Macroscopic Scalar Curvature and Local Collapsing
Exploration of macroscopic scalar curvature in Riemannian geometry, focusing on volume bounds for manifolds with hyperbolic metrics and collapsing techniques in metric geometry.
Michael Farber - Topological Complexity of Spherical Bundles
Explore parametrized motion planning algorithms and the topological complexity of sphere bundles, examining characteristic classes and specific examples in applied algebraic topology.
Wasserstein Distances, Geodesics and Barycenters of Merge Trees
Explore computational frameworks for merge trees, including Wasserstein distances, geodesics, and barycenters. Learn efficient algorithms and applications in visualization, feature tracking, and ensemble clustering.
Persistent Homotopy Groups of Metric Spaces
Exploring persistent homotopy groups of metric spaces, blending topology and geometry to capture dataset features beyond persistent homology, with applications and stability properties.
Linear Obstacles in Linear Systems and Ways to Avoid Them
Explore topology in control theory, focusing on obstacle-avoiding paths and cohomology rings using homotopy limits. Gain insights into theoretical computer science applications.
Parametrized Topological Complexity of Hyperplane Arrangement Bundles
Exploring parametrized motion planning in hyperplane arrangement bundles, focusing on topological complexity under supersolvability conditions. Joint work with Dan Cohen.
Robert Adler Interviewed by Omer Bobrowski
Insightful interview exploring Robert Adler's contributions to applied algebraic topology, offering valuable perspectives on the field's development and future directions.
The Gromov-Hausdorff Distance Between Spheres
Explore upper and lower bounds for Gromov-Hausdorff distances between spheres, including optimal correspondences and topological concepts related to the Borsuk-Ulam theorem.
Extracting Persistence Features with Hierarchical Stabilisation
Explore hierarchical stabilisation for extracting stable invariants from persistence modules, focusing on the stable rank and its applications in data analysis and classification tasks.
Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature
Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.
Enabling a Machine to Sense Geometry
Explore how to construct a reach space of kernels on persistent modules, enabling machine intelligence to sense geometry, with applications in synthetic and real scenarios.
Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions
Explore signed barcodes: a new visual representation for multi-parameter persistence modules, encoding rank invariants and enhancing exploration of complex topological structures.
Discrete Morse Theory Meets Multi-Parameter Persistence
Exploring connections between discrete Morse theory and multiparameter persistence in topological data analysis, focusing on critical cells, fibered rank invariant, and computational efficiency.
The Intrinsic Volumes of a Space Filling Diagram and Their Derivatives
Explore intrinsic volumes in molecular dynamics, focusing on space-filling diagrams and their derivatives. Learn formulas for weighted volumes and curvatures in Alpha shape representations.
Instantons, Suspension, and Surgery
Explore advanced concepts in gauge theory, including instantons, suspension, and surgery techniques for manifolds with boundary components and their applications in cobordism maps.
Instantons, Suspension, and Surgery - Part 1
Explore Dehn surgery number in 3-manifolds, using mod 2 instanton homology and Froyshov's q_3 invariant to prove existence of integer homology 3-spheres with arbitrarily large surgery numbers.
Smooth Closing Lemma for Area-Preserving Diffeomorphisms of Surfaces
Explore the smooth closing lemma for area-preserving diffeomorphisms on surfaces, featuring a proof based on Weyl formula and Seiberg-Witten Floer homology. Joint work with Cristofaro-Gardiner and Prasad.
Fillable Contact Structures From Positive Surgery
Exploring conditions for fillable contact structures from positive surgery on Legendrian knots, with applications to topological consequences and lens space surgeries.
PL-Surfaces in Homology 4-Balls
Exploration of PL-surfaces in homology 4-balls, discussing minimum genus of PL surfaces and their bounds in homology balls using Heegaard Floer homology. Joint research findings presented.
Tight Contact Structures on Hyperbolic 3-Manifolds - IMSA Topology Seminar
Exploring tight contact structures on hyperbolic 3-manifolds via Dehn surgery on genus one fibered knots in lens spaces, with insights on classification and Stein fillability.
Quasipositive Surfaces and Decomposable Lagrangians in Topology - IMSA Seminar
Explore Legendrian links, knot Floer homology, and Lagrangian link cobordisms in topology. Learn about braiding techniques and the comultiplication property in this advanced mathematical seminar.