Fields Institute Courses

The Non-Lefschetz Locus for Lines and for Conics

Explore the non-Lefschetz locus for lines and conics in algebraic geometry, examining its properties and implications in topology and combinatorics.

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

The Strong Lefschetz Property of Artinian Gorenstein Algebras With Low Sperner Numbers

Explore the Strong Lefschetz property in Artinian Gorenstein algebras, focusing on those with low Sperner numbers. Gain insights into this advanced algebraic concept and its implications.

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

Lefschetz Properties in the Constructible Context

Explore Lefschetz properties in constructible contexts, examining their applications in algebra, geometry, topology, and combinatorics.

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

Jordan Type of Artinian Algebras, Finer Invariants, and Applications

Explore Jordan type of Artinian algebras, their finer invariants, and practical applications in this advanced mathematical lecture by Pedro Macias Marques.

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

Lefschetz Properties of Random Monomial Algebras

Explore Lefschetz properties in random monomial algebras, examining their algebraic and geometric implications in this advanced mathematics talk.

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

Connected Sums of Artinian Gorenstein Algebras and the Lefschetz Properties

Explore the intersection of algebra, geometry, and topology through connected sums of Artinian Gorenstein Algebras and their Lefschetz Properties in this advanced mathematical talk.

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

Opening up Quantum Criticality

Explore quantum criticality, long-range entanglement, and open quantum systems. Discover local adaptive circuits, critical mixed states, and their implications for quantum information theory.

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

On Modeling Investors in Simulated Markets

Explore multi-agent market simulations, from market replay to advanced AI-driven models. Learn about trading agent design, market impact analysis, and applications in financial research.

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

Animal Movement and Emergent Patterns of Space Use - A Personal Journey With Plentiful References to Mark Lewis

Explore animal movement, territoriality, and space use patterns through mathematical models and ecological insights, featuring personal research experiences and collaborative work.

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

The Planar Stochastic Heat Equation and the Directed Landscape

Explore stochastic heat equations and directed landscapes in probability theory, focusing on models, solutions, and applications in mathematical physics and statistical mechanics.

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

Out of the Closet and Into the Mirror

Explore algebraic geometry, Calabi-Yau varieties, and mirror symmetry with insights on finding the right mathematical community and research spaces for LGBTQ+ mathematicians.

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

Quantum Algorithms - From Far to Near Future

Explore quantum algorithms' evolution, from Hamiltonian simulations to empirical hardness models, and their applications in quantum field theory and state preparation.

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

Combinatorial Atlas for Log-Concave Inequalities

Explore log-concave inequalities in combinatorics, focusing on matroids, Mason's Conjecture, and hyperbolic inequalities. Learn about refinement techniques and equality conditions.

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

Equal Risk Option Pricing with Deep Reinforcement Learning

Explore innovative option pricing using deep reinforcement learning, focusing on equal risk approaches, hedging strategies, and market dynamics. Gain insights into advanced quantitative finance techniques.

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

Varieties of Mathematical Understanding

Explore diverse forms of mathematical comprehension, challenges in theorem-proving, and the evolving nature of understanding in mathematics through historical and philosophical lenses.

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