Theoretical physics has historically driven humanity’s greatest discoveries, yet it remains critically underdeveloped in Pakistan today. The School on Mathematics for Physics is a 4-week, high-intensity workshop jointly organized by The Black Hole and ICTP PWF. It is designed to equip and motivate the brightest minds with the essential mathematical toolkit required for cutting-edge physics research.

The Core Curriculum
This intensive program covers five foundational pillars essential for pre-graduate and graduate-level physics globally:

Linear Algebra for Quantum Mechanics: vector spaces, operators, spectral theory, density matrices.
Differential Equations: Sturm–Liouville systems, Green’s functions, nonlinear dynamics.
Complex Variables: analyticity, complex integration, causal relations.
Group Theory for Quantum Mechanics: group axioms, representations, Lie groups, Wigner–Eckart theorem.
Differential Geometry: manifolds, tensors, differential forms, applications to general relativity.

Speakers
Dr. Pervez Hoodbhoy (Nuclear Theory, MIT PhD)
Dr. Hassan Azad (Group Theory, Notre Dame PhD)
Dr. Jamil Aslam (Particle Physics, QAU PhD)
Dr. Waqas Masood (Plasma Theory, University of London PhD)
Dr. Ahsan Zeb (Condensed Matter Theory, University of Cambridge PhD)

Modalities & Structure
Rigorous pace: 2 lectures daily of 90 minutes each for four weeks (8 lectures per instructor).
Interactive: dedicated time built in daily for in-depth discussions.
Exclusive cohort: a maximum of 20 students will be selected globally based on a strict competitive review.
Recognition: a formal certificate will be awarded upon successful completion of the school.

Who Should Apply?
Advanced undergraduate or early-stage graduate students ready to bridge the gap between intuition and mathematical rigor are encouraged to apply. Selection will be based on a written test. Participants are expected to arrange their own accommodation in Islamabad.

Test Requirement
A 90-minute test, to be held at TBH in the last week of July, will assess competence in basic vector calculus, elementary differential equations, and linear algebra. If you have not already studied these subjects, this workshop will not be useful for you.

Application Deadline
Applications must be submitted online before 10 July 2026.

Apply here:
https://docs.google.com/forms/d/e/1FAIpQLSd4rlnGYNALPAXiOaLsUO6nWm2EGPChdEVYfFfzGViEg-OAYA/viewform