On the Geometry of Cubics
Explore classical and new results on the geometry of cubics in three, four, and five dimensions, delving into their fascinating mathematical properties and structures.
Quantum Representations and Bogomolov-Katzarkov Surfaces
Exploring quantum representations and their application to Bogomolov-Katzarkov surfaces, addressing the Shafarevich conjecture on holomorphic convexity in algebraic geometry.
Hilbert Schemes of Plane Curve Singularities and Matrix Factorizations
Explore connections between algebraic geometry and topology through plane curve singularities, Hilbert schemes, and matrix factorizations in this advanced mathematics lecture.
Representations of the Classical, Virtual, and Welded Braid Groups
Explore generalizations of classical braid groups with new crossings and relations, focusing on extended representations in virtual and welded braid groups.
Welded Tangles and a Topological Interpretation of the Kashiwara-Vergne Group
Explores welded tangles and foams as higher-dimensional knot theory, connecting their automorphisms to the Kashiwara-Vergne group in Lie theory and relating to knot invariants and Baker-Campbell-Hausdorff series.
On the Deleted Squares of Lens Spaces
Explores homotopy equivalence of configuration spaces in lens spaces, using differential characters and Massey products to investigate topological properties of deleted squares.
Divergence in Coxeter Groups
Explores divergence in Coxeter groups, introducing the 'hypergraph index' to characterize linear, quadratic, and exponential divergence in these mathematical structures.
Moduli Spaces for Rational Elliptic Surfaces - of Index 1 and 2
Explore rational elliptic surfaces, their construction from pencils of curves, and recent developments in moduli space construction for surfaces with multiple fibers.
The Average Genus of a 2-Bridge Knot Grows Linearly with Respect to Crossing Number
Explore the linear growth relationship between Seifert genus and crossing number in 2-bridge knots using Chebyshev billiard table diagrams, building on previous research and experimental data.
Virtual Reductions and Intersection Theory on Moduli Space of Sheaves on Calabi-Yau 4 Folds
Explore virtual reductions of fundamental classes on moduli spaces of sheaves in Calabi-Yau 4-folds, examining applications to Donaldson-Thomas invariants and connections to threefold theories.
Braids and Line Arrangements - Old and New
Explore the interplay between braid groups, configuration spaces, and hyperplane arrangements, focusing on recent advances in understanding fundamental groups of complex line arrangement complements.
Braidings and Braid Equivalences
Explore braiding algorithms and braid equivalences for various knot types, including classical, virtual, and singular, with a focus on knotoids and braidoids.
Degeneration of Cubic Threefolds with Nodes
Explore the degeneration of cubic threefolds with nodes, focusing on intermediate Jacobians, Fano varieties, and Prym varieties. Gain insights into irrationality proofs and limiting behaviors.
Holomorphic Lagrangian Foliation and Gaiotto's Conformal Limit
Explore holomorphic Lagrangian foliation and Gaiotto's conformal limit in this advanced mathematics lecture by UC Davis professor Motohico Mulase.
Quantum Toric Geometry II - Non-Commutative Geometric Invariant Theory
Explore quantum geometric invariant theory, extending classical GIT to non-commutative cases. Gain insights into cutting-edge research in quantum toric geometry.
Mirror Symmetry and Cluster Varieties
Explore symplectic geometry of cluster varieties and their applications to mirror symmetry, including homological mirror symmetry for Gross-Hacking-Keel cluster varieties.
A Construction of Apéry Constants from Landau Ginzberg Models
Explores construction of Apéry constants from Landau-Ginzberg models, linking quantum differential equations of Fano threefolds to mirror symmetry and geometric higher normal functions.
Topological Recursion for Masur-Veech Volumes
Explore geometric recursion's impact on multicurve length statistics and Masur-Veech volumes in moduli spaces of quadratic differentials, based on collaborative research findings.
Topological Recursion: From A to Z
Comprehensive exploration of topological recursion, covering fundamental concepts to advanced applications in mathematics and physics.
From Ribbon Graphs to CohFT
Explore the mathematical connection between ribbon graphs and Cohomological Field Theories (CohFT) in this advanced topology lecture by Olivia Dumitrescu from Central Michigan University.
Geometric Recursion for Combinatorial Teichmüller Spaces and Applications
Explores geometric recursion in combinatorial Teichmüller spaces, covering Mirzakhani-McShane identity, Topological Recursion, and discrete versions, with applications to Witten-Kontsevich theorem and Norbury's polynomials.