Erwin Schrödinger International Institute for Mathematics and Physics (ESI) Courses

Connections in Infinite-Dimensional Grassmann Manifolds

Explore operator theoretic methods and covariant derivatives in infinite-dimensional Grassmann manifolds, focusing on conjugated points along geodesics and their mathematical implications.

• YouTube
• 27 minutes
• On-Demand
• Free Video

Central Extensions of the Group of Exact Volume Preserving Diffeomorphisms

Delve into advanced mathematical concepts exploring Roger's conjecture on universal central extensions, focusing on exact divergence-free vector fields and their applications in 3D manifolds.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Geometric Mechanics - Tulczyjew Triples, Algebroids, and Dirac Structures - Part 2

Delve into advanced geometric mechanics concepts, exploring Tulczyjew triples, algebroids, and Dirac structures through the lens of variational calculus and symplectic geometry in physical systems.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Infinite-dimensional Geometry and Integrable PDEs - Part 2

Delve into integrable systems theory through an infinite-dimensional geometric lens, exploring fundamental concepts and their applications in partial differential equations.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Conjugate Points Along Spherical Harmonics and Quasi-geostrophic Motion

Explore geometric principles of quasi-geostrophic flows, examining curvature, conjugate points, and Coriolis effects on spherical harmonics for enhanced understanding of flow stability and evolution.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Banach Manifolds and Integrable Systems - KdV and Toda-Lattice Applications

Explore integrable systems like KdV and Toda-lattice through the lens of Banach manifolds, examining their Poisson and symplectic structures in infinite-dimensional geometry.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Hamiltonian Dynamics on Poisson Manifolds and Symplectic Groupoids

Delve into advanced mathematical concepts exploring Hamiltonian dynamics through symplectic Lie groupoids, covering approximation methods and applications in conservative mechanics and PDEs.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Rare Event Statistics and Molecular Bet-Hedging in Enzyme Systems

Explore how cells optimize enzyme placement through molecular bet-hedging strategies, revealing localization-delocalization transitions and design principles for synthetic systems.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Thymic Selection of T Cells - A Problem in Extreme Value Statistics

Explore how extreme value statistics models T cell selection, analyzing thymic survival rates and CTL recognition of foreign antigens through mathematical frameworks.

• YouTube
• 31 minutes
• On-Demand
• Free Video

How Can Superstatistics Approach Be Applied to Investigate Complex Biological Systems

Explore superstatistics framework for modeling complex biological systems, moving beyond traditional analytical approaches with practical examples from environment to cosmic rays.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Extreme Statistics in Molecular and Cellular Biology

Explore rare stochastic events in cell biology through asymptotic computations and discover how modeling reveals molecular organizations in synaptic transmission.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Inhibition of Bacterial Growth by Antibiotics - A Minimal Model

Explore a minimal mathematical model describing how bacteriostatic antibiotics inhibit essential autocatalytic cycles in bacterial metabolism and growth dynamics.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Effective Parameters in Population Biology

Explore when effective parameters fail in population biology models with time-varying environments and discover the mathematical implications for biological realism.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Extreme First Passage Times for Populations of Identical Rare Events

Explore extreme first passage times for rare events using large deviation theory to analyze the fastest occurrence among N identical independent processes.

• YouTube
• 30 minutes
• On-Demand
• Free Video

Evolutionary Advantage of Cell Size Control

Discover how cell size control strategies provide evolutionary advantages in growing populations, exploring mortality constraints, optimal sizing, and heritability effects on survival.

• YouTube
• 20 minutes
• On-Demand
• Free Video