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

X-Y Symplectic Transformation in Topological Recursion - Lecture 1

Explore x-y symplectic transformation in topological recursion through an in-depth lecture by Alexander Hock at the ESI workshop on non-commutative geometry.

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

Tropical Contributions to Enumerative Geometry of Target Dimension One - Lecture 1

Explore tropical geometry's impact on enumerative problems in moduli spaces of curves. Delve into tropical Hurwitz numbers, branch polynomials, and k-DR cycles, uncovering new perspectives in algebraic combinatorics.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Nonlinear Dynamics Insights into Golden Tides in the Caribbean Sea

Explore nonlinear dynamics of Sargassum transport in the Caribbean Sea, examining mesoscale eddies as carriers and mechanisms of coastal inundation using satellite data and minimal models.

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

Wind-Forced Seasonal Exchange Between Marginal Seas and the Open Ocean

Explore wind-driven circulation in marginal seas and ocean exchange using numerical models. Analyze interior and shelf dynamics, coastal wave impacts, and deep water exchange through straits.

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

Enumeration of Maps via Integrability

Explore map enumeration techniques, from Tutte's work to KP hierarchy, deriving recurrence formulas for oriented and non-oriented maps using integrability methods in mathematics and physics.

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

Around the Joint Behavior of Independent Random Tensor Matrices - Lecture 1

Explore joint behavior of independent random tensor matrices with smaller symmetry groups. Learn about tensor structures, generalizations of free probability, and new analytical techniques.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Higher Rank Voronoi Decompositions and Metric Degenerations of Tori

Explore higher rank Voronoi decompositions and their applications in studying asymptotic geometry of Riemann surfaces and moduli spaces.

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

Tropicalization of the Universal Jacobian: Logarithmic and Non-Archimedean Views

Explore tropicalization of universal Jacobians, examining logarithmic and non-archimedean perspectives. Gain insights into moduli spaces, cone stacks, and new stability conditions for compactified Jacobians.

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

Mechanisms of Offshore Solid and Liquid Freshwater Flux from the East Greenland Current

Explore mechanisms controlling freshwater export from East Greenland Current using numerical models and scaling theory. Analyze offshore ice flux, liquid freshwater flux, and key parameters influencing these processes.

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

Study of a Simple Equation Describing the Ground-State Energy of a Bose Gas

Explore the ground-state energy equation of a Bose gas, from its 1963 origins to recent discoveries in 3D Monte Carlo calculations across all densities.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

"Nice" Future Causal Boundary at Finite Distance and Low-Regularity Extension

Explore the Causal Boundary construction in spacetime geometry, focusing on generic spacetimes and conditions for continuous metric extension to the Future Causal Boundary.

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

Static Near Horizon Geometries and Quasi-Einstein Metrics

Explore extreme black hole horizons and quasi-Einstein metrics, focusing on rigidity theorems for closed manifolds with closed 1-forms and their implications for static near horizon geometries.

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

On the Uniqueness Problem for Spacetime Extensions

Explore uniqueness conditions for Lorentzian manifold extensions, analyzing boundary agreement and presenting recent findings on necessary conditions and non-uniqueness mechanisms.

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

Quantum Field Theory on Low-Regularity Spacetimes

Explore quantum field theory on low-regularity spacetimes, focusing on massless scalar fields, Cauchy problems, Green operators, and physical states in a mathematically rigorous framework.

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

Sobolev Calculus in Synthetic Lorentzian Geometry

Explore Sobolev calculus in synthetic Lorentzian geometry, focusing on time functions, weak lower differentials, and d'Alembert comparison results in measured Lorentzian length spaces.

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