Second Moment of the GL_3 Standard L-function on the Critical Line
Explore advanced number theory concepts, focusing on GL_3 L-functions, moments of the Riemann zeta function, and applications to the Rankin-Selberg problem.
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.
Hidden Symmetries of the Work of Jan Nekovář
Explorez les principes unificateurs de la recherche de Jan Nekovar, des systèmes d'Euler aux variétés de Shimura quaternioniques, en passant par les résultats de parité pour les fonctions L.
Galois Representations and Statistics - Lecture 1
Explore Galois representations and statistics in arithmetic through an advanced mathematical lecture by René Schoof.
Subconvexity of L-functions - Part 2
Explore advanced concepts in subconvexity of L-functions through an in-depth mathematical lecture by Philippe Michel, expanding on previous discussions.
Modularity of Some Geometric Objects - Definitions, Reasons and State of the Art
Explore zeta functions, L-functions, and Galois representations in geometric objects, focusing on plane projective curves and their conjectured relationships with analytic functions.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Eigenvarieties and Arithmetic - Connection to L-Functions
Explore eigenvarieties, p-adic automorphic forms, and their connection to L-functions. Discover the local geometry of eigenvarieties and its significance in arithmetic.
Some Research Problems in Number Theory
Explore intriguing research problems in number theory with Ram Murty, delving into advanced mathematical concepts and unsolved questions in this fascinating field.
One-level Densities in Families of Grossencharakters Associated to CM Elliptic Curves
Explore one-level densities in Grossencharakters families linked to CM elliptic curves, delving into advanced number theory concepts and their applications.
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.
Motivic Galois Theory of Algebraic Mellin Transforms
Explore the intricate connections between algebraic geometry and number theory through the lens of motivic Galois theory and Mellin transforms.