Compactifications Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Baily-Borel Compactifications of Period Images and the b-semiampleness Conjecture

Explore advanced Hodge theory through functorial compactifications of period maps and prove the b-semiampleness conjecture using o-minimal GAGA techniques.

• YouTube
• 1 hour 9 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

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

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 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

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

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

BIMSA

Massive Gauge/Gravity Scattering Amplitudes, Geometric and Topological Mass Generations and Double Copy

Explore massive gauge/gravity scattering amplitudes, geometric and topological mass generations, and double copy constructions in Kaluza-Klein and Chern-Simons theories.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Different Notions of Tameness Revisited in Étale Morphisms

Explore different approaches to defining tameness in étale morphisms of schemes, focusing on valuation-theoretic methods and nonarchimedean geometry to overcome limitations of compactification-based approaches.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Tropicalization of the Universal Jacobian: Logarithmic and Non-Archimedean Views

Explore tropicalization of universal Jacobians, examining logarithmic and non-archimedean perspectives. Gain insights into moduli spaces, cone stacks, and new stability conditions for compactified Jacobians.

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

Institut des Hautes Etudes Scientifiques (IHES)

Universally Counting Curves in Calabi-Yau Threefolds

Explore a universal enumerative invariant for curves in algebraic varieties, focusing on threefolds with nef anticanonical bundle and its implications for the MNOP conjecture.

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

IPhT-TV

String Universality and Classification of String Vacua - Landscapia

Explore string universality and classification of string vacua in this advanced physics lecture by Miguel Montero, delving into complex theoretical concepts.

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