Point-Counting and the Zilber-Pink Conjecture - Lecture 2
Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.
Point-Counting and the Zilber-Pink Conjecture - Lecture 1
Explore the Zilber-Pink conjecture, its relation to classical conjectures, and point-counting strategies for proving cases, focusing on curves in modular curve powers.
Stable Homotopy Groups, Higher Algebra, and the Telescope Conjecture
Explore stable homotopy groups, spectra, and their applications in topology and geometry. Gain insights into fundamental concepts shaping modern algebraic topology and related fields.
Kummer Extensions: Applications to Generalized Cross-Ratios and Functions on Hilbert Schemes
Explore Kummer extensions in geometry and arithmetic, including generalized cross-ratios and functions on Hilbert schemes. Gain insights into advanced algebraic geometry concepts.
Plectic Cohomology of Mixed Shimura Varieties and Stacks
Explore joint work on plectic cohomology of mixed Shimura varieties and stacks with Tony Scholl from the University of Cambridge.
Mathematical Grand Unification
Explore the concept of mathematical grand unification through a thought-provoking lecture by Bartosz Naskręcki, delving into conjectures and potential connections across mathematical fields.
Isolated and Parameterized Points on Algebraic Curves
Explore isolated and parameterized points on algebraic curves, examining their behavior in families and implications for elliptic curve arithmetic. Gain insights into curve geometry and its connection to arithmetic properties.
Special Points on Moduli Spaces
Explore the distribution of special points in moduli spaces, examining algebraic and analytic aspects, including the Andre-Oort conjecture and p-adic distribution.
The Langlands Project - Connecting Automorphic Forms and Number Theory
Explore the Langlands project's deep connection between automorphic forms and arithmetic, tracing its roots and current challenges in mathematics.
Rigidity and Uniformity in Algebraic Dynamics
Explore connections between algebraic dynamics and arithmetic geometry, focusing on preperiodic points and torsion points in abelian varieties. Learn about recent breakthroughs in uniform bounds and conjectures.
New Geometric Structures in the Langlands Program
Explore new geometric structures in the Langlands program, including the moduli space of G-bundles on the curve, and their role in constructing the semi-simple local Langlands correspondence.
Average Heights of Abelian Varieties with Complex Multiplication
Explore the arithmetic properties of abelian varieties with complex multiplication, focusing on Colmez's conjecture and its implications for periods and L-functions.
Heights of Algebraic Cycles and Special Values of L-Series - ICBS 2024
Explore heights of algebraic cycles and their connections to L-series special values, focusing on CM points and Gross-Schoen cycles on elliptic curves.
What Does Machine Learning Have to Offer Mathematics? - Theoretically Speaking
Explore the intersection of machine learning and mathematics, focusing on novel techniques in combinatorics and potential impacts on mathematical practice.
Quasi Jacobi Forms and Moduli Space of Enhanced Elliptic Curves - GADEPs Conference III
Explore quasi Jacobi forms and moduli space of enhanced elliptic curves in this advanced mathematics lecture by Jin Cao, part of the GADEPs conference on Noether-Lefschetz and Hodge loci.
Is the Universe Geometric or Algebraic? by Minhyong Kim
Explore the interplay between geometry and algebra in understanding the universe, from ancient concepts to modern physics, with insights on perception, reality, and mathematical foundations.
Towards a Formulation of the Birch and Swinnerton-Dyer Conjecture for Abelian Schemes Over Varieties Over Finite Fields
Delve into advanced number theory concepts exploring the Birch and Swinnerton-Dyer conjecture's formulation for abelian schemes over finite field varieties, presented by mathematician Amilcar Pacheco.
On Lehmer's Problem and Hyperbolic Geometry
Delve into the fascinating connection between Lehmer's problem and hyperbolic geometry through an advanced mathematical exploration of number theory concepts and geometric principles.
Counting Points on Bun_G - Talk 35
Delve into advanced algebraic geometry as Matthew Emerton explores G-L trace formula for Bun_G, providing a detailed proof of Conjecture 8 from Lurie's earlier lectures.
On the Prismatization of the Field with One Element
Delve into advanced mathematical concepts of prismatic cohomology and its relationship to the theoretical field with one element, exploring geometric and arithmetic implications.
Heuristics for the Arithmetic of Elliptic Curves and Abelian Varieties
Explore probabilistic models for elliptic curve arithmetic, examining theoretical evidence and predictions for higher-dimensional abelian varieties.