TQFTs and the Renaissance of the Algebraic Topology of Manifolds
Explore the resurgence of algebraic topology in manifold studies, focusing on Topological Quantum Field Theories and their impact on modern mathematical research.
An Invitation to Graph Braid Groups
Explore graph braid groups, from basic concepts to advanced topics like homology and polynomial growth, with insights on various graph types and their properties.
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.
Introduction to Lagrangian Fillings of Legendrian Links - Part 1
Explore Lagrangian fillings of Legendrian links, their construction, and techniques to distinguish Hamiltonian isotopy classes. Delve into the connection with cluster algebras and key proof elements.
Poincaré Duality Fibrations and Graph Complexes
Explore Poincaré duality fibrations and graph complexes in advanced mathematics. Gain insights from Alexander Berglund's conference talk at CIRM's thematic meeting on higher algebra, geometry, and topology.
Ample Groupoids, Topological Full Groups, Algebraic K-Theory Spectra and Infinite Loop Spaces
Explore ample groupoids, topological full groups, and their connections to algebraic K-theory spectra and infinite loop spaces in this advanced mathematics seminar.
Cluster Duality and Non-Holomorphic Spectral Curves
Explore cluster duality, geometric interpretations of tropical points, and their connections to local systems on curves through graphs, Lagrangian coverings, and affine group-valued local systems.
Enumerative Geometry Through Sheaves
Explore enumerative geometry, sheaf counting, and their applications in algebraic geometry. Discover new approaches to generalized Donaldson-Thomas invariants on Calabi-Yau threefolds.
Real Loci of Non-Real Varieties - Mathematics Department Colloquium
Explore cooriented submanifolds in real algebraic geometry, focusing on their properties, intersections, and linking numbers. Gain insights into the geometry of pencils and real projective spaces.
How Many Quivers Does a Knot Have? - Knots-Quivers Correspondence and Symmetries
Explore knots-quivers correspondence, equivalent quivers classification, and implications for symmetric quiver invariants in knot theory.
Computing Differentials in the Adams Spectral Sequence and the Last Kervaire Invariant Problem
Explore advanced methods for computing differentials in the Adams spectral sequence and uncover recent progress on the Last Kervaire Invariant Problem in dimension 126.
Knots and Categories
Explore connections between knot theory and category theory, delving into mathematical concepts and their interrelationships in topology and algebra.
Correspondences, K-Theory and Homology for Étale Groupoids
Explore advanced mathematical concepts in étale groupoids, focusing on correspondences, K-theory, and homology. Gain insights from expert Alistair Miller in this specialized seminar.
Modeling Shapes and Fields - A Sheaf Theoretic Perspective
Explore topological transforms for shape and field modeling, including Euler Characteristic and Lifted Euler Characteristic. Learn about sheaf theory in shape space construction and its applications in statistical analysis.
Homology of Graphs and Hypergraphs
Explore topological structures of graphs and hypergraphs, including recent findings on homology and persistent homology, with applications in combinatorial and metric space analysis.
Laying Foundations for Very Large Scale Comparative Genomics
Explore foundations for large-scale comparative genomics, focusing on techniques and challenges in analyzing vast genomic datasets across species.
Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules
Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.
Gauge Fields and Categorification of Quantum Group Invariants of 3-Manifolds
Explore new link and 3-manifold invariants associated with Verma modules of U_q(sl_N), their properties, and potential categorification in 3-manifold homology.