Events for 08/26/2020 from all calendars

Geometry Seminar

Time: 10:00AM - 11:15AM

Location: zoom

Speaker: Anna Seigal, Oxford

Title: Ranks of Cubic Surfaces

Abstract: There are various notions of rank, which measure the complexity of a tensor or polynomial. Cubic surfaces can be viewed as symmetric tensors. We consider the non-symmetric tensor rank and the symmetric Waring rank of cubic surfaces, and show that the two notions coincide over the complex numbers. The results extend to order three tensors of all sizes, implying the equality of rank and symmetric rank when the symmetric rank is at most seven. We then explore the connection between the rank of a polynomial and the singularities of its vanishing locus, and we find the possible singular loci of a cubic surface of given rank. This talk is based on joint work with Eunice Sukarto.

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Giovanni Landi, Trieste University

Title: Solutions to the quantum YB equation and related deformations

Abstract: We present natural families of coordinate algebras of noncommutative Euclidean spaces and noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an R-matrix which is involutive and satisfies the quantum Yang–Baxter equation. As a consequence they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have spherical manifolds, and noncommutative quaternionic planes as well as noncommutative quaternionic tori. On these there is an action of the classical quaternionic torus SU(2)×SU(2) in parallel with the action of the torus U(1)×U(1) on a complex noncommutative torus.

URL: Event link

Topology Seminar

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Hongbin Sun, Rutgers University - New Brunswick

Title: Subgroup separability and subgroup distortion of 3-manifold groups

Abstract: For a (finitely generated) subgroup of a (finitely generated) group, we will consider two properties of this subgroup: the separability of this group and its subgroup distortion. The separability of a subgroup measures whether the property of an element not lying in this subgroup is visible by taking some finite quotient. We will give a characterization on whether a subgroup of a 3-manifold group is separable. The subgroup distortion compares the intrinsic and extrinsic geometries of a subgroup. For an arbitrary subgroup of a 3-manifold group, we prove that the subgroup distortion can only be linear, quadratic, exponential and double exponential. It turns out that these two properties (subgroup separability and subgroup distortion) are closed related for subgroups of 3-manifold groups. The subgroup distortion part is joint work with Hoang Nguyen.