RECORD- BREAKING 19 students earn Ph.D.s in 2018 See Pages 3, 19 { { Fall 2018 MathA publication of the Department of Mathematics News at the University of Nebraska–Lincoln Peterson reaches 50 years at UNL our faculty members earned 50-year Service Awards Ffrom the University of Nebraska–Lincoln in 2018. One was the math department’s own Allan Peterson. Peterson joined fellow Professors Edward Becker, Roger Bruning, and Brett Ratcliffe in receiving the award from Chancellor Ronnie Green in September. Peterson also was recognized at the Department’s April reception. Peterson has taught 51 years without interruption — he has never taken a sabbatical since he arrived in 1968, because he loves teaching so much. “In the history of the math department, I’ve taught more than anybody,” Peterson added. However, he plans to retire at the end of 2018-2019 academic year for health reasons. Peterson was diagnosed LINDSAY AUGUSTYN/UNL CSMCE with prostate cancer three years ago. Allan Peterson accepts a gift from the Department and Chair See PETERSON on Page 10 Tom Marley (left) at the April 2018 recognition reception. Peterson’s achievements, as well delivered a campaign speech on UNL’s as his completion of 50 years as a campus in advance of the Nebraska VIEW FROM THE faculty member, are nothing short of primary. This anecdote brought home remarkable. He has published over to me that Al’s tenure has covered 200 research articles, supervised 32 some truly fascinating times and seen CHAIR Ph.D. students, and consistently been many changes. However, through it regarded as one of the top teachers in all, Al has been a steady beacon for Tom Marley the Department for five decades. In excellence in research and teaching chatting with Al about his early days and a role model for our faculty. t has been a year of records at Nebraska, I was reminded that his The Department also hit a new Ifor the Nebraska Department job interview in 1968 took place on milestone by graduating 19 Ph.D.s of Mathematics. Professor Al the same day that Bobby Kennedy See CHAIR on Page 8 DEPARTMENT NEWS: FACULTY NEWS: Hermiller ALUMNI NEWS: Bors { Two Rowlee lectures named AMS Fellow, Walker retires from U.S. Strategic hosted this year Page 4 an AWM Fellow Page 11 Command Page 14 { INSIDE: www.math.unl.edu/friends Fall 2018 1 {Research News Larios streamlines turbulence models f you have ever looked up at the the initial state of a Richardson’s careful calculations were Iclouds and marveled at their fluid, the equations incorrect by two orders of magnitude seemingly unlimited complexity, or choreograph the for a six-hour forecast. watched the cream in a cup of coffee motion of the fluid. To get around these difficulties, spiral into ever more intricate patterns Imagine trying modern researchers use a class of until it diffuses into a brownish haze, to predict how a techniques known as data assimilation. then you have glimpsed the strange particular dance Data assimilation eliminates the need and chaotic world of turbulence. would progress, for complete initial data. It instead Turbulence is nearly ubiquitous given only the incorporates incoming data into in science as well as everyday life, Adam Larios starting positions simulations by asking the simulated appearing in diverse areas such of the dancers, and solution to strike a balance between as weather prediction, aerospace a description of the choreography. For following the rules of the dynamical technology, and blood flow in the a slow simple dance, we might have system, and staying close to the heart. Understanding, quantifying, and some luck, but to bring the analogy observed data. It is as if, in trying to predicting turbulence have become closer to turbulence, imagine a fast, predict the outcome of our billion extremely important, yet elusive goals highly chaotic dance involving billions chaotic dancers, we had livestreaming in science and engineering. of dancers. Also imagine that the video cameras set up in several On a mathematical level, turbulent choreography is only a list of local locations to get an idea of the current fluids (including air and gasses) are rules for how dancers should interact state of the dance as it progressed. thought to be governed by the Navier- with their nearest neighbors. Such a This data could be fed into a computer Stokes equations, a system of partial dance might take on wildly complex, running a simulation that knows differential equations (PDEs) that is large-scale patterns that would be the local rules, but was started with simple to write down, but is so difficult nearly impossible to predict and inaccurate initial data. to work with that, in 2000, the Clay may be highly dependent on starting Classic data assimilation is based Mathematics Institute issued a $1 positions. In turbulent fluids, the local on a set of techniques known as the million prize to show mathematically rules are given by the Navier-Stokes Kalman filter. However, the Kalman whether the solutions remain physically equations, and the large-scale patterns filter is computationally expensive to realistic for all times. This problem has are things like hurricanes, solar storms, compute and limited in what it can been open since the work of Jean Leray or rapidly varying ocean currents. be applied to. In a 2014 paper by A. in 1932. Nevertheless, the effort to find Although the Navier-Stokes Azouani, E. Olson, and E. Titi, a new accurate, practical tools for predicting equations are hard, there is an even approach was proposed (now called the turbulence continues. The research of more fundamental difficulty: In real AOT algorithm). The idea abandons Assistant Professor Adam Larios has life, one typically does not fully know the expensive statistical methods of helped to further this effort. the initial condition. For example, in the Kalman filter and instead uses a To describe Dr. Larios’ work, we weather prediction, the current state feedback-control term at the PDE level. need to understand the notion of a of the weather is measured at locations This new approach is far less expensive dynamical system. A dynamical system spaced apart by roughly 1 kilometer and was mathematically proven to consists of a starting condition and on average, but the Navier-Stokes force the simulation to converge to the some laws that describe how things equations require initial data at every true solution exponentially quickly in change in time. Picture a group of location in space, down to roughly time. This paper set off a storm in the dancers just before the dance starts, millimeter scales. One option is to research world, with over 30 papers frozen in their starting positions. In interpolate the data, e.g., by assuming based on the AOT algorithm coming a dynamical system, this is known as the data vary linearly in between out in the last four years. the initial condition. Suddenly, the weather stations, but such a scheme Larios’ recent research has music starts, the scene comes to life, introduces a tremendous amount proposed several modifications to and the dance progresses according of error into the initial condition, the AOT algorithm. The first was a to its internal choreography. This which then grows exponentially fast nonlinear version of the algorithm, choreography is analogous to the in time due to the system’s underling which resulted in super-exponential governing laws of the dynamical chaos. Such an idea was tried by convergence rates. In 2017, Larios system. The Navier-Stokes equations mathematician Lewis Fry Richardson was awarded an individual investi- of fluids are a dynamical system in 1922, in the first-ever attempt gator grant by the National Science governing the motion of fluids. Given at numerical weather forecasting. See RESEARCH on Page 6 2 Fall 2018 www.math.unl.edu/give { Department News 2018 Ph.D. class breaks records with many firsts 018 marks the 120th year since 2Albert Candy earned the first Ph.D. in mathematics awarded by the University of Nebraska. It would take 55 years for Clinton Burke Gass to become the mathematics department’s MATHEMATICS 10th Ph.D. in mathematics and 65 years for Mildred Gross to become the first woman to earn a Ph.D. in mathematics. That year, 1963, was a banner year as the Department awarded four Ph.D.s, including the Renovations add new Department’s 19th Ph.D. It is interesting to contrast the Department’s early doctoral education Calculus classrooms history with 2018, a year in which 19 outstanding graduate students earned a Ph.D. from the Department hings are looking different for Lecturer Janet Emery, who has of Mathematics. This was the most Math 106 and 107 (Calculus I and taught a range of introductory courses T Ph.D.s ever awarded in one year, II) students this semester. Based on the for more than 15 years, said she uses breaking the record of 15, which was positive feedback from the Brace Labs the interactive features of the new set in 2015. renovations, the Math Department boards in the classrooms as much as The 2018 Ph.D. class is unusual transformed five rooms in Louise she can, which helps her students pay in several ways. First, the majority Pound Hall (formerly CBA) into active more attention. of the class is female (10). This learning classrooms to allow for more Undergraduate math and compares well with the fact that, student collaboration. secondary math education major nationally, only about 26% of new Classrooms that used to look like Elizabeth Tyler (see Page 17) has been Ph.D.s are women, and continues the rows of desks facing one instructor teaching recitations for five semesters Department’s reputation as being a now feature projectors, document and has seen a dramatic increase in place where female graduate students cameras, whiteboards on every wall, attendance, which she credits to these are successful.