Compactifications Courses and Certifications

An Introduction to Point-Set-Topology Part-II

Explore advanced point-set topology concepts, including compactness, paracompactness, metrization theorems, and function spaces. Develop a deeper understanding of topological properties and their applications in mathematics and physics.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Institute for Advanced Study

Pseudoholomorphic Curves with Boundary - Can You Count Them? Can You Really? - Sara Tukachinsky

Explore pseudoholomorphic curves with boundary, their counting challenges, and innovative approaches in Gromov-Witten theory with Sara Tukachinsky's advanced mathematical seminar.

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

Institute for Advanced Study

Mirrors of Curves and Their Fukaya Categories - Denis Auroux

Explore symplectic geometry with Denis Auroux as he delves into mirrors of curves and their Fukaya categories, covering topics from monomial examples to Lagrangian admissibility.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Dual-Frame Generalized Harmonic Gauge on Hyperboloidal Slices - IPAM at UCLA

Explore advanced techniques in general relativity, focusing on including future null-infinity in computational domains for cosmic censorship studies and gravitational wave astronomy applications.

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

International Centre for Theoretical Sciences

Representations of Fuchsian Groups, Parahoric Group Schemes by Vikraman Balaji

Explore advanced mathematical concepts including Fuchsian groups, parahoric schemes, and root systems. Delve into complex algebraic structures and their representations in this in-depth lecture on geometric group theory.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Geometric Langlands Conjecture and Non-Abelian Hodge Theory - Lecture 1

Explore the Geometric Langlands conjecture and non-abelian Hodge theory, examining connections between quantum fields, geometry, and representation theory in modern mathematics and theoretical physics.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

IMSA

Kato-Usui Type Extension of General Period Map

Explore Kato-Usui theory for extending non-classical period maps, its applications, and potential future directions in algebraic geometry and Hodge theory.

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

IMSA

Compactification of Moduli Spaces of Quantum Toric Stacks

Explores moduli spaces of quantum toric stacks and their compactification, extending toric varieties to stacky generalizations with finitely generated subgroups of R^d as "lattices".

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

IMSA

Period Mappings at Infinity - Recent Developments II

Explores recent advancements in Hodge theory, focusing on asymptotic properties of period maps and their applications to moduli spaces beyond classical cases of ppav and K3s.

• YouTube
• 1 hour 4 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

Compactifications of Moduli — Geometry vs. Hodge Theory

Exploration of geometric and Hodge theoretic approaches to compactifying moduli spaces in algebraic geometry, with focus on classical cases and H and I-surfaces.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Arvin Ash

The Battle for Reality - String Theory vs Quantum Field Theory

Explore the battle between String Theory and Quantum Field Theory, examining their approaches to explaining fundamental particles, forces, and the challenge of quantizing gravity.

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

Fields Institute

Cohomology of Compactifications of Hypersurface Arrangement Complements

Explore advanced algebraic geometry concepts, focusing on cohomology of compactifications in hypersurface arrangement complements with expert Alex Fink.

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

Galileo Galilei Institute

Modularity and Resurgence in Calabi-Yau Compactifications

Explore modularity and resurgence in Calabi-Yau compactifications, delving into advanced concepts in theoretical physics and mathematics.

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

Institut des Hautes Etudes Scientifiques (IHES)

Different Notions of Tameness Revisited in Étale Morphisms

Exploración de diferentes enfoques para definir la mansedumbre en morfismos étale de esquemas, utilizando geometría no arquimediana y curvas ádicas para evitar la resolución de singularidades.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video