Knot Quantum Invariants, Graphs, and Combinatorics - Part 2
Explore advanced concepts in knot theory, focusing on quantum invariants, graph theory, and combinatorial techniques. Delve into intricate mathematical relationships.
Knot Quantum Invariants, Graphs, and Combinatorics - Part 1
Explore quantum knot invariants, their connections to graph theory, and combinatorial applications in this advanced mathematical lecture.
Categorification of Quantum Invariants: From Knots to 3-Manifolds - Part 1
Explore categorification of quantum invariants, focusing on knots and 3-manifolds. Delve into advanced mathematical concepts with expert Sergei Gukov from Caltech and Dublin IAS.
Knots-Quivers Correspondence: Generalizations and Combinatorics
Explore knots-quivers correspondence, its extensions, and applications in enumerative combinatorics, including lattice paths and Schröder paths counting.
Detecting Positivity from Link Homology
Explore Khovanov homology's applications in detecting link positivity and its extension to fibered positive links and L-space knots.
From the Kauffman and Dubrovnik Polynomials to Cubic Skein Modules and Beyond
Explore the rich world of skein theory, from linear and quadratic modules to the untapped potential of cubic skein modules and their connections to various mathematical disciplines.
On the Structure of Skein Modules
Explore Kauffman bracket skein modules, examining conjectures and theorems. Discover counterexamples and new insights into the structure of these modules in 3-manifolds.
Bordered Floer Theory, Hochschild Homology, and Links in S^1 × S^2
Explore spectral sequences linking Khovanov homology to Heegaard Floer homology and their analogues for links in S^1×S^2, involving bordered Floer theory and Hochschild homology.
Algebras for Knots and Their Connections to Quiver Yangians
Explore quiver Yangian algebras, their representations, and connections to knots through the knot-quiver correspondence and gluing construction.
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.
Quiver Structures of Knot Invariants, Open Strings, and Recursion
Explore quiver structures in knot theory, connecting HOMFLY-PT polynomials to motivic Donaldson-Thomas invariants through string theory and M-brane interactions.
Z-Disks in CP^2 - Enumeration and Boundary Knot Analysis
Explore locally flat Z-disks in CP^2, focusing on enumeration and boundary conditions. Gain insights into topological isotopy and related smooth category problems.
Cluster Algebras and Hyperbolic Geometry
Explore the application of cluster algebra to 2D and 3D hyperbolic geometry, examining ideal triangulations, Teichmuller spaces, and knot volumes through mutations and cluster variables.
Orderability of 3-Manifold Groups and the L-Space Conjecture
Explore orderability of 3-manifold groups, focusing on the L-space conjecture and its connections to group orderability, taut foliations, and Heegaard Floer homology in hyperbolic 3-manifolds.
Left-Orderability and Toroidal 3-Manifolds
Explore left-orderability in 3-manifolds with incompressible tori, using order-detection of slopes. Gain insights into the L-space conjecture through new evidence.
Non-standard Orders on Torus Bundles with One Boundary
Explore non-standard bi-orderings of fundamental groups in torus bundles with one boundary, extending Perron-Rolfsen's work on standard orderings and Alexander polynomials.
The Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators
Explore Loop Braid Group, Loop Hecke Algebras, and charge conserving Yang-Baxter operators. Gain insights into recent mathematical developments in quantum symmetries and topological quantum field theories.
Towards the Quantum Exceptional Series
Explore continuous families of planar algebras interpolating exceptional Lie algebras and their quantum counterparts. Discover a potential new exceptional knot polynomial through skein theoretic analysis.
Polynomial Bounds on Reidemeister Moves in Knot Theory
Explore polynomial bounds on Reidemeister moves in knot theory, examining algorithms for trivial knot recognition and the relationship between diagram complexity and move sequences.
Skein Valued Counts of Open Curves in Calabi-Yau Threefolds
Explore holomorphic curve counting in Calabi-Yau threefolds using HOMFLYPT skein module, examining deformation invariance and recursion relations in non-compact cases.
An Approach to Simon's Conjecture
Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.