Schubert Calculus Courses and Certifications

Institute for Pure & Applied Mathematics (IPAM)

Schubert Calculus and Quantum Integrability

Explore recent advancements in Schubert calculus and its connection to quantum integrable systems, focusing on combinatorial formulae for intersection numbers and their extensions.

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

International Mathematical Union

Allen Knutson- Schubert Calculus and Quiver Varieties

Explore Schubert calculus, quiver varieties, and their connections through puzzle rules, Yang-Baxter equations, and representation theory in this advanced mathematics lecture.

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

Institute for Advanced Study

Gröbner Objects in Schubert Calculus

Explore Gröbner objects and their applications in Schubert calculus, delving into advanced algebraic geometry concepts.

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

Institute for Advanced Study

Cotangent Schubert Calculus and Cohomology Rings in Flag Varieties

Delve into advanced mathematical concepts of Cotangent Schubert Calculus, exploring cohomology rings, characteristic classes, and their connections to Hecke algebra and Kazhdan-Lusztig theory.

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

Institute for Advanced Study

Total Positivity and Real Schubert Calculus

Delve into the history and modern applications of total positivity, exploring its connections to Schubert calculus, real-rooted polynomials, cluster algebras, and representation theory in this advanced mathematical seminar.

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

Institute for Advanced Study

Combinatorics in Quantum K-theory Schubert Calculus

Delve into the combinatorial model for quantum K-theory of flag manifolds, exploring Weyl group combinatorics, Chevalley-type multiplication formulas, and solutions to longstanding conjectures in Schubert calculus.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

International Mathematical Union

Beyond Linear Algebra

Explore advanced mathematical concepts beyond linear algebra, including critical point equations, nonlinear algebra in PDE, and geometric interpretations in optimization and statistics.

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

Fields Institute

The Two Lives of the Grassmannian

Explore the dual nature of Grassmannian manifolds in this mathematical lecture by Bernd Sturmfels from U.C. Berkeley at the Fields Institute.

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

Institute for Advanced Study

Valuative Invariants of Matroids and Their Geometric Interpretations

Delve into the geometric interpretations of matroid invariants, exploring valuative properties and their connections to Chow rings of toric varieties through advanced mathematical concepts.

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

Institute for Advanced Study

Three Proofs of the Reverse Khovanskii-Teissier Inequality

Delve into three distinct mathematical approaches proving the reverse Khovanskii-Teissier inequality, exploring analytic, algebraic, and convex geometric perspectives in advanced geometry.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

BIMSA

Stable Envelopes for Critical Loci

Explore advanced mathematical concepts in algebraic geometry through Andrei Okounkov's presentation on stable envelopes and their applications to critical loci in modern research.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Positive m-Divisible Non-crossing Partitions and Their Cyclic Sieving

Delve into geometric interpretations of Kreweras lattice embeddings and their connections to toric geometry, exploring non-crossing partitions through algebraic combinatorics and cohomology rings.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Non-crossing Partitions, Equivariant Cohomology, and Polynomials

Explore geometric interpretations of non-crossing partitions through toric geometry, examining connections between Kreweras lattice, flag variety cohomology, and algebraic combinatorics.

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

Fields Institute

Positivity of Schubert Coefficients

Explore the mathematical concept of positivity in Schubert coefficients with Colleen Robichaux from UCLA in this Fields Institute talk.

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

Fields Institute

Schubert Problems of Types A and C in Macaulay2

Explore Schubert problems in types A and C using Macaulay2, focusing on computational approaches in enumerative geometry and algebraic combinatorics.

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