Optimal Transport: Theory and Applications

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Convex Optimization: Elementary Results

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Unconstrained Optimization Theory

Explores unconstrained optimization theory, covering global and local minima, convexity, and gradient concepts.

Convex Functions

Covers the properties and operations of convex functions.

Cones of convex sets

Explores optimization on convex sets, including KKT points and tangent cones.

Optimal Transport: Regularity and Brenier's Theorem

Explores optimal transport regularity and Brenier's theorem, discussing continuity and convexity concepts.

WireGuard: Cryptographic Protocol for VPNs

Explores the WireGuard Protocol, a modern VPN replacement for IPsec and OpenVPN, focusing on encrypted tunnelling and security properties.

Convex Optimization: Sets and Functions

Introduces convex optimization through sets and functions, covering intersections, examples, operations, gradient, Hessian, and real-world applications.

Diophantine Approximation: Minbowski's Theorem

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.

Formal Proofs: Checking Invariants and Bounded Model Checking

Explores formal proofs, satisfiability problems, and inductive invariants using SAT queries in sequential circuits.