INI Seminar Room 2 Courses

Conformal Blocks from Vertex Operator Algebras

Explore the mathematical foundations of conformal blocks, their construction from vertex operator algebras, and their properties in relation to moduli spaces of curves with marked points.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Fluid Mixing in Ideal Systems and Large-Scale Oceans

Explore fluid mixing dynamics from microscopic to oceanic scales, examining turbulent phase-separation, mathematical models, and real-world applications in multiphase fluid systems through analytical and numerical approaches.

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

Okounkov's Conjecture via BPS Lie Algebras

Delve into Okounkov's conjecture and its proof through BPS Lie algebras, exploring connections between Yangian algebras, quiver varieties, and Kac polynomials in algebraic geometry.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Moduli Spaces of Sheaves and Blow-ups of Projective Spaces

Explore advanced mathematical concepts in moduli spaces of sheaves, Gale correspondence, and blow-ups of projective spaces, focusing on Mori chamber decomposition and effective cone analysis.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Products of K-moduli Spaces in Algebraic Geometry

Delve into the structural analysis of K-moduli spaces for Fano varieties, exploring their products, local-global properties, and explicit examples of reduced connected components in threefolds.

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

Fourier Transform: From Abelian Schemes to Hitchin Systems - Part 3

Delve into advanced mathematical concepts exploring Fourier transforms and their applications in abelian schemes and Hitchin systems through an in-depth mathematical analysis led by Yale's Professor Shen.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Fourier Transform: From Abelian Schemes to Hitchin Systems - Part 2

Delve into advanced mathematical concepts exploring Fourier transforms and their applications in abelian schemes and Hitchin systems through an in-depth mathematical analysis by Yale's Prof. Shen.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Physics of Velocity and Magnetic Shears in Toroidal Geometries

Explore the physics of velocity and magnetic shears in tokamak plasmas, examining resonance effects, shearing coordinates, and their impact on plasma dynamics and confinement performance in toroidal geometries.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Temperature Front Formation in Stably Stratified Turbulence

Delve into the dynamics of stably stratified turbulence, exploring temperature front formation, wave-vortex interactions, and sawtooth wave structures through DNS of Navier-Stokes equations under Boussinesq approximation.

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

Internal Wave Packet Tunnelling Across a Thermohaline Staircase

Explore the fascinating dynamics of internal wave packets interacting with density staircases in the Arctic Ocean, examining transmission patterns and theoretical predictions through numerical simulations.

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

A Critical Look at Quasilinear Theory in Anti-Diffusive Dynamics

Delve into a critical analysis of quasilinear theory in plasma physics, examining its foundations, validity, and challenges through the lens of the Vlasov-Poisson system and mode coupling effects.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Family 3-5 and δ-Invariant of Polarized del Pezzo Surfaces

Explore the computation of δ-invariant for del Pezzo surfaces and their connection to K-stability, focusing on explicit examples and applications to Kähler-Einstein metrics in algebraic geometry.

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

Large-Scale Structure Formation by Turbulent Kinetic Helicity

Delve into turbulent kinetic helicity's role in large-scale structure formation, exploring mathematical models of rotating turbulence and applications in geophysical and astrophysical flows.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Directed Percolation and Critical Phenomena in Reaction-Diffusion Systems - Lecture 2

Delve into directed percolation theory, exploring critical phenomena, universality classes, and stochastic PDEs through advanced mathematical concepts and their applications in turbulence modeling.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Directed Percolation and Critical Phenomena in Reaction-Diffusion Systems - Lecture 1

Delve into directed percolation theory, critical phenomena, and universality classes with focus on reaction-diffusion models, absorbing states, and applications to turbulence onset through stochastic PDEs.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video