L-functions Courses and Certifications

International Mathematical Union

The Distribution of Values of Zeta and L-Functions

Explore the intricate world of zeta and L-functions, delving into their value distribution patterns and mathematical implications with renowned number theorist Kannan Soundararajan.

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

Fields Institute

Eisenstein Cocycles and Values of L-Functions

Explore Eisenstein cocycles, equivariant cohomology, and their applications to L-functions. Gain insights into recent constructions and their connections to theta kernels and arithmetic groups.

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

Institut des Hautes Etudes Scientifiques (IHES)

Conjectures on L-functions for Varieties over Function Fields and Their Relations

Explore conjectures on L-functions for varieties over function fields, focusing on abelian varieties and the BSD-rank conjecture. Examine relationships using rigid cohomology.

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

Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 3

Explore advanced concepts in subconvexity of L-functions with mathematician Paul Nelson in this in-depth conference talk from the "Building bridges 6th EU/US" meeting.

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

Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 1

Explore advanced concepts in analytic number theory, focusing on subconvexity bounds for L-functions and their applications in mathematics.

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

Centre International de Rencontres Mathématiques

Subconvexity of L-functions - Part 4

Explore advanced concepts in subconvexity of L-functions with mathematician Paul Nelson in this in-depth conference talk from the "Building bridges 6th EU/US" meeting.

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

Simons Foundation

Moments of One-Level Densities for a Large Orthogonal Family of L-functions

Explore advanced number theory connecting L-function statistics with random matrix theory, verifying Katz-Sarnak conjecture for orthogonal families of holomorphic Hecke newforms.

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

Institute for Advanced Study

On the Kudla-Rapoport Conjecture - Chao Li

Explore the Kudla-Rapoport conjecture, Hurwitz class numbers, and their connections to Eisenstein series and L-functions in this advanced number theory seminar by Chao Li.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Number Theory Seminar - Advanced Topics in Arithmetic Geometry and L-Functions

Explore advanced number theory through expert lectures on L-functions, Galois representations, modular forms, and arithmetic geometry from leading mathematicians worldwide.

• YouTube
• 6 days 10 hours 57 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Siegel Modular Forms - Classical and Adelic Aspects by Ameya Pitale

Explore Siegel modular forms from classical and modern perspectives, including functions on Siegel upper half spaces and automorphic representations of the symplectic group.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Simons Foundation

Joint Linnik Problems and Siegel Zeros

Explore advanced number theory through simultaneous equidistribution conjectures for torus embeddings in PGL_2 forms, connecting Siegel zeros to L-function bounds.

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

International Centre for Theoretical Sciences

Elliptic Curves and the Special Values of L-Functions (2022)

Explore advanced mathematical theories connecting elliptic curves, L-functions, and arithmetic geometry through expert lectures on Iwasawa theory, Selmer groups, and special values.

• YouTube
• 2 days 4 hours 3 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

The Orbit Method, Microlocal Analysis and Applications to L-Functions

Explore quantitative orbit method in microlocal analysis, its applications to representation theory, and implications for L-functions, including moment estimates and subconvex bounds.

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

Fields Institute

Quantum Complexity and L-functions

Explore quantum algorithms for L-functions and zeta functions, examining complexity results, cohomology's role, and applications to modular forms and Mordell-Weil theorem.

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

BIMSA

Weyl-Strength Subconvexity for Dirichlet L-Functions

Explore Weyl-strength subconvexity for Dirichlet L-functions, examining the subconvexity problem and progress on obtaining the Weyl exponent via the method of moments.

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