**Abstract:** In this talk we present a review on stochastic symplecticity (multi-symplecticity) and ergodicity of numerical methods for stochastic nonlinear Schrodinger (NLS) equation. The equation considered is charge conservative and has the multi-symplectic conservation law. Based a stochastic version of variational principle, we show that the phase flow of the equation, considered as an evolution equation, preserves the symplectic structure of the phase space. We give some symplectic integrators and multi-symplectic methods for the equation. By constructing control system and invariant control set, it is proved that the symplectic integrator, based on the central difference scheme, possesses a unique invariant measure on the unit sphere. Furthermore, by using the midpoint scheme, we get a full discretization which possesses the discrete charge conservation law and the discrete multi-symplectic conservation law. Utilizing the Poisson equation corresponding to the finite dimensional approximation, the convergence error between the temporal average of the full discretization and the ergodic limit of the symplectic method is derived (In collaboration with Dr. Chuchu Chen, Dr. Xu Wang and Dr. Liying Zhang).

# News Archive

## Stochastic PDE Seminar: Professor Jialin Hong (Chinese Academy of Mathematics and Systems Sciences)

## Robert Lang

Abstract: The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami and its underlying math has enabled safer airbags, Brobdingnagian space telescopes, and more.

Robert J. Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. With a Ph.D. in Applied Physics from Caltech, he has, during the course of work at NASA/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored over100 papers and 50 patents in lasers and optoelectronics as well as authoring, co-authoring, or editing 25 refereed papers, 17 books, and a CD-ROM on origami. Since 2001, he has been a full-time artist and consultant on origami and its applications to engineering problems. He received Caltech’s Distinguished Alumni Award, in 2009 and was elected a Fellow of the American Mathematical Society in 2013.

## Pamela Harris (Williams College)

Abstract: This talk is about the invisibility of points on the integer lattice ℤ ✕ ℤ, where we think of these points as (infinitely thin) trees. Standing at the origin one may notice that the tree at the integer lattice point (1, 1) blocks from view the trees at (2, 2), (3, 3), and, more generally, at (n, n) for any n ∈ ℤ≥0. In fact any tree at (ℓ, m) will be invisible from the origin whenever ? and m share any divisor d, since the tree at (ℓ/D, m/D), where D = gcd(ℓ, m) blocks (ℓ, m) from view. With this fact at hand, we will investigate the following questions. If the lines of sight are straight lines through the origin, then what is the probability that the tree at (ℓ, m) is visible? Meaning, that the tree (ℓ, m) is not blocked from view by a tree in front of it. Is possible for us to find forests of trees (rectangular regions of adjacent lattice points) in which all trees are invisible? If it is possible to find such forests, how large can those forests be? What happens if the lines of sight are no longer straight lines through the origin, i.e. functions of the form f(x) = ax with , but instead are functions of the form f(x) = axb with b a positive integer and a ∈ ℚ? Along this mathematical journey, I will also discuss invisibility as it deals with the underrepresentation of women and minorities in the mathematical sciences and I will share the work I have done to help bring more visibility to the mathematical contributions of Latinx and Hispanic Mathematicians.

Math work is joint with Bethany Kubik, Edray Goins, and Aba Mbirika. Diversity work with Alexander Diaz-Lopez, Alicia Prieto Langarica, and Gabriel Sosa.

Biography: Pamela E. Harris is a Mexican-American Assistant Professor in the department of Mathematics and Statistics at Williams College. She received her B.S. from Marquette University, and M.S. and Ph.D. in mathematics from the University of Wisconsin-Milwaukee. Her research interests are in algebra and combinatorics, particularly as these subjects relate to the representation theory of Lie algebras. Her recent research on vector partition functions and projects in graph theory has been supported through awards from the National Science Foundation and the Center for Undergraduate Research in Mathematics. Harris co-organizes research symposia and professional development sessions for the national conference of the Society for the Advancement of Chicanos/Hispanics and Native Americans in Science, was a Mathematical Association of America’s Project NExT (New Experiences in Teaching) Fellow from 2012-2013, and is an editor of the e-Mentoring Network blog of the American Mathematical Society. In 2016, she co-founded www.Lathisms.org an online platform that features prominently the extent of the research and mentoring contributions of Latins and Hispanics in the Mathematical Sciences. She is also the lead editor for the Special Issue on Motherhood and Mathematics of the Journal of Humanistic Mathematics.

## Ross Curtis (AncestryDNA)

Title: From Science to Product at AncestryDNA

Abstract: Converting cutting-edge research into everyday consumer products is exciting and challenging. In this talk I will discuss recent groundbreaking research (published in Nature Communications) that identifies recent populations using genetic data from our direct to consumer DNA business. Then, I will highlight some of the process that went into turning that research into a product that helps users connect with recent populations their ancestors may have come from.

Biography: Ross Curtis joined the AncestryDNA team in January of 2012. He is a computational biologist specializing in genetics and visual analytics and loves applying his expertise to family history and genealogy. Before AncestryDNA, Dr. Curtis focused on using visualization and statistics to discover genetic mutations that contribute to disease. Dr. Curtis received his B.S. from Brigham Young University and his Ph.D. in Computational Biology from Carnegie Mellon University.

Join us Thursday, November 16 at 4:30 in TMCB 1170 to hear about Ross’ experience on the AncestryDNA team.

## Emily Evans (BYU)

Talk Title: The Secret Life of Math

Abstract: How does computer-aided design work? How can you use probability to find integrals? How does Google know the best web pages to list? How are realistic animations of sand and snow made? How can you win your March Madness pool? Come hear the answer to these and other questions, and discover the secret life of math.

Date: Thursday, March 1, 2018

Place: 1170 TMCB

Time: 4:00 PM

## Dana Richards(George Mason)

The vast majority of mathematical puzzles ask for the existence of a solution. It is merely an exercise when the method is known and it is more of a puzzle when the method is not clear. An algorithmic puzzle takes this further by only asking for the method itself or a property of the method. It is in this sense that much of computer science is puzzle solving. We discuss the theory behind this in the context of material taken from Martin Gardner’s Scientific American column. The answer to the following puzzle will be given:

There are five pirates dividing up 100 gold coins. Pirates are strictly ordered by seniority, are very logical and wish to live. The rule pirates use to divide gold is: (1) the most senior pirate suggests a division, (2) all pirates vote on it, (3) if at least half vote for it then it is done, otherwise the senior pirate is killed and the process starts over. What happens?

Dana Richards is an associate professor of Computer Science at George Mason University. His research is on theoretical and algorithmic topics. He has been a friend of Martin Gardner for nearly four decades and has edited Gardner’s book

The Colossal Book of Short Puzzles and Problems.

Join us at 4:00 on March 22nd to hear from Dana in 1170 TMCB.

## Daryl Cooper (University of California – Santa Barbara)

The hyperreals are an ordered field containing the real

numbers as well as infinitesimals and infinitely large

numbers. In some sense they have ALL the properties of

the real numbers. They have languished for 60 years,

spurned by most professionals. The situation recalls the

slow acceptance of other extensions of the concept of

number. I will construct the hyperreals, and say a few

words about doing geometry and topology with these guys.

Refreshments at 3:30 294 TMCB

## Rodney Forcade (BYU)

The open problem of covering k-dimensional space with laice translates of

a simplex as efficiently as possible is related to the problem of generating a

finite Abelian group with k generators and with shortest possible maximum

word-length. For k≥3 the best answer is not known, but it leads into many

interesting corners of mathematics — calculus, combinatorics, convexity,

groups, even a lile algebraic geometry.

Refreshments at 3:30 294 TMCB

## Bob Pego (Carnegie Mellon)

Coaglation-fragmentation equations are simple, nonlocal models for

evolution of the size distribution of clusters, appearing widely in science

and technology. But few general analytical results characterize their

dynamics. Solutions can exhibit self-similar growth, singular mass

transport, and weak or slow approach to equilibrium. I will review some

recent results in this vein, discussing: the cutoff phenomenon (as in card

shuffling) for Becker-Doering equilibration dynamics; equilibrium and

spreading profiles in a data-driven model of fish school size; and an

individual-based jump-process description of group-size dynamics. A

special role is played by Bernstein transforms and complex function

theory for Pick or Herglotz functions.

Refreshments at 3:30 294 TMCB

## Chris Jones – Where Does Mathematics Come into Climate Science?

Climate science currently revolves

around massive computational

models that run at just a few

centers around the world. These

are mathematical objects in that

they offer mathematical replicas

of the world we inhabit.

Nevertheless, it is hard to see how

the art of mathematics fits in with

computational modeling at this

scale. Why we mathematicians

are badly needed will be

discussed in this lecture, as well as

how we can contribute to the

climate science enterprise.