Arithmetic Geometry Courses and Certifications

International Centre for Theoretical Sciences

Singular Moduli for Real Quadratic Fields - An Update by Jan Vonk

Explore singular moduli for real quadratic fields with Jan Vonk. Learn about recent developments, theoretical insights, and computational aspects in this advanced arithmetic geometry lecture.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Equidistribution of Matrix Valued Gauss Sums by C. S. Rajan

Explore equidistribution of matrix-valued Gauss sums in this advanced mathematics lecture, delving into arithmetic geometry and modular curves.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Quadratic Twist of Epsilon Factor of Symmetric Cube Transfers of Modular Form by Sudipa Mondal

Explores quadratic twists of epsilon factors for symmetric cube transfers of modular forms, delving into advanced concepts in arithmetic geometry and number theory.

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

International Centre for Theoretical Sciences

On the Pseudonullity of Fine Selmer Groups Over Function Fields by Sohan Ghosh

Explores pseudonullity of fine Selmer groups over function fields, advancing understanding in arithmetic geometry and modular curves. Contributes to research on rational points and algebraic structures.

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

International Centre for Theoretical Sciences

Uniform Versions of Shafarevich Conjecture by Plawan Das

Exploring uniform versions of Shafarevich Conjecture in arithmetic geometry, focusing on rational points on modular curves and their implications for elliptic curves and modular forms.

• YouTube
• 54 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

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

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

Institute for Advanced Study

On the Converse to Eisenstein's Last Theorem

Explore Eisenstein's theorem and its converse, examining algebraic functions, Taylor expansions, and ODEs. Delve into joint research on conditions for algebraicity and related conjectures.

• YouTube
• 1 hour 9 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

IAS | PCMI Park City Mathematics Institute

Arithmetic Properties of Local Systems in Motivic Homotopy Theory

Delve into fundamental group theory and local systems in arithmetic geometry, exploring classical conjectures and recent developments in motivic representations and their arithmetic properties.

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

Institute for Advanced Study

Higher Singularities in Positive Characteristic

Delve into Hodge-theoretic invariants of complex singularities and explore positive characteristic methods like Cartier operators for studying such singularities, based on joint research with Tatsuro Kawakami.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video