## Computational and Applied Mathematics Seminar

## Novel Coronavirus (COVID-19) Update

Due to the pandemic, the seminar will not operate from March 12 until the end of the semester.

## Location and Time

University of Wyoming, Ross Hall 247, Fridays from 4:10-5:00 (unless otherwise stated).

## Seminar Chairs

Professors Craig C. Douglas and Man-Chung Yeung.

## Support

The CAM seminar series is currently supported through volunteers and the financial contributions by the UW Mathematics Department, MGNet.org, and and an energy grant from ExxonMobil.

## Schedule

For Spring 2020, the speakers are as follows:

Date Speaker From/Note February 20 Dan Stanescu University of Wyoming February 27 Man-Chung Yeung University of Wyoming March 6 Chengyi (Charlie) Zhang University of Wyoming March 9** Hakima Bessaih University of Wyoming * Thursday Colloquium in AG 1032, ** Joint CAM - Analysis seminar, *** Joint CAM - ACNT seminar

We are constantly looking for speakers for the current academic year! The topics can be original research, a survey of an area, or an interesting paper or papers that would interest the CAM community. If you would like to speak, please contact me by email.

The schedule, titles, and abstracts from Fall 2019 are here.

## Titles and Abstracts

## February 20

## Interactive and Automated Theorem Provers: Mathematical Logic with LEAN

Prof. Dan Stanescu, Department of Mathematics and Statistcs, University of WyomingFrom the modern foundational work of Turing, Church, and Godel in the 1930s through the formalization of lambda calculus, the Curry-Howard equivalence and the advent of functional languages, automated theorem proving experienced a slow but steady development. A large number of theorems have already been formalized and a plethora of new results continue to appear. This talk will focus on obtaining the basic results in propositional calculus with LEAN, a last-generation prover based on dependent type theory and the calculus of inductive constructions. The talk is conceived as the first in a short series aiming to show the advantage of using proof assistants to not only do research, but also both learn and teach mathematics.

## February 27

## A FEAST variant for eigenvalue problems

Prof. Man-Chung Yeung, Department of Mathematics and Statistics, University of WyomingWe present a variant of the FEAST matrix eigensolver for solving restricted real and symmetric eigenvalue problems. The method is derived from a combination of a variant of the FEAST method, which employs two contour integrals per iteration, and a power subspace iteration process. Compared with the original FEAST method, the new method does not require that the search subspace dimension must be greater than or equal to the number of eigenvalues inside a search interval, and can deal with narrow search intervals more effectively. Empirically, the FEAST iteration and the power subspace iteration are in a mutually beneficial collaboration to make the new method stable and efficient.

## March 6

## Automated Progress Control Using Laser Scanning Technology

Prof. Chengyi (Charlie) Zhang, Civil Engineering Department, University of WyomingAssessing progress in different construction activities at the end of every payment period is time consuming and requires specialized personnel employed by the contractor and the owner. Automatic progress control that requires a minimum amount of human involvement could reduce the time spent on this activity, reduce the number of personnel used, reduce the cost involved, reduce disagreements between contractor and owner, and add to the overall efficiency of project management. Attempts have been made in the past to resolve this issue using image processing and other techniques but the results have not been satisfactory. A new attempt was made to set up a system that can assess progress control with minimum human input and the results are presented in this paper. The experiment made use of laser scanning technology and was conducted both in laboratory conditions and construction sites. The initial results from laboratory condition appear to be promising but there are still obstacles to surmount. The system is robust and accurate in laboratory conditions and constitutes proof of concept. Improvements are made to accelerate the registration process of multiple scans, to reduce the noise data, to recognize objects of irregular shape, and to assess the practicality and economic feasibility of such a system when applying this system in real construction sites.

## March 6

## Invariant Measures for Stochastic Differential Equations

Prof. Hakima Bessaih, Department of Mathematics and Statistics, University of WyomingStochastic differential equations (SDESs) driven by a Brownian motion (Bm) will be introduced. The definition of the stochastic integral will be given. The asymptotic behavior of the solution will be studied using the notion of invariant measures. These techniques will be used for the study of stochastic partial differential equations as well.

## April 3

## TBD

Lauren Shoemaker, University of Wyoming...