Instituto de Matemática Pura e Aplicada Courses

A Family of Birational Models of Generalized Kummer Varieties as Coverings of a Projective 4-Space

Explore a collaborative study on constructing birational models of generalized Kummer varieties using degree 15 ramified coverings of projective 4-space, based on geometric interpretations of Jacobian group laws in genus 2 curves.

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

Stability of Systolic Inequalities for the Klein Bottle

Explore stability of systolic inequalities for the Klein bottle in this mathematical presentation by Jan Eyll from Ruhr-Universität Bochum, part of the Systolic and Diastolic Geometry conference at IMPA.

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

Systolic and Diastolic Geometry - Growth of k-dimensional Systoles in Congruence Coverings

Explore Mikhail Belolipetsky's lecture on growth of k-dimensional systoles in congruence coverings, part of the "Systolic and Diastolic Geometry" event at IMPA examining geometric comparison problems.

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

Systolic and Diastolic Geometry - The Toda Lattice and Symplectic Balls

Dive into the mathematical exploration of the Toda lattice and its relationship with symplectic balls in this lecture by Yaron Ostrover from Tel Aviv University, part of the Systolic and Diastolic Geometry event.

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

Zoll Families and Isosystolic Inequalities

Explore Zoll families and isosystolic inequalities in this mathematical talk by Luciano Luzzi Junior, part of the "Systolic and Diastolic Geometry" event at IMPA focusing on geometric comparison problems.

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

Weyl Law for 1-Cycles and Applications

Dive into Bruno Staffa's exploration of Weyl Law for 1-cycles and its applications in systolic and diastolic geometry, examining relationships between volume and length in mathematical spaces.

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

Systolic and Diastolic Geometry - Free Curvature Generalizations of Hyperbolic Identities

Explore free curvature generalizations of hyperbolic identities in this mathematical lecture by Florent Balacheff, part of the "Systolic and Diastolic Geometry" event at IMPA focusing on geometric comparison problems.

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

Systolic and Diastolic Geometry - Half-volume Spectrum and Constant Mean Curvature Hypersurfaces

Delve into the mathematical exploration of half-volume spectrum and constant mean curvature hypersurfaces in this lecture by Xin Zhou from Cornell University, part of the Systolic and Diastolic Geometry event at IMPA.

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

Existence and Confinement of Closed Magnetic Geodesics at Low Energies

Explore the existence and confinement of closed magnetic geodesics at low energies in this mathematical presentation by Valerio Assenza from IMPA's Systolic and Diastolic Geometry conference.

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

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