Moduli Space Courses and Certifications

IMSA

Twistor Space for Moduli of Local Systems on Open Curves

Explore Deligne-Hitchin twistor spaces for moduli of framed local systems on open curves, examining harmonic bundles, preferred sections, and mixed twistor structures in moduli space geometry.

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

IMSA

The KSBA Moduli Space of Log Calabi-Yau Surfaces

Explore the geometry of log Calabi-Yau surfaces and their KSBA moduli space in this advanced mathematical lecture, delving into complex algebraic geometry concepts.

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

Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields

Explore the deep analogy between integers and polynomials over finite fields, connecting number theory to geometry, topology, and Langlands theory through modern techniques.

• YouTube
• 12 hours 8 minutes
• On-Demand
• Free Video

Institut Henri Poincaré

Combinatorics and Interactions - Asymptotic Representation Theory, Random Maps, and Enumerative Geometry

Explore advanced combinatorics through asymptotic representation theory, random maps, dimer models, and enumerative geometry in this comprehensive research trimester program.

• YouTube
• 3 days 8 hours 29 minutes
• On-Demand
• Free Video

NCCR SwissMAP

Master Class in Geometry, Topology and Physics

Explore advanced mathematical physics through algebraic geometry, symplectic geometry, quantum topology, field theory, and Poisson geometry in this intensive master class series.

• YouTube
• 1 week 20 hours 28 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Algebraic Geometry Seminar - Drinfeld's Lemma, Moduli Spaces, Hodge Theory, and Geometric Langlands

Explore advanced algebraic geometry through expert lectures on Drinfeld's lemma, moduli spaces, Hodge theory, Chow motives, and the Geometric Langlands Conjecture.

• YouTube
• 5 hours 1 minute
• On-Demand
• Free Video

ICTP Mathematics

Advanced School and Workshop on Geometry of Discrete Actions

Explore discrete group actions in geometry through hyperbolic spaces, complex dynamics, Teichmüller theory, and holomorphic dynamics with leading mathematicians.

• YouTube
• 1 day 16 hours 38 minutes
• On-Demand
• Free Video

ICTP Mathematics

Moduli Spaces, Mirror Symmetry, and Enumerative Geometry

Explore advanced algebraic geometry through moduli spaces, mirror symmetry, and enumerative geometry with leading experts from top institutions worldwide.

• YouTube
• 1 day 9 hours 46 minutes
• On-Demand
• Free Video

Harvard CMSA

Spacetime and Quantum Mechanics Master Class Workshop

Explore advanced mathematical structures connecting spacetime geometry, quantum mechanics, and scattering amplitudes through intersection theory, cluster algebras, and the amplituhedron.

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

IAS | PCMI Park City Mathematics Institute

Advanced Topics in Mathematical Gauge Theory - Higgs Bundles

Delve into advanced mathematical gauge theory and Higgs bundles through expert lectures covering sophisticated theoretical frameworks and their geometric applications.

• YouTube
• 4 hours 11 minutes
• On-Demand
• Free Video

Insights into Mathematics

One-Dimensional Objects - Algebraic Topology

Explore one-dimensional objects in algebraic topology, focusing on lines and circles. Learn about their diverse representations and fundamental properties in this introductory lecture.

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

Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 3

Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.

• YouTube
• 2 hours
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 2

Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.

• YouTube
• 2 hours
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Number Theory over Function Fields - Lecture 1

Explore recent progress in number theory using polynomial analogues over finite fields, connecting to topology, probability, and geometric Langlands theory.

• YouTube
• 2 hours 4 minutes
• On-Demand
• Free Video

Institute for Advanced Study

On the Arithmetic of Genus 4 Curves

Delve into the arithmetic invariants of non-hyperelliptic genus-4 curves, focusing on canonical "quadratic" points on Jacobians, height-theoretic bigness, and finiteness of low-height curves using adelic Arakelov intersection theory.

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