K3 Surfaces Courses and Certifications

Harvard CMSA

Orientifolds for F-theory on K3 Surfaces

Explore F-theory orientifolds on elliptically fibered K3 surfaces, connecting string theory compactification with D-brane classifications using real K-theory and antiholomorphic involutions.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

BIMSA

Analysis of ALH* Gravitational Instantons

Explore ALH* gravitational instantons, their Laplacian properties, and moduli space compactification. Gain insights into Calabi-Yau metrics and their applications in SYZ conjecture and K3 surface collapsing.

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

Institute for Advanced Study

Picard Ranks of Non-Ordinary K3 Surfaces

Explore advanced algebraic geometry through K3 surfaces over finite fields, focusing on Picard rank behavior in non-ordinary families and classification results.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

On K3 Surfaces with Non-Elementary Hyperbolic Automorphism Group

Explore advanced research on K3 surfaces with non-elementary hyperbolic automorphism groups, focusing on finiteness of Néron-Severi lattices under optimal conditions.

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

IMSA

Correspondence Between Elliptic-Elliptic Surfaces and K3 Surfaces

Delve into the correspondence between elliptic-elliptic surfaces and K3 surfaces, exploring Hodge structures, algebraic relationships, and extensions of Shioda-Inose's work through rational double covers of Kummer surfaces.

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

Instituto de Matemática Pura e Aplicada

Foliations on Projective K3 Surfaces

Explore foliations on projective K3 surfaces in this mathematical celebration honoring Frank Loray's 60th birthday, connecting complex geometry with advanced differential equations.

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

Institut Henri Poincaré

Reinventing Rational Points

Explore advanced techniques in arithmetic geometry, from Brauer-Manin obstructions to counting rational points on algebraic varieties through analytic and geometric methods.

• YouTube
• 2 days 3 minutes
• On-Demand
• Free Video

ICTP Mathematics

On the Geometry of Hyperkähler Manifolds

Explore hyperkähler manifolds, their properties, and examples. Delve into deformation types, moduli spaces of stable sheaves, and the birational geometry of K3-type manifolds with symplectic actions.

• YouTube
• 1 hour 43 minutes
• On-Demand
• Free Video

Harvard CMSA

Homological Mirror Symmetry and Hodge Theory - January 2018

Explore advanced mathematical concepts in homological mirror symmetry, Hodge theory, and algebraic geometry through expert lectures from leading researchers in the field.

• YouTube
• 20 hours 7 minutes
• On-Demand
• Free Video

Harvard CMSA

Donaldson-Thomas and Gromov-Witten Theories

Explore advanced mathematical theories connecting Donaldson-Thomas and Gromov-Witten invariants through K3 fibrations, stable pairs, and S-duality conjectures in algebraic geometry.

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

Hausdorff Center for Mathematics

Arend Bayer- Non-Commutative Abelian Surfaces and Generalised Kummer Varieties

Explore non-commutative abelian surfaces and generalized Kummer varieties, examining deformations of derived categories and their impact on moduli spaces of stable objects in algebraic geometry.

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

IMSA

Periods, Shafarevich Maps and Applications - Nodal Surfaces and Coding Theory

Explore nodal surfaces and coding theory in K3 geometry. Learn about period maps, Torelli theorem, and binary codes in relation to polarized nodal K3 surfaces and their components.

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

IMSA

The Mirror Clemens-Schmid Sequence

Explore a four-term exact sequence in cohomology, its relation to filtrations, and a proposed mirror to the Clemens-Schmid sequence, with applications in K3 surface settings.

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

IMSA

Comparing Geometric and Hodge-Theoretic Compactifications I

Explores compactifications of moduli spaces for abelian varieties and K3 surfaces, comparing geometric and Hodge-theoretic approaches. Discusses recent work on stable K3 surfaces and recognizable divisors.

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

IMSA

Comparing Geometric and Hodge-Theoretic Compactifications II

Explores compactifications of moduli spaces for abelian varieties and K3 surfaces, focusing on geometric interpretations and connections to Hodge theory and polyhedral decompositions.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video