Homological Mirror Symmetry - Homological Link Invariants from Floer Theory
Explore a groundbreaking connection between homological mirror symmetry and representation theory, solving the knot categorification problem and generalizing Heegard-Floer theory to simple Lie superalgebras.
Fundamentals of Lie Groupoids and Algebroids - Lecture Series
Introducción a la teoría de Lie de grupoides y algebroides, explorando sus definiciones, propiedades y aplicaciones en diversas estructuras geométricas.
Danny Ruberman- Diffeomorphism Groups of 4-Manifolds
Exploring unique 4-dimensional phenomena: infinite families of homeomorphic but non-diffeomorphic manifolds, and exotic behavior in diffeomorphism and homeomorphism groups.
The Geometric Andre-Grothendieck Period Conjecture
Explore complex algebraic varieties, period integrals, and the Ax-Schanuel conjecture. Delve into transcendence theory of period maps and the Andre-Grothendieck period conjecture's functional version.
Hyperbolicity in Presence of a Large Local System
Explore hyperbolicity in complex algebraic varieties with Yohan Brunebarbe. Learn about Green-Griffiths and Lang conjectures, and their validity for varieties with large complex local systems.
Hyperbolicity of Algebraic Varieties via Fundamental Groups
Explore hyperbolicity of algebraic varieties through fundamental groups, examining linear representations and their implications for complex quasi-projective varieties and the Green-Griffiths-Lang conjecture.
Twistor Space for Moduli of Local Systems on Open Curves
Explore Deligne-Hitchin twistor spaces for moduli of framed local systems on open curves, examining harmonic bundles, preferred sections, and mixed twistor structures in moduli space geometry.
Semi-Affineness of Wrapped Invariants on Affine Log Calabi-Yau Varieties
Explore mirror symmetry in affine log Calabi-Yau varieties, examining finiteness properties of Floer theoretic invariants and their implications for categorical crepant resolutions.
Fixed Loci of Anti-Symplectic Involutions
Explore geometric constructions linking Fano manifolds and hyperkähler manifolds, focusing on reversing the process to recover Fano manifolds from hyperkähler structures.
Birational Calabi-Yau's and Floer Cohomology
Explore the relationship between Gromov-Witten invariants of birational Calabi-Yau manifolds using Hamiltonian Floer theory, including the generalized McKay correspondence and small quantum products.
Functional Inequalities and Improvements: Stability - Part 1
Explore functional inequalities, their applications, and recent developments in stability theory. Learn strategies for optimizing constants and functions in various mathematical fields.
Laurent Saloff-Coste - Breaking Heat Kernel Estimates Into Pieces
Breaking heat kernel estimates on Riemannian manifolds by analyzing pieces separately and reconstructing the whole. Explores Brownian motion within segments and transitions between them.
Mean Curvature and Variational Theory
Explores recent developments in prescribing mean curvature equations, focusing on existence theory, min-max theory for CMC/PMC surfaces, and Morse theory for area functional. Includes solution to Multiplicity One Conjecture.
Oscar Randal-Williams: Diffeomorphisms of Discs
Explore the mathematical intricacies of diffeomorphisms on discs with Oscar Randal-Williams in this insightful 45-minute lecture from the International Mathematical Union.
Kähler Manifolds with Curvature Bounded Below
Explore Kähler manifolds with curvature bounded below, covering Yau's uniformization conjecture, compactification of manifolds, and Gromov-Hausdorff limits in this advanced mathematical survey.
Aravind Asok, Jean Fasel - Vector Bundles on Algebraic Varieties
Explore vector bundles on algebraic varieties with experts Aravind Asok and Jean Fasel, delving into advanced mathematical concepts and their applications in algebraic geometry.
Metric Reconstruction via Optimal Transport
Explores metric reconstruction using optimal transport theory, introducing Vietoris-Rips thickening to recover metric information from point samples in metric spaces, with applications to Riemannian manifolds.
Entropy in Mean Curvature Flow
Explore entropy in hypersurfaces and its role in mean curvature flow. Survey recent progress on conjectures about sharp lower bounds and extensions in geometric complexity.
Stochastic Ricci Flow on Surfaces
Explores stochastic Ricci flow in 2D, introducing its formulation, symmetry properties, and construction of weak solutions. Discusses implications for compact surfaces and open questions.
Intrinsic Volumes on Pseudo-Riemannian Manifolds
Explore intrinsic volumes in pseudo-Riemannian geometry, covering Hadwiger's theorem, Weyl's principle, and Crofton formulas. Learn about recent developments in this advanced mathematical field.
The Restriction Problem and the Polynomial Method - Lecture IV
Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.