Events for 02/12/2021 from all calendars

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 951 5490 42

Speaker: Henry Yuen, Columbia University

Title: Testing low-degree polynomials in the noncommutative setting

Abstract: In low-degree testing the following question is considered: given a multivariate function over a finite field, if a sufficiently large fraction of “local views” of the function are consistent with low-degree polynomials, does this imply that the function is _globally_ consistent with a single low-degree polynomial? Many low-degree testing theorems have been proved over the years, and have had important applications in theoretical computer science, including complexity theory and property testing. Low-degree testing also plays an important role in the recent quantum complexity result MIP* = RE. Here, low-degree testing is considered in the _noncommutative_ setting: “local views” of a function are given via a sequence of measurements on a state, but the measurement operators do not necessarily commute with each other. Despite noncommutativity, there is still a sense in which local consistency with low-degree polynomials implies global consistency with low-degree polynomials. In this talk, I will give an introduction to low-degree testing and discuss its analysis. This is based on joint work with Ji, Natarajan, Vidick, and Wright. (https://arxiv.org/abs/2009.12982 )

URL: Event link

Mathematical Physics and Harmonic Analysis Seminar

Time: 2:00PM - 2:50PM

Location: Zoom

Speaker: Benito Juarez-Aubry, IIMAS-UNAM

Title: Semiclassical gravity in static spacetimes as a constrained initial value problem

Abstract: Semiclassical gravity is the theory in which gravity is treated classically and matter is treated in the framework of quantum field theory. The spacetime metric tensor, which encodes gravitational effects in its curvature, interacts with matter through the semiclassical Einstein equations: matter sources the dynamics of the spacetime metric via the expectation value of the stress-energy tensor of the quantum fields, while the quantum fields propagate in curved spacetime. It is currently unknown whether semiclassical gravity has a well-posed initial value formulation even for free fields. In this talk, I will discuss the situation in static spacetimes, where time-translation symmetry greatly reduces the difficulty of the problem, and where one can show well-posedness. I will also discuss the main ideas on how to generalise these results to non-static spacetimes under some special circumstances. Based on arXiv:2011.05947 and on some unpublished work in progress with S. Modak.

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Alexander Ruys de Perez, TAMU

Title: Wheels of Neural Codes: A New Criterion for Nonconvexity

Abstract: A neural code C on n neurons is a collection of subsets of the set of integers {1,2,...,n}. Usually, C is paired with a collection of n open subsets of some Euclidean space, with C encoding how those open sets intersect. A central problem concerning neural codes is determining convexity; that is, if the code can encode the intersections of n convex open subsets. In this talk, I will generalize an example of Lienkaemper, Shiu, and Woodstock (2017) into a new criterion for nonconvexity called a 'wheel'. I will show why it forbids convexity, explain how one can find it combinatorially, and provide examples of previously unclassified codes that we now know to be nonconvex due to containing a wheel.