INI Seminar Room 2 Courses

Holomorphic Curves in Abelian Varieties and Intersections with Higher Codimensional Subvarieties - Lecture 1

Delve into advanced mathematical concepts exploring holomorphic curves in Abelian varieties and their intersections with higher codimensional subvarieties through Yamanoi's groundbreaking research.

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

Pseudo Kobayashi Hyperbolicity of Subvarieties of General Type on Abelian Varieties - Part 1

Delve into advanced mathematical concepts exploring pseudo Kobayashi hyperbolicity of subvarieties in abelian varieties, focusing on Yamanoi's groundbreaking work and its applications in algebraic geometry.

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

Bifurcations of the Large-Scale Tropical Atmospheric Circulation

Explore the dynamics of tropical atmospheric circulation, focusing on tipping points, bifurcations, and their impact on climate change through Rossby wave resonance and superrotation phenomena.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video

Large-scale Structures in Transitional Turbulence

Explore the fascinating dynamics of transitional turbulence in wall-bounded shear flows, focusing on large-scale periodic patterns and their emergence through mathematical modeling and dynamical systems analysis.

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

Quadratic Euler Characteristics of Singular and Non-commutative Varieties

Delve into advanced mathematical concepts exploring quadratic Euler characteristics, covering both singular and non-commutative varieties, with applications in motivic homotopy theory and dg-categories.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Intersection Theory of Jet Moduli Spaces - Part 2

Delve into non-reductive integral formulas through practical examples, exploring their applications in jet moduli spaces and intersection theory within algebraic and differential geometry.

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

The Role of Nonlinear Phase Averaging in Highly Oscillatory PDEs for Time-Parallel Numerical Methods

Explore advanced phase averaging techniques for highly oscillatory PDEs, focusing on time-parallel numerical methods and their applications in atmospheric and oceanic modeling systems.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

The Rayleigh-Taylor Instability - Variable Density and Phase Fields Models Tutorial

Delve into the mathematical principles of Rayleigh Taylor Instability through variable density and phase fields models, exploring anti-diffusive dynamics across multiple scales.

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

Intersection Theory of Jet Moduli Spaces - Part 1

Delve into non-reductive integral formulas through practical examples, exploring their applications in intersection theory and jet moduli spaces with Professor Berczi from Aarhus Universitet.

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

Elliptic Algebra and Characteristic Classes of Link Patterns

Delve into geometric objects and their characteristic classes in equivariant elliptic cohomology, exploring relationships between Schubert varieties, matrix varieties, and Borel orbits through permutations and link patterns.

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

Zonal Winds and Torsional Oscillations in Jupiter's Interior

Explore Jupiter's interior dynamics through analysis of Juno mission data, examining zonal wind patterns, magnetic field variations, and torsional oscillations that shape the gas giant's complex atmospheric behavior.

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

Moduli of Coverings Branched Along Hypersurfaces

Explore the geometry of moduli spaces and coverings branched along hypersurfaces, examining their topology, birational geometry, and connections to K-polystable log del Pezzo surfaces.

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

The Limits of Beta-plane Turbulence in Quasigeostrophic Shallow-Water Systems

Explore the dynamics of beta-plane turbulence through analysis of jet separation scales, Rhines scale effects, and flow structure transitions in quasigeostrophic shallow-water systems.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Generalised Geometry, Moment Maps and Stability: How Physics Can Guide Us to New Slopes

Explore the intersection of string theory and geometry through AdS/CFT correspondence, examining how supersymmetry connects Calabi-Yau algebras with generalized geometries and Sasaki-Einstein spaces.

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

Layering Mechanisms - Universal vs System-Specific

Explore the fundamental physics behind layering phenomena across different scales, comparing geophysical examples and examining whether they represent universal or system-specific mechanisms.

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