Institut des Hautes Etudes Scientifiques (IHES) Courses

Mathematics of Post-quantum Cryptography in the AI Era

Explore post-quantum cryptography's mathematical foundations and its intersection with AI, focusing on cutting-edge developments and future implications for cybersecurity.

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

Early Alignment in Two-Layer Networks Training: A Two-Edged Sword

Explore early alignment in two-layer network training, examining its dual nature as both beneficial and potentially problematic for neural network performance.

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

Frugality for Sequential Prediction: Reaching Bounded Regret While Using Expert Advice Sparingly

Explore sequential prediction strategies for bounded regret using expert advice sparingly, focusing on frugal approaches in machine learning.

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

Euclidean Capacitated Vehicle Routing in Random Setting - A 1.55-Approximation Algorithm

Explore a 1.55-approximation algorithm for Euclidean capacitated vehicle routing in random settings, presented by Zipei Nie.

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

Uncertainty Quantification in Machine Learning: Federated Conformal Prediction

Explore uncertainty quantification in machine learning through federated conformal prediction, enhancing model reliability and decision-making in distributed settings.

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

Classical and New Perspectives on Resurgence Theory

Explore classical and modern approaches to resurgence theory, gaining insights into its mathematical foundations and recent developments.

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

Geometry from Donaldson-Thomas Invariants

Explore geometric structures in stability conditions using DT invariants of CY3 triangulated categories, focusing on hyperkähler structures and complexified Hitchin systems.

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

Periodic Pencils of Flat Connections and Their p-Curvature

Explore periodic pencils of flat connections, their properties, examples, and p-curvature in characteristic p. Learn about isospectral operators and applications to various mathematical connections.

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

Shimurian Analogs of Barsotti-Tate Groups

Explore Grothendieck's n-truncated Barsotti-Tate groups and their modulo p reductions. Discover conjectures on Shimura varieties and modern Dieudonné theory developments.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Prospects for Spectral Mirror Symmetry

Explore advanced Fukaya categories, spectral ring coefficients, and mirror symmetry in symplectic geometry. Delve into cutting-edge research on generalizing Lagrangian Floer theory.

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

Moduli Spaces of Points on the Projective Line and Other Varieties with Many Symmetries

Explore equivariant birational geometry through recent results and constructions presented by Yuri Tschinkel from SCGP & NYU.

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

Modular Forms and Differential Equations: Connections and Applications

Explore connections between modular forms and differential equations, from historical origins to modern applications in mathematics and physics.

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

Noncommutative Elliptic Poisson Structures on Projective Spaces

Explore noncommutative Poisson structures on affine and projective spaces, focusing on examples in complex projective spaces and their connections to elliptic Poisson algebras.

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

Counting in Calabi-Yau Categories

Explore advanced concepts in homotopy cardinality, Calabi-Yau structures, and Hall algebras for pre-triangulated dg-categories, with applications to Legendrian knot theory.

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

Billiards, Arithmetic and Hodge Theory

Explore connections between billiard paths, cusps, curves, heights, and spectral gaps in polygons, encountering chaos and decidability issues in 7 and 12-sided shapes.

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