Systems Core Courses

Institute for Pure & Applied Mathematics (IPAM)

The Quantum Linear Systems Problem - IPAM at UCLA

Explore quantum algorithms for solving linear systems, including improved methods and complexity analysis, with a focus on potential exponential speedups and verification challenges.

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

Institute for Pure & Applied Mathematics (IPAM)

Computational Challenges with Modeling Core Collapse Supernovae - IPAM at UCLA

Explore computational challenges in modeling core collapse supernovae and gravitational wave emission, covering recent progress, physics requirements, and future directions in multi-dimensional simulations.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Quantum Field Theory of Exotic Systems - IPAM at UCLA

Explore quantum field theory of exotic systems, focusing on fracton phases and their challenges to conventional understanding. Delve into subsystem symmetries, tensor gauge theories, and peculiar UV/IR mixing phenomena.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Analytical and Empirical Tools for Nonlinear Network Observability in Autonomous Systems

Explore nonlinear network observability in autonomous systems, covering analytical and empirical tools for sensor selection, network analysis, and applications in engineering and biology.

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

Institute for Pure & Applied Mathematics (IPAM)

Towards Assurance-Based Learning-Enabled Cyber-Physical Systems

Exploring formal verification, monitoring, and safety case formalization for assurance-based learning-enabled cyber-physical systems, focusing on autonomous vehicles and their complex components.

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

Institute for Pure & Applied Mathematics (IPAM)

Algebraic Entropy in Combinatorial Dynamical Systems

Explore algebraic entropy in combinatorial dynamical systems, focusing on T-systems and R-systems. Discover classification results and connections to Cartan matrices and dynamical algebraic combinatorics.

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

Hausdorff Center for Mathematics

The Dynamical Systems Approach to Spatially Homogenous Einstein-Vlasov Cosmology

Explore spatially homogenous Einstein-Vlasov cosmology using dynamical systems analysis. Investigate asymptotic solutions near singularities and expanding futures, focusing on Kantowski-Sachs models with Vlasov matter.

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

Hausdorff Center for Mathematics

Antonio Esposito: Nonlinear Degenerate Cross Diffusion Systems with Nonlocal Interaction

Explores nonlinear degenerate cross-diffusion systems with nonlocal interaction, proving global existence of weak solutions using a semi-implicit JKO scheme for applications in social sciences, finance, and biology.

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

Hausdorff Center for Mathematics

Topological Generalizations of Possible Worlds Semantics and Their Proof Systems

Topological generalizations of possible worlds semantics and their proof systems for modal and conditional logics, focusing on structural and computational aspects.

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

Hausdorff Center for Mathematics

Ricci Curvature and Functional Inequalities for Interacting Particle Systems

Explore entropic Ricci curvature bounds and their applications to interacting particle systems, focusing on functional inequalities and convergence rates to equilibrium in nonnegative curvature scenarios.

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

Hausdorff Center for Mathematics

Mathematics of Signal Design for Communication Systems and Szemerédi’s and Green-Tao’s Theorems

Explore signal design for communication systems, focusing on orthogonal transmission schemes and their dynamics. Delve into mathematical connections with functional analysis and additive combinatorics.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Randomized Composable Core-Sets for Submodular Maximization

Explores randomized composable core-sets for distributed submodular and diversity maximization, presenting improved algorithms and analysis techniques for big data optimization problems.

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

ICTP Mathematics

Markov Partition for Hyperbolic Systems with Singularities - ICTP 2021

Explore Markov partitions in hyperbolic systems with singularities, covering scatters, collision maps, uniform hyperbolicity, and SRB measures. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 4

Explore advanced techniques in nonuniformly hyperbolic dynamics, focusing on symbolic coding and statistical properties of complex systems using Markov Partitions and Young Towers.

• YouTube
• 2 hours 9 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 3 of 5

Explores advanced techniques in nonuniformly hyperbolic systems, focusing on symbolic dynamics and Markov partitions. Covers key concepts, challenges, and recent developments in the field of dynamical systems.

• YouTube
• 2 hours 13 minutes
• Self-Paced
• Free Video