Events for 11/13/2020 from all calendars

Numerical Analysis Seminar

Time: 11:00AM - 12:00PM

Location: ZOOM

Speaker: Ruiwen Shu, University of Maryland

Title: Positivity-preserving asymptotic-preserving second order schemes for stiff kinetic equations

Abstract: Kinetic equations like the Boltzmann and the BGK equations naturally have multiscale features because of the possibly small Knudsen number, which makes them numerically challenging. To solve them efficiently without resolving the small Knudsen number, one usually needs to treat the stiff collision term more or less implicitly, to achieve the asymptotic-preserving (AP) property. Also, it is desired to preserve the positivity of the particle density function. However, a well-known result by Gottlieb-Shu-Tadmor 01' is that there is no strong-stability-preserving (SSP) implicit scheme of order higher than one. To overcome this order barrier, we developed new schemes for stiff kinetic equations based on the frameworks of implicit-explicit Runge-Kutta (IMEX-RK) and exponential Runge-Kutta. These schemes preserve the positivity and asymptotics, as well as achieve second order accuracy in both the kinetic and the fluid regimes.

Spectral Theory Reading Seminar

Time: 11:00AM - 11:50PM

Location: Zoom

Speaker: Wencai Liu, TAMU

Title: Floquet Theory I

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Jay Yang, U of Minnesota

Title: Virtual Resolutions of Monomial Ideals

Abstract: Virtual Resolutions a concept introduced by Berkesch, Erman, and Smith to provide a more meaningful theory of syzygies for modules over the Cox ring of a toric variety. I will discuss recent progress on applying the tools of monomial ideals to the problem of virtual resolutions, in particular a virtual analog of Hilbert's Syzygy Theorem, as well as recent progress on virtually Cohen-Macaulay modules and current work towards a virtual Auslander-Buchsbaum formula. This includes upcoming joint work with Christine Berkesch, Patricia Klein, and Michael C. Loper.

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: ZOOM

Speaker: Daniel Massatt, University of Chicago

Title: Momentum space in relaxed incommensurate bilayers

Abstract: Momentum space techniques are fundamental to the understanding of electronic structure of materials and for computing observables such as conductivity and the density of states. The basic formulation of momentum space comes from the Bloch operator for periodic materials. We show that momentum space can be formulated for homogenous incommensurate bilayers, and go further by extending the approach to include mechanical relaxation effects. This leads immediately to efficient algorithms for computing electronic observables in an appropriate class of materials. It further allows a qualitative analysis of the quasi-band structure, which is used for example to understand the famous magic angle in twisted bilayer graphene.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: zoom

Speaker: Joe Kileel , University of Texas Austin

Title: Fast symmetric tensor decomposition

Abstract: Tensors are higher-order matrices, and decomposing tensors can reveal structure in datasets. In recent years, tensor decomposition has found applications in statistics, computational imaging, signal processing, and quantum chemistry.

In this talk, we will present a new numerical method for low-rank symmetric tensor decomposition, building on the usual power method and ideas from classical algebraic geometry. The approach achieves a speed-up over the state-of-the-art by roughly one order of magnitude. We will also discuss an “implicit” variant of the algorithm for the case of moment tensors which avoids the explicit formation of higher-order moments, analogously to matrix-free techniques in linear algebra. Finally, we will make some quantitative statements about the non-convex optimization landscape underlying our method.

This talk is based on joint works with Joao Pereira, Tammy Kolda and Timo Klock.

Student/Postdoc Working Geometry Seminar

Time: 10:00PM - 11:00PM

Location: zoom

Speaker: A. Huang, TAMU

Title: Def. theory, curves of genus 0 and 1.