Skip to content
# Events for January 22, 2018 from General and Seminar calendars

## Geometry Seminar

**Abstract:** Newton-Okounkov bodies were introduced by Kaveh-Khovanskii and Lazarsfeld-Mustata to extend the theory of Newton polytopes to functions more general than Laurent polynomials. This theory has at least two implications for applications. First is that Newton-Okounkov bodies provide an approach to counting the number of solutions to systems of equations that arise in applications. Another is that when the Newton-Okounkov body is an integer polytope (there is a Khovanskii basis), there is a degeneration to a toric variety which in principal should give a numerical homotopy algorithm for computing the solutions. This talk will sketch both applications.

## Hiring Candidate - Dr. Shawn Cui

**Description:**

## Student/Postdoc Working Geometry Seminar

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 628

**Speaker:** Frank Sottile, TAMU

**Title:** *Newton-Okounkov Bodies for Applications*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Dr. Shawn Cui , Stanford University

Title: Four Dimensional Topological Quantum Field Theories

Abstract:

We give an introduction to topological quantum field theories (TQFTs) which have wide applications in low dimensional topology, representation theory, and topological quantum computing. In particular, TQFTs provide invariants of smooth manifolds. We give an explicit construction of a family of four dimensional TQFTs. The input to the construction is a class of tensor categories called $G$-crossed braided fusion categories where $G$ is any finite group. We show that our TQFTs generalize most known ones such as Yetter's TQFT and Crane-Yetter TQFT. It remains to check if the resulting invariant of 4-manifolds is sensitive to smooth structures. It is expected that the most general four dimensional TQFTs should be from a spherical fusion 2-category whose definition has not been universally agreed.

We prove that a $G$-crossed braided fusion category corresponds to a 2-category which does not satisfy the criteria of a spherical fusion 2-category defined by Mackaay. Thus the question of what axioms properly define a spherical fusion 2-category is open.

**Time:** 5:00PM - 6:00PM

**Location:** BLOC 628

**Speaker:** JM Landsberg, TAMU

**Title:** *Tightness of tensors and beyond*