Events & Learning

Advanced workshops, mini-courses, seminars, and reading groups.

Planned Workshops)

Semester 1: Foundations in Probability & Analysis

Linear Algebra & Functional Foundations

Spectral theory, singular value decomposition (SVD). Quadratic forms, semidefinite matrices. Foundational functional tools for later analysis.

Measure & Integration Theory

σ-algebras, measurable functions, Lebesgue measure. Lebesgue vs. Riemann integration. Lebesgue–Stieltjes integrals, convergence theorems. Expectation as Lebesgue integral, conditional expectation.

Stochastic Processes (Introductory)

Probability spaces and random variables. Martingales and stopping times. Markov chains. Brownian motion.

Semester 2: Functional Spaces & Analysis

Lp Spaces

Norms, completeness. Hölder and Minkowski inequalities. Applications to probability and PDEs.

Functional Analysis (Introductory)

Banach and Hilbert spaces. Riesz representation theorem. Duality theory. Weak vs. strong convergence.

Stochastic Calculus

Itô integrals. Itô’s lemma. Stopping times and martingale properties. Girsanov theorem and measure change.

Semester 3: Advanced Methods (Optimization, Control, PDEs)

Convex Optimization

Duality and separation theorems. Karush–Kuhn–Tucker (KKT) conditions. Applications to finance and control.

Variational Calculus

Euler–Lagrange equations. Functional minimization problems. Direct methods in calculus of variations.

Optimal Control Theory

Pontryagin Maximum Principle. Hamilton–Jacobi–Bellman (HJB) equations. Applications to portfolio optimization and dynamic programming.

Partial Differential Equations (PDEs)

Elliptic and parabolic PDEs. Weak solutions and Sobolev spaces. Applications to diffusion processes and stochastic control.