telescope

Students were expected to complete the group onboarding tutorial and then continue to the Launchpad tutorials to prepare for research in extragalactic astronomy.

Prerequisites: Introductory physics courses including mechanics, electromagnetism, waves, optics, thermodynamics, statistical mechanics, and differential equations.

Topic 1: Vacuum Decay in Quantum Field Theory

Prerequisites: Advanced Quantum Mechanics, Special Relativity, and optionally basic Quantum Field Theory.

Topic 2: Einstein-Maxwell Theories in Diverse Dimensions

Prerequisites: General Relativity, Electrodynamics, and optionally basic Quantum Field Theory.

Topic 1: Quantum to Classical Map for Toric Codes

Prerequisites: Strong linear algebra, familiarity with quantum mechanics and statistical mechanics, and exposure to Ising models or toric codes is helpful.

Topic 1: Oscillon Formation in the Post-inflationary Universe

Prerequisites: Basic knowledge of inflationary cosmology and comfort with programming in Python or Julia.

Topic 2: Analytical and Numerical Investigation of Stochastic Inflation with Consequences for PBH Formation

Prerequisites: Basic knowledge of inflationary cosmology and comfort with programming in Python or Julia.

Topic 1: Properties of Scattering Amplitudes

A reading and project-oriented introduction to analytic properties of Feynman integrals as building blocks of perturbation theory.

Prerequisites: Mathematical Methods in Physics and Complex Analysis.

Topic 2: Reading Project on D-branes and Gauge Fields

Prerequisites: Electrodynamics, Classical Mechanics, and Quantum Mechanics, with prior exposure to classical field theory as a plus.

Topic 3: String Thermodynamics and Boltzmann Equations

Prerequisites: Mathematical Methods in Physics, Quantum Mechanics, Statistical Mechanics, and numerical methods for students interested in simulations.

Topic 1: Path Integral Approach to QFT for Simple Systems

Prerequisites: Strong background in the Lagrangian formulation of classical mechanics and a good understanding of quantum mechanics. Familiarity with the path integral approach to quantum mechanics is helpful but not required.

Topic 2: Free Bosonic String Theory

Prerequisites: Strong background in the Lagrangian formulation of classical mechanics and the basics of canonical quantization in quantum field theory.

Topic 1: Scattering Amplitudes, Symmetry and Soft Theorems

Prerequisites: Quantum Mechanics and basic Quantum Field Theory and General Relativity.

Topic 2: Causality Constraints on Effective Field Theory and Gravity

Prerequisites: Quantum Mechanics and basic Quantum Field Theory and General Relativity.

Topic 3: Conformal Field Theory

Prerequisites: Quantum Mechanics and basic Quantum Field Theory and General Relativity.

Topic 1: Matrix Models and JT Gravity

A project on random matrix models and their connection to JT gravity, with a stated goal of numerically solving string equations and extending the analysis to modified JT gravity theories. The note in the call specified a September to November internship period for this topic.

Prerequisites: Quantum Mechanics, basic Quantum Field Theory with path integrals, General Relativity, and numerical methods for nonlinear differential equations.

Topic 1: Anomalies and Generalized Symmetries in QFT and 2D CFT

Prerequisites: Basic knowledge of Quantum Field Theory is essential. Knowledge of Conformal Field Theory is useful but can be learned during the project.

Topic 2: Classifying Rational Conformal Field Theories Using Number-theoretic Techniques

Prerequisites: Finite Groups and their Representations, ODEs, and Complex Analysis are essential. Knowledge of Lie groups, Lie algebras, and Conformal Field Theory is useful.

Topic 3: Laws of Black Hole Mechanics and Hawking Radiation

Prerequisites: General Relativity, Quantum Field Theory, and Statistical Mechanics.

Topic 1: Computation of Band Structures of Solids Using Quantum ESPRESSO

Prerequisites: Classical Mechanics, Quantum Mechanics, and a basic understanding of the command line and compiling C/C++/Fortran programs.

Topic 1: Design of Superconducting Quantum Circuits

Prerequisites: Basic understanding of classical mechanics, electromagnetism, and Python programming.