Fields Institute Courses

Detecting Non-Permutative Elements of K1-Var Using Point Counting

Explore advanced algebraic geometry techniques for detecting non-permutative elements in K1(Var) through point counting methods, presented by Cornell University's Inna Zakharevich.

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

Euler Classes, Pairings, and Duality

Explore Euler classes in modules, their connection to Hochschild homology pairings, and implications for various forms of duality in homotopy theory and arithmetic geometry.

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

Topological Cyclic Homology and the Fargues-Fontaine Curve

Explore the connection between localizing invariants and the Fargues--Fontaine curve, with insights on K-theory, topological cyclic homology, and the twistor projective line.

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

The Family Signature Theorem

Explores Hirzebruch's signature theorem and its extension to families of smooth manifolds, relating intersection forms to characteristic classes and the family index theorem.

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

Yang-Baxter Elements and a New Proof of Homological Stability for the Mapping Class Group of Surfaces

Explores Yang-Baxter elements in monoidal categories, introducing a novel approach to prove homological stability for surface mapping class groups using semi-simplicial sets and bimarked surfaces.

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

On the X Y Symmetry in Topological Recursion via Loop Insertion Operator

Explore the x-y symmetry in Topological Recursion through the lens of loop insertion operators, delving into advanced mathematical concepts and their applications.

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

Reflection

Explore homotopy theory's applications in arithmetic and geometry with David Ayala's insightful conference talk, delving into the concept of reflection in mathematical contexts.

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

Weights in Homotopy Theory

Explore the concept of weights in homotopy theory, examining their applications and implications for arithmetic and geometric studies in mathematics.

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

The Mod -p,v1- Motivic Filtration on the Topological Cyclic Homology of Topological K-Theory

Explore the mod (p,v1) motivic filtration on topological cyclic homology of K-theory, delving into advanced concepts in homotopy theory and its applications to arithmetic and geometry.

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

Syntomic Complexes

Explore syntomic complexes in arithmetic and geometry with Akhil Mathew, delving into advanced mathematical concepts and their applications in homotopy theory.

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

Equivariant Enumerative Geometry

Explore equivariant enumerative geometry, delving into advanced mathematical concepts and their applications in arithmetic and geometry.

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

What the Numbers Say - Inflation in the Nation

Experts discuss Canada's inflation crisis, exploring mathematical models behind economic decisions and their impact on citizens. Panel answers audience questions on complex financial variables and national responses.

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

On the K-Theory of Z-P^n

Explore the intricate world of K-theory and its applications to Z/p^n, delving into advanced mathematical concepts and their implications in arithmetic and geometry.

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

Analytic Geometry

Explore advanced concepts in analytic geometry with renowned mathematician Peter Scholze, delving into its applications in arithmetic and homotopy theory.

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

Slices of ΣnHZ over Q8

Explore slices of ΣnHZ over Q8, delving into homotopy theory applications in arithmetic and geometry. Gain insights from expert Carissa Slone's research presentation.

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