Events for 02/19/2020 from all calendars

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Maciej Paszynski, AGH University of Science and Technology, Krakow, Poland

Title: Supermodeling of a tumor dynamics employing isogeometric analysis solvers with piece-wise constant test functions

Abstract: In this talk, we show that it is possible to obtain reliable numerical prognoses about cancer dynamics by creating the supermodel of cancer, which consists of several coupled instances (the sub-models) of a generic cancer model, developed with isogeometric analysis (IGA). Its integration with real data can be achieved by employing a prediction/correction learning scheme focused on fitting several values of coupling coefficients between submodels, instead of matching scores (even hundreds) of tumor model parameters as it is in the classical data adaptation techniques. We also show how to speed up the tumor simulations by employing the piece-wise constant test functions in IGA framework. Namely, we show that the rows of the system of linear equations can be combined, and the test functions can be sum up to 1 using the partition of unity property at the quadrature points. Thus, the test functions in higher continuity IGA can be set to piece-wise constants. This formulation is equivalent to testing with piece-wise constant basis functions, with supports span over some parts of the domain. The resulting method is Petrov-Galerkin's kind. This observation has the following consequences. The numerical integration cost can be reduced because we do not need to evaluate the test functions since they are equal to one. The resulting method is equivalent to a linear combination of the collocations at points and with weights resulting from applied quadrature over the spans defined by supports of the piece-wise constant test functions.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Jintao Deng, Texas A&M

Title: The Novikov conjecture and group extensions

Abstract: The Novikov conjecture is an important problem in higher dimensional topology. It claims that the higher signatures of a compact smooth manifold are invariant under orientation preserving homotopy equivalences. The Novikov conjecture is a consequence of the strong Novikov conjecture in the computation of the K-theory of group C^*-algebras. In this talk, I will talk about the Novikov conjecture for groups which are extensions of coarsely embeddable groups.

Graduate Student Organization Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Tolulope Oke

Title: How contracting Homotopy helps to determine the Lie algebra structure on Hochschild cohomology

Abstract: We are all familiar with when two chain maps f,g between two chain complexes C and D are homotopic i.e there is a chain homotopy s from C to D[1] such that f-g=ds+sd. There is a similar notion of contracting homotopy between chain complexes. Hochschild cohomology possesses a cup product and a Lie bracket of degree -1. I will present how the contracting homotopy technique is used to determine the Lie structure on Hochschild cohomology for certain class of algebras.

Student/Postdoc Working Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 624

Speaker: R. Geng, TAMU

Title: Strong subadditivity via representation theory