Fields Institute Courses

Parametrizations and Complexity of Preparation

Explore parametrizations, preparation complexity, and the Wilkins conjecture. Learn induction methods and recent results in tame geometry and transseries applications.

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

Towards an Algebraic Independence Result for Certain P-adic Series

Explore algebraic independence in p-adic series, covering key concepts, functionality, and infinite transcendence in this advanced mathematical presentation.

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

Introduction to O-Minimality and the Pila-Wilkie Theorem

Explore o-minimality and the Pila-Wilkie Theorem, covering definitions, examples, proofs, and key concepts in tame geometry. Gain insights into this fundamental area of mathematical logic and its applications.

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

Effectivity of Standard O-Minimal Results in the Sharply O-Minimal Setting

Explore the effectiveness of o-minimal results in sharply o-minimal contexts, covering algebraic lemmas, cellular versions, and cylindrical parametrization techniques.

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

Complex Rotation Numbers

Explore complex rotation numbers, their theory, dynamics, and applications in tame geometry and analysis. Delve into bubbles, self-similarity, and normalization concepts.

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

Some New Techniques for the Resolution of Singularities of Differential Operators

Explore innovative techniques for resolving singularities in differential operators, covering key concepts like singular foliations, separatrix theorem, and weighted blowups.

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

Buchi Automata and Fractals on R

Explore Buchi automata and fractals on R, covering regular languages, model theory, and first-order logic. Gain insights into sparse sets and omega languages in this mathematical journey.

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

Tame Control Theory

Explore tame geometry in control theory, covering basic definitions, motivation, logic, and vector fields. Gain insights into descriptive set theory and generic structures.

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

Sampling, Interpolation, and Uncertainty

Explore sampling theory, interpolation techniques, and uncertainty principles in function spaces, with applications in signal processing and control theory.

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

Convergence of Scattering Data and Non-Linear Fourier Transform - Part 1

Explore canonical systems, spectral problems, and Hilbert spaces of entire functions in this advanced mathematical analysis lecture on scattering data and non-linear Fourier transform.

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

Some Reflections on the Work of Udi Hrushovski

Explore David Marker's reflections on Udi Hrushovski's contributions to geometric stability theory, strongly minimal expansions, and differentially closed fields in model theory.

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

Higher-Order Generalizations of Stability and Arithmetic Regularity

Explore higher-order generalizations of stability and arithmetic regularity, focusing on regularity lemmas, stable hereditary graph properties, and arithmetic settings in model theory.

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

Character Varieties of Random Groups

Explore character varieties of random groups, including representation spaces, faithful representations, and hyperbolic groups. Delve into surface groups, random presentations, and boundary limits.

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

Real Invariants in Arithmetic Geometry and Theta Series

Explore arithmetic geometry, theta series, and real invariants in this advanced mathematical lecture, focusing on Euclidean lattices, algebraic geometry, and chromological invariants.

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

DeFi- Finance 2.0?

Explore decentralized finance's potential, risks, and innovations in blockchain technology, covering key concepts, protocols, and security challenges in the evolving financial landscape.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video