Leray Functor in Connection Matrices
Explore the Leray Functor's role in connection matrices, delving into advanced mathematical concepts and their applications in topology and algebra.
Persistence in Functional Topology
Explore functional topology's evolution, connecting persistent homology to critical point theory and calculus of variations. Gain insights into Morse's theory and its application to minimal surfaces.
Generalized Morse Theory of Distance Functions to Surfaces for Persistent Homology
Unifying distance fields, persistent homology, and Morse theory to quantify complex shape textures, with applications in characterizing vascular structures in leukemia samples.
Barcodes for the Topological Analysis of Gradient-Like Vector Fields
Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.
Henry Adams and Enrique Alvarado - An Introduction to Morse Theory
Explore Morse theory's applications in topology, including CW complexes, key theorems, and simplification techniques, with real-world examples in material science.
An Upper Bound on the Topological Complexity of Discriminantal Varieties
Explore upper bounds on topological complexity of discriminantal varieties, with applications to configuration spaces. Combines Morse theory, equivariant homotopy theory, and complex geometry.
Moduli Spaces of Morse Functions for Persistence
Exploring Morse functions on surfaces, focusing on decomposition, elementary moves, and embeddings. Insights into persistence barcodes and the inverse problem through nesting posets of level sets.
Vidit Nanda - Morse Theory for Local Coefficients
Explore Morse theory with local coefficients, covering cohomogeneous complexes, wave graphs, and isomorphisms. Delve into advanced topics and theorems in algebraic topology.
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.
A New Model for Stable Homotopy - Extending Pontryagin-Thom Construction
Explore a new model for stable homotopy, extending the Pontryagin-Thom construction to the entire stable homotopy category through the lens of bordism theory.
On the Fukaya-Morse A-infinity Category
Explore the intricacies of Fukaya-Morse A-infinity category with Pavel Mnev, delving into advanced mathematical concepts and their applications in topology and geometry.
Quantized Integrable Systems, Normal Forms, and Variation of Hodge Structures
Explore quantum Hamiltonians' Birkhoff normal forms, linking quantized integrable systems to Hodge structure variations in complex symplectic geometry.
Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology
Explore bordered Floer homology, dg-modules, and the topological interpretation of module homomorphism composition in Heegaard Floer complexes. Gain insights into cobordism maps and their consequences.
An Update on SYZ Mirror Symmetry and Family Floer Theory
Explore Strominger-Yau-Zaslow approach to homological mirror symmetry, focusing on Lagrangian torus fibrations and Fukaya-Floer algebra construction for mirror symmetry in complex geometry.
Random Algebraic Geometry - Lecture 3
Explore advanced concepts in random algebraic geometry, focusing on cutting-edge research and theoretical developments in this mathematical field.
Parametric Geometric Inequalities and Weyl Law for the Volume Spectrum
Explore parametric geometric inequalities and their connection to the volume spectrum, examining proofs, applications, and implications for minimal surfaces and stationary geodesic nets.
A Morse Model for Stable Homotopy - ICBS 2024
Explore stable homotopy groups, framed bordism, and Morse theory in topological spaces. Gain insights into Floer homotopy foundations and the Pontryagin-Thom construction.
Morse Type Theories with Differential Graded Coefficients - Workshop on Conservative Dynamics and Symplectic Geometry
Explore Morse type theories with differential graded coefficients in this advanced mathematics lecture. Gain insights into Conservative Dynamics and Symplectic Geometry from expert Mihai Damian.
Moduli of G-bundles as a Quotient by the Gauge Group - Talk 6
Delve into complex geometric theory of holomorphic G-bundles, exploring connections, gauge transformations, and symplectic quotients through the Kempf-Ness Theorem and Yang-Mills functional analysis.
Computation of Reeb Graphs in a Semi-Algebraic Setting
Explore semi-algebraic geometry in applied topology, focusing on Reeb graphs and spaces. Learn about an efficient algorithm for computing semi-algebraic descriptions of Reeb graphs.
Low Dimensional Topology and Circle-valued Morse Functions
Explore singular fibrations in knot exteriors and their extensions over handlebodies, connecting handle-ribbon knots to circular Morse functions in low-dimensional topology.