INI Seminar Room 2 Courses

Equivariance and What It Buys You in Algebraic and Differential Geometry

Explore symmetry operations in geometric mathematics, focusing on implosion and contraction in symplectic, algebraic, and hyperkahler contexts, with insights into Moore-Tachikawa categories and symplectic duality.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Singular cscK Metrics on Smoothable Varieties

Explore the mathematical theory of singular cscK metrics on Q-Gorenstein smoothable klt varieties, focusing on Mabuchi functional coercivity and K-stability in normal projective varieties.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

The Universal Structure of Moment Maps in Complex Geometry

Delve into the universal structure of moment maps in complex geometry, exploring canonical metrics, PDEs, and equivariant cohomological perspectives in infinite dimensional spaces through expert analysis.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

The Einstein-Hilbert Functional and the Donaldson-Futaki Invariant - Part 2

Explore advanced mathematical concepts in Kähler geometry, focusing on the Einstein-Hilbert functional's relationship with test configurations and K-semistability of cscK manifolds.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Non-Archimedean Aspects of K-stability

Explore non-Archimedean interpretations of K-stability in Fano varieties, examining valuative criteria and divisorial stability through advanced algebraic geometry concepts.

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

Non-Archimedean Aspects of K-stability

Explore the non-Archimedean interpretations of K-stability in Fano varieties, focusing on valuative criteria and divisorial stability concepts in algebraic geometry.

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

Non-Archimedean Aspects of K-stability in Algebraic Geometry

Explore non-Archimedean interpretations of K-stability in Fano varieties, examining valuative criteria and divisorial stability through advanced mathematical concepts and recent developments.

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

High and Low Reynolds Number Turbulence - Scaling, Universality, and Spottiness

Explore the fascinating comparison between high and low Reynolds number turbulence, examining scaling laws, universality patterns, and chaotic behaviors in bacterial flows and classical fluid dynamics.

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

Numerical Criteria for Pointwise Positivity in Algebraic and Differential Geometry

Delve into numerical criteria for pointwise positivity, exploring the Nakai-Moizeshon criterion, Demailly-Paun criterion, and Lejmi-Szekelyhidi conjecture in algebraic and differential geometry.

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

On Semistable Perturbation Problems for Canonical Metrics

Delve into advanced mathematical concepts of semistable perturbation problems for canonical metrics, exploring solutions for perturbed equations and their algebro-geometric implications.

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

Numerical Criteria for Pointwise Positivity in Algebraic and Differential Geometry

Delve into numerical criteria for pointwise positivity in algebraic geometry, exploring the Nakai-Moizeshon criterion, Demailly-Paun criterion, and Lejmi-Szekelyhidi conjecture for J-equations.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Cytoplasmic Fluid Mechanics - Anti-diffusive Dynamics in Cellular Development

Explore cytoplasmic fluid mechanics and embryonic flows, focusing on multiphase modeling and pattern formation in Drosophila embryos through advanced mathematical and physical principles.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

The Hydrodynamics of Epithelial Tissues - From Symmetry to Cell Migration

Explore the physics of epithelial tissue dynamics through advanced hydrodynamic theory, examining multi-scale orientational order and its role in cellular migration and morphogenesis.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

Double-diffusive Magnetic Layering in Convectively Stable Atmospheres

Explore double-diffusive convection and magnetic layering in stellar atmospheres, examining transport mechanisms and their role in radiative zones through mathematical analysis.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Torsion Sheaves on Stacky Curves - How to Not Quite Compute a Motive

Explore the relationship between torsion sheaves on stacky curves and cyclic quiver representations, examining geometric constructions and their connection to curve motives and Grothendieck-Springer resolution.

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