# News

## Mohamed Amsaad Defense

Well-defined Lagrangian flows for absolutely continuous curves of probabilities on the real line.

It is known from Fluid Mechanics that the time evolution of a probability measure describing some physical quantity (such as the density of a fluid) is related to the velocity of the fluid by the continuity equation. This is known as the Eulerian description of fluid flow. Dually, the Lagrangian description uses the flow of the velocity field to look at the individual trajectories of particles. In the case of flows on the real line, only recently has it been discovered that "some sort'' of dual Lagrangian flow consisting of monotone maps is always available to match the Eulerian flow. The uniqueness of this "monotone flow'' among all possible "flows'' (quotation marks used precisely because traditionally it cannot be called a "flow'' unless it is unique) of the fluid velocity is the centerpiece of this dissertation.

The Lagrangian description of absolutely continuous curves of probability measures on the real line is analyzed in this thesis. Whereas each such curve admits a Lagrangian description as a well-defined flow of its velocity field, further conditions on the curve and/or its velocity are necessary for uniqueness. We identify two seemingly unrelated such conditions that ensure that the only flow map associated to the curve consists of a time-independent rearrangement of the generalized inverses of the cumulative distribution functions of the measures on the curve. At the same time, our methods of proof yield uniqueness within a certain class for the curve associated with a given velocity; that is, they provide uniqueness for the solution of the continuity equation within a certain class of curves. Our proposed approach is based on the connection between the flow equation and one-dimensional Optimal Transport.

This is based on joint work of the author with A. Tudorascu, in which some results on well-posedness (in the one-dimensional case) have been achieved. The results are presented in major conferences and published in a highly ranked mathematical journal.

All are welcome.

## Nurul Wahyuni Master's Thesis 4/20/2016

The Chebyshev polynomials arise in several mathematical contexts such as

approximation theory, numerical integration, and differential equations.

**Date:** 4/20/2016**Time:** 2:30PM-3:30PM**Place:** 121 Armstrong Hall

**Abstract:**

Here we study a combinatorial interpretation of Chebyshev polynomials due to Shapiro, and we use it to give a slight variation of a combinatorial proof of Binet’s Formula due to Benjamin, Derks and Quinn. Another beautiful formula for the Fibonacci numbers involves complex roots of unity. Presently, no combinatorial proof is known. We give combinatorial proofs of some related identities as progress toward a full combinatorial proof.

## 2016 Capstone

Capstone Day will be April 16, 2016 from 10:30am to 1:00pm. Capstone Day is a time for mathematics majors, who are finishing up their senior mathematics projects (capstones), to present their research to WVU mathematics students and faculty. The presentations are poster presentations and we encourage other mathematics students to attend this day to learn about the math capstones and see examples of what others are doing.

The schedule will be the following:

9:30 - 9:45 Students will set up their capstones

9:45 - 10:15 Graduating Capstone Students will take a computerized survey

10:15 - 10:30 Coffee Break and light refreshments

10:30 - 12:00 Capstone Presentations

12:00 - 1:00 Lunch

Please mark your calendar and join us for this event. Parents and friends are welcome.

## Actuarial Talk

Actuarial Student Club in the math department

will host a speaker, Lie Ma

**Date:** 4/8/2016**Time:** 3:30PM-5:00PM**Place:** 315 Armstrong Hall

Lie Ma is a Director and Actuary at Genworth Financial based in Richmond, VA. He obtained his FSA (Fellow of the Society of Actuaries) and CERA (Charter Enterprise Risk Analyst) in 2008.

He has 10 year experience in valuation, projection and modeling of life, health, and long term care products.

In his talk, he will cover the following topics:

1) Introduce a little bit about the company/internship program/actuarial student program

2) Talk about the different functions in the actuarial department (Life vs P&C, Consulting firm vs. Insurance company, Valuation vs. Pricing, etc.)

3) What would be a typical day for an actuary?

4) What are the factors to be considered when company hire from college graduates (Exams, Other technical and non-technical skills)?

5) Q&A

## Mr. Khalid Alsatami Ph.d Defense

A study on dicycles and

Eulerian subdigraphs

**Date:** 4/6/2016**Time:** 3:40PM-5:00PM**Place:** 315 Armstrong Hall

All are welcome.

## 2016 Integration Bee

Third Annual Integration

Bee Contest

This will be an integration contest open to all WVU students.

All integrals can be solved by techniques of Math 156.

More information can be obtained from the following links.

Website

Flyer

Rules

Please direct questions/comments:

Casian Pantea: cpantea@math.wvu.edu

Charis Tsikkou: tsikkou@math.wvu.edu

## Ms. Murong Xu Prospectus 3/3/2016

A study on graph coloring and digraph connectivity

**Date:** 1/29/2016**Time:** 3:40PM-5:30PM**Place:** 315 Armstrong Hall

Murong Xu

Everyone is invited. Following the talk and any discussion there will be an oral examination by his committee that is otherwise open only to graduate faculty that wish to attend in an observing capacity.

Research Prospectus: Download

## Mr. Mansour J. Algefari Ph.D Defense 2/17/2016

On supereulerian digraphs

**Date:** 2/17/2016**Time:** 3:30PM-5:00PM**Place:** 315 Armstrong Hall

All are welcome.

## Mr. Khalid A. Alsatami Prospectus 1/27/2016

A study on Dicycles

and Eulerian Subdigraphs

**Date:** 1/27/2016**Time:** 3:40PM-5:30PM**Place:** 306 Armstrong Hall

Khalid A. Alsatam

Everyone is invited. Following the talk and any discussion there will be an oral examination by his committee that is otherwise open only to graduate faculty that wish to attend in an observing capacity.

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