We welcome all undergraduate/graduate students and faculty to attend the Topology Seminar! Speaker: Claudio Gomez-Gonzales (Carleton College - UC Irvine) Title: How hard could it be? A tour of resolvent degree Abstract: Solving algebraic equations are among the oldest problems in mathematics. In this talk, we offer a concrete, visual, and historical introduction to resolvent […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Vijay Higgins (UCLA) Title: Webs and skein algebras Abstract: The Jones polynomial of a link can be computed diagrammatically by using skein relations, which encode the representation theory of SL(2). By considering the vector space spanned by links drawn on a surface and […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Orsola Capovilla-Searle (UC Davis) Title: Exact Lagrangian fillings of Legendrian links Abstract: An important problem in contact topology is to understand Legendrian submanifolds; these submanifolds are always tangent to the plane field given by the contact structure. Legendrian links arise as wavefronts in […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Reginald Anderson (CMC) Title: Presentations of derived categories Abstract: A modification of the cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels gives a virtual resolution of the diagonal for smooth projective toric varieties and toric Deligne-Mumford stacks which are a global quotient of […]
A modification of the cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels gives a virtual resolution of the diagonal for smooth projective toric varieties and toric Deligne-Mumford stacks which are a global quotient of a smooth projective variety by a finite abelian group. In the past year, Hanlon-Hicks-Lazarev gave a minimal resolution of the diagonal […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Migiwa Sakurai (Shibaura Institute of Technology) Title: Clasp pass moves and arrow polynomials of virtual knots Abstract: For classical knots, clasp pass moves are closely related to Vassiliev invariants of degree 3. Tsukamoto showed that the values of the Vassiliev invariant of degree […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Sam Nelson (CMC) Title: Biquandle Module Quiver Representations Abstract: Biquandle module enhancements are invariants of knots and links generalizing the classical Alexander module invariant. A quiver categorification of these invariants was introduced in 2020. In this work-in-progress (joint with Yewon Joung from Hanyang […]
What are the possible angles between two integer vectors in R^n? If we fix one such possible angle and one integer vector x, is there always another integer vector y that makes this angle with x? Assuming that x makes a given angle with some vector, how can we find the shortest such vector y? […]
We welcome all undergraduates and graduate students to attend topology seminar! Speaker: Elena Wang (Michigan State University) Title: A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance Abstract: Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between graphs […]
For a finite group G, a G-module M, and a field F, an element u in H^d(G,M) is negligible over F if for each field extension L/F and every continuous group homomorphism from Gal(L^{sep}/L) to G, u is in the kernel of the induced homomorphism H^d(G,M) to H^d(L,M). Negligible cohomology was first introduced by Serre […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Joe Breen (University of Iowa) Title: Open books in all dimensions Abstract: I will discuss recent work (joint with K. Honda and Y. Huang) on establishing a relationship, first discovered by Giroux, between "contact structures" and "open books". This relationship has been […]
Imagine the hands on a clock. For every complete the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way. We may think of the hour hand as generating a group such that when we ``move'' twelve times then we get back to where we […]
