Arithmetic Geometry Courses and Certifications

International Centre for Theoretical Sciences

The Eisenstein Cycles and Manin-Drinfeld Properties

Explore Eisenstein cycles and Manin-Drinfeld properties in modular curves, focusing on rational points and their significance in arithmetic geometry. Gain insights from expert Debargha Banerjee.

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

International Centre for Theoretical Sciences

On the Solutions of Certain Diophantine Equations Over Totally Real Fields

Explore solutions to specific Diophantine equations over totally real fields, delving into advanced number theory and algebraic geometry concepts.

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

International Centre for Theoretical Sciences

Bipartite Euler Systems for Certain Galois Representations by Pronay Karmakar

Exploration of bipartite Euler systems for specific Galois representations, discussing advanced concepts in arithmetic geometry and number theory.

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

International Centre for Theoretical Sciences

The Principle of Quadratic Chabauty and Nonsplit Cartan Modular Curves

Explore advanced techniques for studying rational points on modular curves, focusing on quadratic Chabauty methods and nonsplit Cartan modular curves in arithmetic geometry.

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

International Centre for Theoretical Sciences

Ribet's Lemma in Residually Indistinguishable Case by Mahesh Kakde

Exploration of Ribet's Lemma in the context of residually indistinguishable cases, delving into advanced concepts in arithmetic geometry and modular curves theory.

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

International Centre for Theoretical Sciences

Iwasawa Theory for Rankin-Selberg L-Function at an Eisenstein Prime

Explores Iwasawa theory for Rankin-Selberg L-functions at Eisenstein primes, delving into advanced arithmetic geometry concepts and their applications in number theory.

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

Hausdorff Center for Mathematics

Beilinson's Conjecture for the Dwork Family

Explores Beilinson's conjecture for the Dwork family, focusing on constructing classes in higher Chow groups and computing their regulators in relation to motivic L-functions and automorphic forms.

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

Isaac Newton Institute for Mathematical Sciences

Hasse Principle for Simply Connected Groups - Kirk Lecture

Explore the Hasse principle for simply connected groups, its significance in number fields, and recent progress in function fields of curves over p-adic fields.

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

Institut des Hautes Etudes Scientifiques (IHES)

Point-Counting and the Zilber-Pink Conjecture - Lecture 4

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

• YouTube
• 1 hour 52 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Point-Counting and the Zilber-Pink Conjecture - Lecture 2

Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.

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

Centre International de Rencontres Mathématiques

Finite Flat Group Schemes over Z

Explore finite flat group schemes over Z with René Schoof in this advanced arithmetic geometry lecture from the CIRM Symposium.

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

Centre International de Rencontres Mathématiques

Computing Euler Factors of Curves

Explore computational methods for determining Euler factors of curves in arithmetic geometry, focusing on advanced mathematical techniques and applications.

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

Institute for Advanced Study

Arithmetic Quantum Unique Ergodicity for Hyperbolic Manifolds

Explore quantum unique ergodicity in hyperbolic manifolds, focusing on arithmetic aspects and their implications in mathematical physics and number theory.

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

BIMSA

Rigidity and Uniformity in Algebraic Dynamics

Explore connections between algebraic dynamics and arithmetic geometry, focusing on preperiodic points and torsion points in abelian varieties. Learn about recent breakthroughs in uniform bounds and conjectures.

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

BIMSA

Average Heights of Abelian Varieties with Complex Multiplication

Explore the arithmetic properties of abelian varieties with complex multiplication, focusing on Colmez's conjecture and its implications for periods and L-functions.

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