Fields Institute Courses

Blaschke Products and the Crouzeix Conjecture

Explore Blaschke products and their connection to the Crouzeix conjecture in complex analysis, examining numerical ranges, model spaces, and level sets in operator theory.

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

Carathéodory Balls and Proper Holomorphic Maps on Multiply-Connected Planar Domains

Explore Carathéodory balls and proper holomorphic maps on multiply-connected planar domains, focusing on circular domains, proper maps, and related mathematical concepts.

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

Some Differential Operators on the Modular Curves with Infinite Level at P and Applications

Explore differential operators on modular curves with infinite level at p, their applications, and related concepts in algebraic geometry and number theory.

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

Unipotent Categorical Local Langlands

Explores unipotent categorical local Langlands, covering algebraic stacks, shifts, and spectral dynamics. Delves into advanced mathematical concepts with applications in algebraic homology and relative bar resolution.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Topics in Applied Model Theory - Lecture 7

Explore introdefinable sets, residual extensions, and stability in applied model theory with Silvain Rideau-Kikuchi's advanced lecture on disjunction and contradiction.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

Formalizing Macintyre's Theorem in Isabelle-HOL

Exploration of formalizing Macintyre's Theorem in Isabelle/HOL, covering proof strategies, challenges, and foundational elements needed for a verified proof in the context of p-adic numbers.

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

From Representations of P-Adic Groups to Congruences of Automorphic Forms

Explore connections between p-adic group representations and automorphic form congruences, bridging abstract algebra and number theory in this advanced mathematical lecture.

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

Describing Blaschke Products by Their Critical Points

Explore critical points in Blaschke products, inner functions, and related theorems. Gain insights into analytic function spaces and their applications in complex analysis.

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

Mini-course on Blaschke Products and Inner Functions - Part 1

Explore Blaschke products and inner functions in complex analysis, covering definitions, singular inner functions, and dynamical properties in this advanced mathematics lecture.

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

Contractive Inequalities for Hardy Spaces

Explore contractive inequalities in Hardy spaces, covering Henson's inequality, hyperspace, critical exponents, and geometric problems in analytic function theory.

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

Discrete Surface Geometry and Intrinsic Triangulations

Explore discrete surface geometry and intrinsic triangulations, bridging theory and algorithms in geometric computing. Learn about surface meshes, Gaussian curvature, and applications in robust geometry processing.

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

The Hochschild Cohomology of Uniform Roe Algebras

Explores Hochschild cohomology of uniform Roe algebras, discussing bounded derivations, vanishing conditions, and connections between norm-continuous and ultraweak-weak* continuous cohomology.

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

Trace Methods in Algebraic K-Theory

Explore trace methods in algebraic K-theory, focusing on cyclotomic trace and topological cyclic homology. Learn about recent advances and applications in chromatic homotopy theory.

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

Mini-course on Operators on Function Spaces - Part 2

Explore advanced concepts in function spaces, including multiplication operators, Toeplitz operators, and the unilateral shift, with applications in complex analysis and operator theory.

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

Mini-course on Operators on Function Spaces - Part 1

Explore operators on function spaces, focusing on the Volterra operator's properties, spectrum, and related concepts in functional analysis.

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