An Introduction to Polyhedral Products
Explore the foundations of polyhedral products in this graduate-level lecture, covering key concepts and applications in toric topology and geometry.
Some Reflections on the Moduli Spaces of Flat Connections with Involutions
Explore moduli spaces of flat connections with involutions, examining their geometric properties and mathematical implications in this advanced mathematical lecture.
Symplectic Diffeology
Explore symplectic diffeology, a mathematical concept blending symplectic geometry and diffeology, with expert Patrick Iglesias-Zemmour from Hebrew University of Jerusalem.
Lie Groupoids Determined by Their Orbit Spaces
Explore how Lie groupoids are uniquely determined by their orbit spaces, delving into advanced concepts in Hamiltonian geometry and mathematical physics.
Dynamical Systems Arising from the Classification of Geometric Structures
Explore dynamical systems in geometric structure classification, delving into mathematical concepts and their applications in topology and geometry.
Topology and Dynamics of Higher-Order Networks - Lecture 1: General Introduction to Algebraic Topology on Networks and Simplicial Complexes
Explore algebraic topology in networks and simplicial complexes, focusing on homology and boundary operators. Gain insights into higher-order network structures and their impact on complex systems.
Topology and Dynamics of Higher-Order Networks - Lecture 3: Topological Dirac Equation and Discrete Network Geometry
Explore topological Dirac equations and discrete network geometry in higher-order networks. Delve into metric cohomology and its applications in mathematical physics and dynamical systems.
Topology and Dynamics of Higher-Order Networks - Lecture 2: Introduction to Algebraic Topology on Networks and Simplicial Complexes
Explore algebraic topology on networks and simplicial complexes, focusing on Hodge Laplacians and Dirac operators in higher-order networks. Gain insights into topological signals and their applications.
Topology and Dynamics of Higher-Order Networks - Information Theory of Network Geometry and Gauge Fields - Lecture 4
Explore information theory of network geometry and gauge fields in higher-order networks. Delve into topological signals, discrete topology, and emerging dynamical states in complex systems.
Unification of Topological Invariants and Topological Markers
Explore topological invariants and markers in quantum materials, unifying concepts through wrapping numbers and quantum metrics. Apply to 1D and 2D systems.
Commutative Algebra and Algebraic Geometry - 15th ALGA Meeting
Explore mirror symmetry, curve counting, and Landau-Ginzburg models in algebraic geometry. Delve into advanced mathematical concepts with expert insights from Tyler Kelly's ALGA conference talk.
Scalar Quantum Fields on 4-Dimensional Noncommutative Geometry
Explore milestones in renormalisable and solvable scalar QFT models on 4D noncommutative geometry, reflecting on a 25-year collaboration.
Noncommutative U(1) Gauge Theory in the Semiclassical Limit
Explore U(1) gauge theory on Poisson manifolds as a semiclassical limit of noncommutative spacetimes. Examine gauge potentials, transformations, and symplectic realizations in Poisson electrodynamics.
Dual of the Dual Formula for Distance in Noncommutative Geometry
Explore Connes's spectral distance and its dual formula in noncommutative geometry, extending Kantorovich's and Beckmann's concepts from optimal transport theory.
Tamed Spaces: Dirichlet Spaces with Distribution-Valued Ricci Bounds
Explore Dirichlet spaces with distribution-valued Ricci bounds, focusing on tamed spaces theory and singular perturbations of Dirichlet form. Investigate integrated Bochner inequality and Bakry-Émery condition generalizations.
Differentiating in a Non-Differentiable Environment
Explore differentiation in non-differentiable spaces, extending beyond traditional smooth manifolds to spaces with Ricci curvature bounds. Gain insights into advanced mathematical concepts.
On the Regularity Implied by the Assumptions of Geometry
Explore the theory of Regularity Transformation equations and their impact on non-regular spacetime geometry, including applications in General Relativity and Einstein-Euler equations.
Abstract Null Geometry, the Constraint Tensor and Applications
Explore abstract null geometry, constraint tensors, and their applications in non-regular spacetime, degenerate horizons, and Einstein field equations.
A Lorentzian Analog for Hausdorff Dimension and Measure
Explore a novel approach to geometric dimension in Lorentzian spaces, comparing it to Hausdorff dimension and examining applications in spacetime analysis and synthetic curvature bounds.
Lorentzian Functors and Closures of Relevant Subsets of Lorentzian Gromov-Hausdorff Space
Explore recent advances in Lorentzian length spaces theory, including stability of properties, denseness of causal spacetimes, and geometric conditions for Radon measures in Lorentzian Gromov-Hausdorff space.
Synthetic Time-like Ricci Curvature Lower Bounds: The Isoperimetric Inequality
Explore synthetic timelike Ricci curvature lower bounds and their implications for isoperimetric inequality in Lorentzian synthetic spaces.