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.
Higgs Bundles and the Topology of Higher Teichmüller Spaces
Explore advanced mathematical concepts in topology, focusing on Higgs bundles and their role in understanding higher Teichmüller spaces for non-compact real Lie groups.
Closure of Orbits of the Pure Mapping Class Group on the Character
Explore the closure of orbits in pure mapping class groups on character varieties, delving into Zariski dense subgroups and their applications in geometry and number theory.
Components of Higgs Bundle Moduli Spaces - A Legacy of Hitchin's Ideas
Explore Higgs bundle moduli spaces, their components, and the lasting impact of Hitchin's groundbreaking ideas in this mathematical lecture by Steven Bradlow.
Higgs Bundles, Convex Cocompact Subgroups of SU(1,n), and Slodowy Slices
Explore Higgs bundles, SU(1,n) subgroups, and Slodowy slices. Discover connections between stable Higgs bundles and holonomy groups, focusing on SU(1,n) representations and complex hyperbolic manifolds.
Positivity and Higher Teichmüller Spaces
Explore positivity in Lie groups, positive representations, and their connected components. Delve into Hitchin's Teichmüller components and related open questions in higher Teichmüller theory.
Instantaneous Dimension of Metric Spaces via Spread and Magnitude
Explore how spaces exhibit different dimensions at various scales using spread and magnitude concepts. Learn to quantify this phenomenon and its connections to diverse mathematical areas.
Tangent Groupoid in Noncommutative Geometry - Lecture 14
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
A Sheaf-based Approach to Graph Neural Networks
Explore sheaf theory's application to Graph Neural Networks, offering a novel perspective on Geometric Deep Learning beyond traditional geometric structures.
Tangent Groupoid in Noncommutative Geometry - Lecture 15
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
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.
Tangent Groupoid in Noncommutative Geometry - Lecture 16
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Graduate Course on the Tangent Groupoid in Noncommutative Geometry - Lecture 3
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in mathematical physics and operator algebras.
Prime and Semiprime Ideals in C*-Algebras
Explore prime and semiprime ideals in C*-algebras, delving into advanced concepts in operator theory and functional analysis.
Arithmetic Field Theory for Elliptic Curves by Minhyong Kim
Explore advanced arithmetic field theory for elliptic curves, focusing on rational points on modular curves, Chabauty methods, and computational aspects in arithmetic geometry.
Diophantine Stability for Elliptic Curves on Average by Anwesh Ray
Explore Diophantine stability for elliptic curves, focusing on average-case analysis. Gain insights into arithmetic geometry and modular curves through advanced theoretical and computational approaches.
Bifurcation Phenomena in Geometric Variational Problems
Explore classical Bifurcation Theory and its modern applications in Riemannian Geometry, covering minimal and constant mean curvature surfaces and the Yamabe problem.
On Symplectic Transformations of OG10-Type Hyperkähler Manifolds via Cubic Fourfolds
Explore symplectic birational transformations on OG10-type hyperkähler manifolds, focusing on LSV manifolds derived from cubic fourfolds and their cohomological actions.
The Defect of a Cubic Threefold
Explore geometric properties of singular cubic threefolds, relating defect to various characteristics. Insights from ongoing research with Lisa Marquand, inspired by Hyperkähler manifold construction.
Exploring the Real Parameter Space
Delve into enumerative geometry with Margaret Regan as she investigates real parameter spaces, offering insights into this fascinating mathematical realm.
Certified Homotopy Tracking in Enumerative Geometry
Explore certified homotopy tracking in enumerative geometry with Kisun Lee from Clemson University, focusing on advanced mathematical concepts and applications.