Nonabelian Mixed Hodge Structures
Explore nonabelian mixed Hodge structures, their relation to rational homotopy, and applications to character varieties and schematic homotopy types. Examine weights from noncompact bases and parabolic structures.
Quantitative Ell-Adic Sheaf Theory
Explore quantitative bounds for étale cohomology groups and their applications in algebraic geometry. Learn about complexity measures for sheaves and how they interact with various functors.
Non-free Curves and Geometric Manin's Conjecture - Lecture
Explore non-free curves on varieties, their classification, and implications for Geometric Manin's Conjecture in Fano fibrations. Gain insights into algebraic geometry and number theory.
A Finiteness Theorem for Gromov-Hyperbolic Groups
Explore a finiteness theorem for Gromov-hyperbolic groups, delving into δ-hyperbolic, torsion-free, non-cyclic marked groups with bounded entropy. Gain insights into the proof and key concepts.
Conjugate Points and the MC Criterion in Volume-Preserving Diffeomorphisms - Lecture
Explore conjugate points on volume-preserving diffeomorphisms, focusing on the MC criterion and its applications in fluid dynamics and Riemannian geometry.
The Formulation of the Navier-Stokes Equations on Riemannian Manifolds
Explore advanced formulations of Navier-Stokes equations on Riemannian manifolds, focusing on Ebin and Marsden's approach and recent developments in this complex field of fluid dynamics.
On the Applications of Topology
Explore topological methods for analyzing complex data sets, focusing on persistent homology and mapper, with applications in computer vision, biology, and medicine.
Symplectic Capacities, Viterbo Isoperimetric Conjecture, and Contact Manifolds with Closed Reeb Orbits
Explore symplectic capacities, Viterbo's conjecture, and their impact on symplectic geometry. Gain insights into convex geometry applications and closed Reeb orbits in contact manifolds.
Why and How Can a Line be Moved? - Examining Euclid's Elements
Explore ancient mathematicians' efforts to improve proofs of the side-angle-side congruence theorem in Euclid's Elements, examining linguistic peculiarities and textual variations in related propositions.
Comparing Oresme's Curvitas with Riemann's Curvature
Explore the historical evolution of curvature concepts from Oresme's 14th-century insights to Riemann's geometric definitions, examining their mathematical and philosophical implications.
The Congruent Number Problem
Explore the ancient congruent number problem and its connection to the Birch and Swinnerton-Dyer conjecture, one of mathematics' most challenging millennium problems.
The Conundrum of the Fourth Postulate - Euclid's Geometry Revisited
Explore the historical and philosophical aspects of Euclid's fourth postulate, examining its provability within a constructive setting and offering a novel perspective on this classical mathematical problem.
Geometric Laplacians on Self-Conformal Fractal Curves in the Plane
Explore geometric Laplacians on self-conformal fractal curves, examining heat kernels, eigenvalue asymptotics, and their relation to fractal geometry. Delve into construction methods and applications in complex analysis.
A Possible Way to Read and Interpret Euclid's Elements
Explore a novel approach to reading Euclid's Elements, focusing on fundamental theorems in Books I and II as a guide to understanding Euclidean geometry and its philosophical implications.
Geometric Inequalities Between Intrinsic and Extrinsic Curvature Invariants
Explore geometric inequalities between intrinsic and extrinsic curvature invariants in Riemannian manifolds, focusing on Nash's Theorem and recent developments in the field.
Formalization of Infinity Category Theory
Explore ∞-category theory's formalization, unifying mathematics, computer science, and physics. Learn synthetic reasoning and the Yoneda Lemma in this advanced mathematical seminar.
Topology in 1930s America - A Tale of Two Camps
Explore the rivalry between point-set and combinatorial topology camps in 1930s America, examining their approaches, key figures, and impact on the mathematical research community.
From HoTT to HOTT - Exploring Homotopy Type Theory
Explore the evolution from Homotopy Type Theory (HoTT) to Higher-Order Type Theory (HOTT) in this insightful lecture by Michael Shulman.
Barry Mazur and the Infinite Cheese of Knowledge - A Mathematical Documentary
Explore the life and insights of influential mathematician Barry Mazur in this intimate documentary, capturing his wit, profound approach to mathematics, and enduring impact on the field.
Logarithmic Sobolev Inequalities on Homogeneous Spaces
Explore logarithmic Sobolev inequalities on homogeneous spaces with sub-Riemannian structures. Discover how constants depend on Lie group geometry and remain independent of dimension in certain cases.
Quantum Periods for Complements
Explore quantum periods for complements, focusing on polynomial-defined spectral curves and quantization of polynomial algebras. Gain insights into cohomological descriptions of WKB series.