Instituto de Matemática Pura e Aplicada Courses

A Short Introduction to Sarkisov Theory

Explore Sarkisov theory with Sokratis Zikas in this concise introduction, part of IMPA's algebra community showcase featuring new postdoc fellows and their research interests.

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

Algebraic Hyperbolicity and Research Interests in Algebra

Explore algebraic hyperbolicity and other research interests with Lucas Mioranci at IMPA. Gain insights into advanced algebraic concepts and current mathematical investigations.

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

Bilhares

Explore o fascinante mundo dos bilhares matemáticos com Alejandro Kocsard, descobrindo suas aplicações e propriedades únicas na geometria e sistemas dinâmicos.

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

Doutorado: Geometria Algébrica II - Aula 03 (18/03/2025)

Explore advanced algebraic geometry concepts including sheaves, schemes, morphisms, Cartier and Weil divisors, line bundles, differentials, and cohomology in this doctoral-level mathematics lecture.

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

Doutorado: Geometria Algébrica II - Aula 04 (21/03/2025)

Explore advanced algebraic geometry concepts including sheaves, schemes, morphisms, Cartier and Weil divisors, line bundles, differentials, and cohomology in this doctoral-level mathematics lecture.

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

Enriques Varieties

Explore Enriques varieties and their properties as Alessandra Sarti discusses definitions, examples as quotients of holomorphic symplectic manifolds, and extensions to singular settings.

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

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