Centre International de Rencontres Mathématiques Courses

Towards Synthetic Locale Theory

Explore synthetic approaches to locale theory using type theory to build "synthetic mathematics for synthetic mathematics" inspired by Blechschmidt's duality axiom and large sheaves.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Towards an Internal Construction of Meaning in Mathematical Language

Explore an innovative internal approach to mathematical meaning through nested hierarchies of n-categories, blurring syntax-semantics boundaries where objects define themselves inductively.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Towards the Effective 2-Topos

Explore advanced mathematical concepts in topos theory, focusing on Hyland's effective topos and its extensions to higher-dimensional structures with impredicative universes.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Synthetic Perspectives on the Yoneda Lemma

Explore synthetic category theory's approach to the Yoneda lemma as an "arrow induction" principle, making this fundamental theorem more accessible and intuitive.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Synthesising Random Variables - A Synthetic Approach to Probability Theory

Explore a synthetic approach to probability theory through axiomatising primitive random variables and developing foundational mathematical frameworks.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Condensation of Zero-Range Processes

Explore zero-range processes and condensation phenomena where particles accumulate at single sites, revealing Markovian behavior in scaling limits.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Critical Dynamical Fluctuations in Reaction-Diffusion Processes

Explore critical dynamical fluctuations in one-dimensional reaction-diffusion processes at phase transition points, examining non-Gaussian density fluctuations and their scaling limits.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Capacity for Branching Random Walks and Percolation

Explore the mathematical concept of capacity in branching random walks and percolation theory, connecting potential theory with critical bond percolation.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

A Unified Approach to Interacting Particle Systems with Conservation Laws

Explore a unified mathematical framework for analyzing interacting particle systems with conservation laws, covering hydrodynamic limits, fluctuations, and large deviations across multiple models.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Studying the Phase Transitions for Directed Polymers in Random Environment

Explore the phase transition of directed polymers in random environments, examining how disorder intensity affects polymer behavior from diffusive to localized states.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

Quantum Computing Hardware - Cost of Fault-Tolerance

Explore quantum error correction and fault-tolerant computing hardware, examining current progress and approaches to reduce overhead in quantum processors.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

Paradigms for Quantum Algorithms on Different Technologies - Lecture 1

Discover quantum computing algorithms from gate-based computation to variational methods, covering quantum Fourier transform, Shor's algorithm, and VQE for noisy quantum computers.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

Paradigms for Quantum Algorithms on Different Technologies - Lecture 2

Explore quantum algorithms for noisy and fault-tolerant computers, covering quantum Fourier transform, phase estimation, Shor's algorithm, VQE, and error mitigation techniques.

• YouTube
• 1 hour 29 minutes
• Self-Paced
• Free Video

Optimization Problems on Quantum Computers - Lecture 1

Explore quantum optimization algorithms including adiabatic methods, QAOA, and quantum annealing, plus their applications to combinatorial and convex optimization problems.

• YouTube
• 1 hour 27 minutes
• Self-Paced
• Free Video

Optimization Problems on Quantum Computers - Lecture 2

Explore quantum optimization algorithms including adiabatic methods, QAOA, and convex optimization techniques for solving complex mathematical problems on quantum computers.

• YouTube
• 1 hour 25 minutes
• Self-Paced
• Free Video