Instituto de Matemática Pura e Aplicada Courses

Decomposition of Complete 3-Manifolds of Positive Scalar Curvature with Quadratic Decay

Explore a mathematical presentation on the decomposition of complete 3-manifolds with positive scalar curvature and quadratic decay, part of the Systolic and Diastolic Geometry conference at IMPA.

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

From Symplectic Embeddings to Systolic Inequalities on the Sphere

Explore a mathematical talk on symplectic embeddings and systolic inequalities on the sphere, presented by Brayan Cuzzuol Ferreira at the Systolic and Diastolic Geometry event at IMPA.

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

Systolic and Diastolic Geometry - Viterbo's Inequality and Finsler Systolic Inequalities on RP^n

Dive into Viterbo's inequality and Finsler systolic inequalities on RP^n with Shira Tanny's mathematical exploration of geometric comparison problems between volume and length/area relationships.

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

Systolic and Diastolic Geometry - Minimal Area of Finsler Disks with Minimizing Geodesics

Delve into the mathematical exploration of minimal area in Finsler disks with minimizing geodesics, presented by Stéphane Sabourau as part of the Systolic and Diastolic Geometry event at IMPA.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Systolic and Diastolic Geometry - Spectral Optimization with Respect to the Metric on Surfaces

Delve into spectral optimization with respect to metrics on surfaces of any topology, exploring geometric problems that compare volume and length/area in mathematical spaces.

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

A Counterexample to Viterbo's Conjecture

Dive into a counterexample to Viterbo's conjecture in systolic and diastolic geometry, presented by Pazit Haim-Kislev from the Institute for Advanced Study during IMPA's mathematics conference in Rio de Janeiro.

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

Systolic and Diastolic Geometry - Eigenvalues and Minimal Surfaces

Delve into the relationship between eigenvalues and minimal surfaces in systolic and diastolic geometry with Mikhail Karpukhin's mathematical exploration of geometric comparison problems.

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

Systolic and Diastolic Geometry - Area Rigidity of Minimal Surfaces

Delve into André Neves' lecture on area rigidity of minimal surfaces, part of the "Systolic and Diastolic Geometry" event exploring geometric problems related to volume, length, and area comparisons in mathematical spaces.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Systolic Inequalities in Reeb Dynamics

Delve into systolic inequalities in Reeb dynamics with Alberto Abbondandolo, exploring geometric problems that compare volume of spaces with lengths of curves they contain.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Systolic and Diastolic Geometry - Rigidity and Flexibility of Periodic Hamiltonian Flows

Delve into rigidity and flexibility of periodic Hamiltonian flows with Gabriele Benedetti, exploring key concepts in systolic geometry and their applications to mathematical problems involving volume, length, and area comparisons.

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

Systolic and Diastolic Geometry - Min-max Widths Compared to Other Geometric Invariants

Explore Rafael Montezuma's lecture on min-max widths compared to other geometric invariants, part of the "Systolic and Diastolic Geometry" event at IMPA examining relationships between volume and length/area in geometric spaces.

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

Systolic and Diastolic Geometry - Capacities of Disc Tangent Bundles of Symmetric R-Spaces

Explore Johanna Bimmermann's lecture on capacities of disc tangent bundles of symmetric R-spaces, part of the Systolic and Diastolic Geometry event at IMPA examining geometric comparison problems.

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

Systolic Inequalities for S1-Invariant Contact Forms

Dive into systolic inequalities for S1-invariant contact forms with Simon Vialaret from Paris-Saclay, exploring geometric comparisons between volume and length/area in mathematical spaces.

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

Systolic and Diastolic Geometry - How Packing Simplices Helps to Study Symplectic Systoles

Dive into how packing simplices contributes to the study of symplectic systoles in this mathematical exploration by Alexey Balitskiy from Luxembourg, presented at IMPA's Systolic and Diastolic Geometry event.

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

p-adic Integration Theories on Curves

Delve into p-adic integration theories on curves with Enis Kaya's presentation, exploring the intersection of combinatorial methods with algebraic geometry and number theory.

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