The Weil Conjectures and A1-homotopy Theory
Dive into the Weil Conjectures and A1-homotopy theory, exploring connections between algebraic topology and finite field equations in this mathematical colloquium.
Topological Data Analysis of Collective Motion
Explore topological data analysis for collective motion in nature, examining bird flocks, fish schools, and insect swarms through innovative mathematical models and simulations.
The External Activity Complex of a Pair of Matroids
Delve into advanced matroid theory, exploring external activity complexes and their relationship to Schubert varieties, with applications to tautological classes and Speyer's matroid invariant.
Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.
Nonrational Toric Geometry II - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explore complex toric quasifolds, their structure, and relation to rational toric varieties. Learn about extending constructions to nonsimple convex polytopes in symplectic and complex settings.
Statistical Invariance of Betti Numbers in the Thermodynamic Regime
Explore statistical invariance of Betti numbers in random topology, examining conditions for topological inference through parametric statistics lens. Investigates asymptotic behavior and group invariance concepts.
A Limit Theorem for Betti Numbers of Random Simplicial Complexes
Explore asymptotic behavior of Betti numbers in homogeneous and spatially independent random simplicial complexes, extending previous work on Linial-Meshulam complexes using local weak convergence.
Configuration Spaces of Hard Squares
Exploring topology of configuration spaces with hard squares, focusing on Betti numbers' growth rate in confined regions. New insights into complex geometric arrangements.
Torsion Homology Growth and Related Topics
Explore torsion homology growth in compact CW complexes, examining Betti number growth in finite covers and connections to amenable category and minimal volume entropy.
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.
Fake Projective Planes: Properties and Recent Progress
Explore fake projective planes: complex surfaces with unique properties, their construction via uniformization, and recent advancements in understanding their algebraic and geometric characteristics.
What Are the Betti Numbers of a Manifold? - Don Zagier - 2017
Explore the concept of Betti numbers in manifolds with renowned mathematician Don Zagier, delving into their significance and applications in topology and geometry.
Strange Random Topology of the Circle
Explore the intriguing behavior of "topological noise" in random Cech complexes constructed from the circle, revealing unexpected homotopy equivalences and higher Betti numbers in specific filtration radii intervals.
Delta Complexes, Betti Numbers, and Torsion in Algebraic Topology
Explore homology groups of torus and projective plane using delta-complexes. Learn about Betti numbers and torsion in algebraic topology, with practical computations and insights into fundamental concepts.
Lower Dimensional Betti Numbers of Homogeneous Spaces of Lie Groups
Exploration of lower dimensional Betti numbers in homogeneous spaces of Lie groups, discussing mathematical techniques and applications in algebraic topology and differential geometry.
The Asymptotics of Betti Numbers in Preferential Attachment Clique Complexes
Explore the higher-order connectivity of preferential attachment networks through Betti numbers, examining growth rates and asymptotic behavior in this advanced mathematical analysis.
Random Algebraic Geometry - Lecture 1
Explore random algebraic geometry concepts in this advanced mathematics lecture, delving into complex theoretical foundations and applications.
Random Algebraic Geometry - Lecture 4
Explore advanced concepts in random algebraic geometry, focusing on key theories and applications in this fourth lecture of the series.
Random Algebraic Geometry - Lecture 2
Explore advanced concepts in random algebraic geometry, focusing on theoretical foundations and practical applications in mathematical research.
Random Algebraic Geometry - Lecture 3
Explore advanced concepts in random algebraic geometry, focusing on cutting-edge research and theoretical developments in this mathematical field.
Subgroups of Hyperbolic Groups, Finiteness Properties and Complex Hyperbolic Lattices
Explore finiteness properties of subgroups in hyperbolic groups and complex hyperbolic lattices, focusing on cocompact arithmetic lattices with positive first Betti number.