Hodge Theory for the Conservativity Conjecture
Explore Hodge theory's application to the conservativity conjecture in algebraic geometry and number theory with Joseph Ayoub's insightful lecture.
The Lonely Runner Conjecture - Simulation and Explanation
Explore the intriguing Lonely Runner Conjecture through simulation, understanding its simplicity and the challenge of proving it conclusively.
Magic Squares of Squares - Are Probably Impossible
Explore the fascinating world of magic squares and their mathematical impossibility through surprising insights and advanced mathematical concepts.
Some Vanishing Results for Rational Completed Cohomology of Shimura Varieties
Explore p-adically completed cohomology in Shimura varieties, focusing on vanishing results for regular infinitesimal characters using Bhatt's Kodaira vanishing and translation functors.
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.
Why 1 Is Never Prime, and Sometimes Neither Are Some of Your Favorites
Explore the concept of prime numbers, focusing on why 1 is not considered prime and examining other surprising non-prime numbers in mathematics.
On the Brumer-Stark Conjecture and Refinements
Explore recent advancements in the Brumer-Stark Conjecture, its connections to explicit class field theory, and the proof's completion, including implications for the Equivariant Tamagawa Number Conjecture.
Computational Aspects of Nonabelian Chabauty - Lecture 1
Explore computational techniques for Nonabelian Chabauty methods in arithmetic geometry, focusing on rational points on modular curves and advanced number theory concepts.
Generalised Eigenvalues via Flach Classes
Explore the connection between generalized eigenvalues for mod p cusp forms and Galois cohomology classes, focusing on Flach's geometric construction and its implications for Hecke algebra actions.
The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 3
Exploring advanced techniques in arithmetic geometry for analyzing rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its practical applications.
Classical and Quadratic Chabauty - Lecture 3
Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.
The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 2
Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.
The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 1
Explore advanced techniques for studying rational points on modular curves, focusing on the Chabauty-Coleman-Kim method and its theoretical and practical applications in arithmetic geometry.
The Chabauty-Coleman-Kim Method: From Theory to Practice - Lecture 4
Explore advanced techniques in arithmetic geometry, focusing on the Chabauty-Coleman-Kim method for studying rational points on modular curves. Gain insights into theoretical foundations and practical applications.
Classical and Quadratic Chabauty - Lecture 3
Explore advanced techniques in arithmetic geometry: Classical and Quadratic Chabauty methods for studying rational points on modular curves, with applications to elliptic curves.
Duality in P-adic Pro-etale Cohomology of Analytic Curves
Explore duality theorems in p-adic pro-etale cohomology of analytic curves, delving into advanced mathematical concepts and recent research findings in this specialized field.
The Finite Slope Part of Overconvergent Cohomology & Coherent Sheaves on Spaces of
Explores overconvergent cohomology, eigenvarieties, and coherent sheaves in p-adic automorphic forms. Discusses a conjecture on computing coherent sheaves using Galois representation stacks and its relation to p-adic Langlands program.
Tony Feng- A New Approach to Breuil-Mezard Cycles
Explore a novel local and group-theoretic approach to the Breuil-Mezard Conjecture, connecting it to quantum groups and homological mirror symmetry in algebraic number theory.
The Weight Part of Serre's Conjecture and the Emerton-Gee Stack
Explore the Breuil-Mezard conjecture's impact on local deformation rings and its connection to Serre's conjecture, focusing on recent advancements in moduli stack theory and p-adic Galois representations.
Categorical Local Langlands for GL_n - The Irreducible Case with Integral Coefficients
Explore the Fargues-Scholze conjecture for GL_n, focusing on irreducible parameters with integral coefficients. Learn about category localizations and L-packets in this advanced mathematical lecture.
Strong Bounds for 3-Progressions
Explore advanced additive combinatorics, focusing on 3-term arithmetic progressions in integer sets. Learn about recent breakthroughs and their implications for number theory.