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Topology Seminar — Matthew vonAllmen

Zoom meeting , United States

Title: Untying Knots with Neural Nets Abstract: Neural networks can transform 3-dimensional data in a manner reminiscent of an ambient isotopy. With some modifications, a neural network can be trained to manipulate the vertices of a knot while respecting its topological structure. We use the discrete Mo ̈bius energy as a loss function to incentivize […]

Claremont Topology Seminar: Robert Bowden (HMC)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 the case of surfaces with punctures, the skein algebra is generated by links as well as arcs between the punctures, and there are additional skein […]

Claremont Topology Seminar: Reginald Anderson (CMC)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 collection of line bundles. Bayer-Popescu-Sturmfels generalized Beilinson's result to a cellular resolution of the diagonal for what they called "unimodular" toric varieties (a more restrictive […]

Claremont Topology Seminar: Reginald Anderson (CMC)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 exceptional collection of line bundles. Bayer-Popescu-Sturmfels generalized Beilinson's result to a cellular resolution of the diagonal for what they called "unimodular" toric varieties (a more […]

Claremont Topology Seminar: Julian Chaidez (USC)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 […]

Claremont Topology Seminar: Christopher Perez (Loyola University New Orleans)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 […]

Claremont Topology Seminar: Wenyuan Li (USC)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 […]

Claremont Topology Seminar: Konstantinos Varvarezos (UCLA)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 […]

Claremont Topology Seminar: Hyunki Min (UCLA)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 […]

Geometry and Topology Seminar: Claremont Colleges Course Previews for Spring 2024

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

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 […]

Claremont Topology Seminar: Melody Molander (UCSB)

Fletcher 110, Pitzer College 1050 N Mills Ave, Claremont, CA, United States

Title: Skein Theory of Affine ADE Subfactor Planar Algebras Abstract: Subfactor planar algebras first were constructed by Vaughan Jones as a diagrammatic axiomatization of the standard invariant of a subfactor. These planar algebras also encode two other invariants of the subfactors: the index and the principal graph. The Kuperberg Program asks to find all diagrammatic […]