Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is the most extensively studied of all. However, computing the KBSM of a 3-manifold is notoriously hard, especially over the ring of Laurent polynomials. With […]
Convex real projective structures generalize hyperbolic structures in a rich way. We will discuss a class of manifolds introduced by Cooper Long and Tillmann, which include finite-volume cusped hyperbolic manifolds and other manifolds with well-controlled ends. These manifolds have nice deformation theoretic properties, and we will conclude with an existence theorem for novel structures on […]
The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball spanning the knot. It is defined to be zero if […]
Title: Chebyshev Threadings in Skein Algebras for Punctured Surfaces Abstract: Skein algebras are algebras of links in a surface quotiented by diagram-based equivalence relations based on the Kauffman bracket. In […]
Title: Cellular resolutions of the diagonal and exceptional collections for toric Deligne-Mumford stacks Abstract: Beilinson gave a resolution of the diagonal for complex projective space which yields a strong, full exceptional […]
Title: Cellular resolutions of the diagonal and exceptional collections for toric Deligne-Mumford stacks (Continued) Abstract: Beilinson gave a resolution of the diagonal for complex projective space which yields a strong, full […]
Title: Quantum 4-Manifold Invariants Via Trisections Abstract: I will describe a new family of potentially non-semisimple invariants for compact a 4-manifold whose boundary is equipped with an open book. The invariant is computed using a trisection, along with some additional combing data, and a piece of algebraic data called a Hopf triple. The relationship with […]
Title: Towers and elementary embeddings in total relatively hyperbolic groups Abstract: In a remarkable series of papers, Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers. It was later proved by Chloé Perin that if H is an elementarily embedded subgroup (or elementary submodel) of […]
Title: Generating families on Lagrangian cobordisms Abstract: An important question in contact topology is to understand Legendrian knots and their relations given by Lagrangian cobordisms. In the contact manifold T*M x R, an important tool to study Legendrian knots and their Lagrangian cobordisms is called generating families or generating functions, which are generalizations of the […]
Title: Cosmetic Surgeries on Knots and Heegaard Floer Homology Abstract: A common method of constructing 3-manifolds is via Dehn surgery on knots. A pair of surgeries on a knot is called purely cosmetic if the resulting 3-manifolds are homeomorphic as oriented manifolds, whereas it is said to be chirally cosmetic if they result in homeomorphic […]
Title: Contact structures and the mapping class group of lens spaces Abstract: One important problem in contact topology is to classify contact structures on a given manifold. Around 20 years ago, Giroux and Honda classified contact structures on lens spaces. A natural question to ask after that is how the transformations on lens spaces interact […]
On November 14th, Tuesday from 3-4pm in Fletcher 110, Geometry and Topology Seminar invites students and faculty to a course preview session devoted to a discussion and presentations about upcoming Spring 2024 courses in geometry, topology and/or with applications in geometry and topology to help students make their enrollment choices. We will have some refreshments […]
