Modular Forms, Elliptic Polylogarithms and Feynman Integrals
Explores advanced mathematical concepts in Feynman integrals, focusing on epsilon-form solutions, modular forms, and elliptic polylogarithms, with applications in number theory and physics.
Symmetric Power Functoriality for Hilbert Modular Forms
Explore symmetric power functoriality for Hilbert modular forms, comparing with elliptic modular cases in this advanced mathematics lecture by James Newton.
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.
Rational Points on Modular Curves - Lecture 3
Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
Rational Points on Modular Curves - Lecture 2
Explore advanced techniques for studying rational points on modular curves, focusing on geometry, Q-rational points, Chabauty methods, and computational aspects in arithmetic geometry.
Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 3
Explores advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Builds on previous lectures to deepen understanding of these fundamental objects.
Rational Points on Modular Curves by Jan Vonk
Explore advanced techniques for studying rational points on modular curves, focusing on theoretical and computational aspects in arithmetic geometry.
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.
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.
Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 1
Explore modular forms, elliptic curves, and modular curves in this advanced lecture. Gain insights into arithmetic geometry and the study of rational points on varieties.
Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 2
Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights into rational points and their significance in number theory.
Introduction to Modular Forms, Elliptic Curves, and Modular Curves - Lecture 4
Explore advanced concepts in arithmetic geometry, focusing on modular forms, elliptic curves, and modular curves. Gain insights from expert Eknath Ghate in this in-depth lecture.
Rational Points on Modular Curves - Lecture 1
Explore advanced concepts in arithmetic geometry, focusing on rational points on modular curves. Gain insights into theoretical and computational aspects of this fascinating field of mathematics.
Quantum Unique Ergodicity for Powerful Level via Shifted Convolution Sum
Explore advanced mathematical concepts in number theory, focusing on QUE for powerful levels using shifted convolution sum techniques.
Hypergeometric Functions, Galois Representations, and Modular Forms
Explore connections between hypergeometric functions, Galois representations, and modular forms in advanced number theory and algebraic geometry.
Moments of Families of Elliptic Curves
Explore new developments in higher moment sums of elliptic curve families, their connections to modular forms, and applications to rigid Calabi-Yau threefolds and intermediate Jacobians.
Constructing Polylogarithms on Higher-Genus Riemann Surfaces
Generalization of elliptic polylogarithms to higher-genus Riemann surfaces, exploring homotopy-invariant iterated integrals, modular tensors, and connections to Enriquez-Zerbini polylogarithms and Fay identities.
Modular Regulators and Multiple Modular Values
Explore recent advancements in computing Goncharov regulator integrals for K_4 classes on modular curves, relating them to multiple modular values and single L-values of modular forms.
Counting Rational Points on Modular Curves of Genus 0 Over Number Fields by Peter Bruin
Explore techniques for counting rational points on modular curves of genus 0 over number fields, advancing understanding in arithmetic geometry and algebraic number theory.
Modularity and Monodromy
Explore the intricate relationship between modularity and monodromy in mathematics, delving into advanced concepts and their applications in number theory and algebraic geometry.
A Summary of Methods for Solving Differential Equations Involving Automorphic Forms
Explore advanced techniques for solving differential equations with automorphic forms, enhancing mathematical problem-solving skills in complex analysis and number theory.