L-functions Courses and Certifications

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

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

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

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

Hausdorff Center for Mathematics

The Ratios Conjecture Over Function Fields

Explore the Ratios Conjecture for quadratic L-functions over function fields, including upper bounds for negative moments and partial results for various L-function ratios.

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

Fields Institute

Primes, Postdocs and Pretentiousness - 2021 CRM-Fields-PIMS Prize Lecture

Explore prime numbers, academic careers, and mathematical concepts in this engaging lecture by renowned mathematician Andrew Granville, offering insights into number theory and research.

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

Fields Institute

Automorphic Forms and Representation Theory - Introduction to the Langlands Program - Lecture 18

Explore the Langlands Program through automorphic forms and representation theory, delving into advanced mathematical concepts and their interconnections.

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

IMSA

Extensions of Hodge Structure and Completions of Fundamental Groups

Explore extensions of mixed Hodge structures, unipotent and relative completions of fundamental groups, and their geometric interpretations in L-functions and motives theory.

• YouTube
• 1 hour 2 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

Hausdorff Center for Mathematics

Valentin Blomer - The Polynomial Method for Point Counting and Exponential Sums, Lecture III

Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using auxiliary polynomials and character sums.

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