Arithmetic Geometry Courses and Certifications

Institut des Hautes Etudes Scientifiques (IHES)

Arithmetic and Diophantine Geometry via Ergodic Theory and O-Minimality

Explore cutting-edge research in arithmetic geometry, Diophantine theory, ergodic systems, and Hodge theory through expert presentations honoring Emmanuel Ullmo's contributions.

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

Institut des Hautes Etudes Scientifiques (IHES)

Franco-Asian Summer School on Arithmetic Geometry

Delve into advanced arithmetic geometry through expert lectures on p-adic cohomology, Galois representations, and Simpson correspondence from leading mathematicians.

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

Institute for Advanced Study

Arithmetic Geometry Seminar - Advanced Topics in p-adic Geometry and Algebraic Number Theory

Explore cutting-edge research in arithmetic geometry through expert presentations on p-adic Hodge theory, moduli spaces, and geometric Langlands correspondence.

• YouTube
• 1 day 5 hours 45 minutes
• On-Demand
• Free Video

Simons Institute

Effective Arithmetic Geometry

Explore advanced concepts in arithmetic geometry, focusing on effective methods and their applications in number theory and algebraic geometry.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Complex Dynamics and Arithmetic Geometry by Laura DeMarco

Exploring connections between dynamical systems and arithmetic geometry, focusing on periodic points, torsion points, and algebraic curves in genus 2. Insights from polynomial dynamics and Julia sets illustrate key concepts.

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

Fields Institute

Real Invariants in Arithmetic Geometry and Theta Series

Explore arithmetic geometry, theta series, and real invariants in this advanced mathematical lecture, focusing on Euclidean lattices, algebraic geometry, and chromological invariants.

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

IAS | PCMI Park City Mathematics Institute

Local Systems in Arithmetic Geometry - Lecture 3

Delve into fundamental group theory and local systems in arithmetic geometry, exploring motivic conjectures and their implications for complex quasi-projective varieties and geometric representations.

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

IAS | PCMI Park City Mathematics Institute

Local Systems in Arithmetic Geometry

Delve into fundamental group theory in arithmetic geometry, exploring local systems and their motivic aspects through deep conjectures and geometric obstructions in complex quasi-projective varieties.

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

Institute for Advanced Study

Extensions of Globally Valued Fields and Arithmetic Geometry

Explore globally valued fields as generalizations of global fields, connecting first-order logic to Arakelov geometry, heights, lattices, and adeles in arithmetic geometry.

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

Centre International de Rencontres Mathématiques

Transforming Numbers - Why is Arithmetic Geometry Geometry?

Explore how arithmetic geometry bridges discrete numbers and continuous geometry through innovative mathematical structures, transforming our understanding of fundamental concepts like number and space.

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

Institute for Advanced Study

Galois, Grothendieck and Voevodsky - George Shabat

Explore the mathematical legacies of Galois, Grothendieck, and Voevodsky, focusing on their contributions to group theory, algebraic geometry, and category theory, with insights into dessins d'enfants and Belyi pairs.

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

Tom Rocks Maths

Mordell Conjecture and the 1986 Fields Medal - Interview with Gerd Faltings

Explore Gerd Faltings' groundbreaking work on the Mordell Conjecture, his Fields Medal journey, and insights into Arithmetic Geometry through an engaging interview with Oxford mathematician Dr Tom Crawford.

• YouTube
• 18 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

Fields Institute

The Perfectoid Approach to Purity Questions

Explore advanced mathematical concepts in purity theory using perfectoid techniques, presented by Kęstutis Česnavičius from Paris-Saclay University and CNRS.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

ICTP Mathematics

Superficies Racionales sobre un Cuerpo - AGRA IV Minicourse 2 - Lecture 5

Explora superficies racionales sobre cuerpos en esta conferencia avanzada de matemáticas, examinando conceptos clave y resultados recientes en geometría algebraica aritmética.

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