INI Seminar Room 2 Courses

Restriction Theorems for Hankel Operators

Delve into advanced mathematical concepts of Hankel operators and restriction theorems through rigorous analysis and theoretical exploration of their properties and applications.

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

A Martingale Approach for the Elephant Random Walk with Stops and the Ewens-Pitman Process

Delve into advanced stochastic processes as Professor Bercu explores martingale approaches for elephant random walks with stops and the Ewens-Pitman process in this mathematical sciences seminar.

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

Anomalous Thermal Relaxation of Physical Systems

Delve into the mathematical principles of anomalous thermal relaxation in physical systems through an advanced physics seminar exploring stochastic processes and diffusion phenomena.

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

Selector Form of Weaver's Conjecture and Frame Sparsification

Delve into advanced mathematical concepts exploring Weaver's conjecture, frame sparsification, and their applications in high-dimensional spaces through expert analysis and theoretical frameworks.

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

Colliding Surface Waves and Novel Mechanisms of Laser Energy Absorption by Plasma

Explore novel mechanisms of laser energy absorption in plasma, including colliding surface waves and magnetic field applications for electron and ion energy transfer in fusion research.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

How Helicity Helps Create Finite Dissipation Without Singularities

Delve into advanced fluid dynamics research examining how helicity influences vortex interactions, dissipation patterns, and mathematical modeling of Navier-Stokes equations in various vortex configurations.

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

Self-gravitating Bosonic and Axionic Systems and a Minimal Model for Pulsar Glitches

Delve into self-gravitating bosonic systems and dark matter halos through numerical simulations, exploring compact object formation, pulsar glitches, and axionic condensates in astrophysical contexts.

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

Non-archimedean Integration on Quotients

Explore advanced mathematical concepts in non-archimedean integration, focusing on quotient singularities, stringy Hodge numbers, and their connections to orbifold formulas and BPS-invariants.

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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video