Events
Department of Mathematics and Statistics
Texas Tech University
The tangle hypothesis is a variant of the cobordism hypothesis that considers cobordisms embedded in some finite-dimensional Euclidean space (together with framings). Such tangles of codimension k can be organized into an Ek-monoidal d-category, where d is the maximal dimension of the tangles. The tangle hypothesis then asserts that this category of tangles is the free Ek-monoidal d-category with duals generated by a single object.
In this talk, based on joint work in progress with Yonatan Harpaz, I will describe an infinitesimal version of the tangle hypothesis: instead of showing that the Ek-monoidal category of tangles is freely generated by an object, we show that its cotangent complex is free of rank 1. This provides support for the tangle hypothesis (of which it is a direct consequence), but can also be used to reduce the tangle hypothesis to a statement at the level of Ek-monoidal (d+1, d)-categories by means of obstruction theory.In this talk we show how the Balmer spectrum of an essentially small
tensor triangulated category can be used to classify radical thick
tensor ideals.
Abstract: Asymptotic compatibility, loosely speaking, refers to the unconditional convergence of solutions for some family of problems when two distinct parameters approach their limits simultaneously. In our context one parameter pertains discretization, whereas the other measures the degree of nonlocality. The goal, then, is to use nonlocal, discrete problems to approximate solutions to a local, continuous problem.
We develop an abstract asymptotic compatibility (AC) framework for families of optimal design problems, to demonstrate unconditional convergence of numerical schemes in the discretization limit and the limit of a modeling parameter. We apply this framework to two different classes of nonlocal optimal design problems: a nonlocal conductivity problem, and a model coming from peridynamics.
Joint work with Tadele Mengesha and Joshua M. Siktar
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this
Direct Link that embeds meeting and ID and passcode.
- Choice #2: Join the Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 949 9288 2213
* Passcode: Applied
TTU Math Circle Spring Flyer 6:30-7:30 PM Thursdays in the basement of Math, room 010
With a single circulating tick-borne pathogen in a population of ticks and vertebrate hosts, the basic reproduction number incorporates contributions from tick-to-tick, tick-to-vertebrate host, and vertebrate host-to-tick transmission routes. With two co-circulating tick-borne pathogens, resident and invasive, and under the assumption that tick-to-tick is the only transmission route in a tick population feeding on vertebrate hosts, the invasion reproduction number is a measure of the ability of the invasive strain to take over the population at the resident-strain equilibrium. Whether an invasive strain that is identical to the resident one is predicted to dominate depends on whether the mathematical model characterising the system possesses Alizon's neutrality property. However, even if a model is neutral and the strains not identical, its associated invasion reproduction number depends on model structure. We propose a two-slot model for tick-borne pathogen transmission in the presence of tick co-feeding, co-infection, and co-transmission, which is an extension of Alizon's model. Our two-slot model, with one population of susceptible (not infected) ticks, two populations of ticks infected with a single strain (resident or invasive), one population of co-infected (infected with both strains) ticks, and two populations doubly-infected with the same strain (resident or invasive), satisfies the neutrality property. We analyse the invasion reproduction number with the next-generation method and via numerical simulations. We apply the two-slot model to compute the fraction of co-infected questing adult ticks at the end of a season as a function of the co-transmission probability, and discuss the potential risk to humans.
abstract 2 PM CDT (UTC-5)
Zoom link available from Dr. Brent Lindquist upon request.
