Algebraic Geometry Courses and Certifications

IMSA

Equivariant Birational Geometry of 3-Dimensional Projective Space

1 review

Explore G-equivariant birational geometry of 3D projective space, focusing on finite group actions and their impact on fibrations into rational curves or surfaces.

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

Institute for Advanced Study

Drinfeld's Lemma for Schemes - Kiran Kedlaya

Explore Drinfeld's lemma for schemes with Kiran Kedlaya, covering fundamental groups, base points, and the Stax project in algebraic geometry.

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

Institute for Advanced Study

A Gentle Approach to Crystalline Cohomology - Jacob Lurie

Explore crystalline cohomology and the de Rham-Witt complex in algebraic geometry, with insights on alternative constructions and applications in positive characteristic fields.

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

Institute for Advanced Study

Independence of ℓ for Frobenius Conjugacy Classes Attached to Abelian Varieties - Rong Zhou

Explore Frobenius conjugacy classes in abelian varieties, focusing on independence of ℓ, Mumford-Tate groups, and connections to Shimura varieties and CM liftings.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Exceptional Splitting of Reductions of Abelian Surfaces With Real Multiplication - Yunqing Tang

Explore real multiplication in abelian surfaces, focusing on exceptional splitting of reductions. Delve into simple reduction, finite extension, and density zero concepts with insights on special devices and intersection numbers.

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

Insights into Mathematics

Seminar - Some Fundamental Formulas from Metrical Algebraic Geometry

Explore fundamental formulas in metrical algebraic geometry, connecting classical theorems to modern discoveries. Gain insights into affine and projective variants applicable across various fields.

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

Hausdorff Center for Mathematics

Some Remarks on Prismatic Cohomology of Rigid Spaces

Explore advanced mathematical concepts with renowned mathematician Peter Scholze as he delves into prismatic cohomology of rigid spaces in this insightful lecture.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Residues and Trace Maps in Grothendieck Duality - Lecture 3

Explores residues and trace maps in Grothendieck duality theory, advancing understanding of algebraic geometry and commutative algebra concepts for researchers and advanced students.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

On Compactly Supported P-Adic Proétale Cohomology of Analytic Varieties

Explore p-adic proétale cohomology with compact support for analytic varieties, including properties, comparison theorems, and connections to de Rham cohomologies.

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

Hausdorff Center for Mathematics

Alexander Petrov: On de Rham Cohomology in Positive Characteristic

Explores de Rham cohomology in positive characteristic, discussing Hodge decomposition analogs, isomorphism failures, and structures on de Rham complexes over F_p, including Sen operators and Frobenius pullback decompositions.

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

IMSA

Intersection Cohomology of the Moduli Spaces of Stable Bundle I

Explore intersection cohomology of semistable bundle moduli spaces on Riemann surfaces, including Decomposition Theorem analysis and new formula for intersection Betti numbers.

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

IMSA

Orbifold Jet Differentials and Hyperbolicity Conjectures

Explore orbifold jet differentials and their role in hyperbolicity conjectures. Discuss limitations in extending classical results to orbifold contexts, based on collaborative research.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IMSA

Fake Projective Planes: Properties and Recent Progress

Explore fake projective planes: complex surfaces with unique properties, their construction via uniformization, and recent advancements in understanding their algebraic and geometric characteristics.

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

IMSA

Exploring the Boundary of the Moduli Space of Stable Surfaces - I-Surfaces as a Test Case

Exploring I-surfaces: minimal complex surfaces with K^2=1 and p_g=2. Recent research on boundary points of KSBA compactification for I-surfaces' moduli space.

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

IMSA

The Geometric Andre-Grothendieck Period Conjecture

Explore complex algebraic varieties, period integrals, and the Ax-Schanuel conjecture. Delve into transcendence theory of period maps and the Andre-Grothendieck period conjecture's functional version.

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