Summer 2008 Reckonings Reckonings: (n. pl.) 1. Computations or summations 2. Acts of thought or reasoning 3. The newsletter of the Department of Mathematical Sciences at the University of Delaware

Chair’s Message The Family Tree of Peter Monk I shall advice – because it was clear to me Mathematics remember at the time that tenure could only be this year obtained by working every hour of for a very consciousness. significant Besides Ivar’s departure, we reason: after have also had an important arrival. 33 years at Professor Alfinio Flores has joined Delaware, us from Arizona State University. Professor Alfinio is the first Hollowell Professor Ivar Stakgold of Mathematics Education. This has left professorship was endowed by the Delaware great generosity of Drs David and for the University of San Diego where Kathy Hollowell. Alfinio is currently he has been offered a position as an Director of Secondary Mathematics emeritus professor, and where he will Education in the Department and has be closer to his family. For as long as I been working hard to establish ties have been at Delaware, Ivar has been a in the University, and settle into the respected member of the Department. Department. Ivar arrived at Delaware as Chair in Mathematicians have families too 1975, serving as Chair until 1991. At a higher level, the University has also welcomed as President, and now they can be tracked through He retired in 1995 but remained the Mathematics Genealogy Project. In an active emeritus faculty member Patrick Harker from the University of mathematics, family relationships are through March of 2008. I think it is Pennsylvania. Academically, President true to say that Ivar deserves a great continued on page 2 defined through the advisor-student deal of the credit for building the relationship. If Professor Smith earned Department to its present position as Chair’s Message...... 1 his Ph.D. under the advisement of a recognized research unit. His arrival The Family Tree of Mathematics...... 1 Professor Jones, then Professor Smith coincided with a brave investment is considered the mathematical son by the UNIDEL foundation in our From the Editor ...... 2 or daughter of Professor Jones. More Department and also with the hiring New Approaches in Solving Saddle than just a frivolous “six degrees of several of our best known faculty. Point Problems...... 3 of freedom” type exercise, tracking Under his leadership, Delaware became Where Do We Come From and Where Are mathematical family trees allows one known as a center of excellence in areas We Going?...... 3 to trace mathematical influences and such as Applied Mathematics, Analysis and Combinatorics. Optimization of Density Functional Methods study the intellectual development of for Atomic Structure Calculations...... 4 the various branches of mathematics. Besides nurturing the Department The Mathematics Genealogy Project was (with an iron fist – at least from the Brief News Items from the Math point of view of a junior assistant Department...... 5 begun by University of Delaware alumni professor when I arrived at UD in Connections-The Department and Local Harold Coonce. Professor Coonce, now 1982!), he also added to our national High Schools...... 6 an adjunct professor at North Dakota stature by serving as President of the International Conference on Inverse State University, completed his Ph.D. in Society for Industrial and Applied Scattering Problem...... 7 1969 under Professor Malcom Robertson Mathematics (SIAM) from 1989 to Seminar on stochastic processes conference in the area of complex variables. A quick 1990. 2008 at UD...... 7 search of the Mathematics Genealogy To me Ivar exemplifies a love of Project’s database reveals that Professor Donald Marquardt (1929-1997)...... 8 applied mathematics, and scholarship Coonce is a direct descendent of in mathematics. But he could also give UD Math Students Score Big in the Putnam Weirstrauss and an academic cousin of interesting advice. At one point when I and MCM Competition...... 9 Erdos and Von Neumann! You can trace was a junior assistant professor he told New Faculty...... 9 your own mathematical family tree or me not to work more than eight hours Featured Graduate: Derek Moulton...... 10 that of your favorite professor at www. a day! He told me that if I could not genealogy.ams.org. do the job in that time, I wasn’t up 2008 Student Award Recipients...... 10 to the job. This was quite worrying Donors...... 11 Chairs Message continued from cover Harker works on operations consisting of Tobin Driscoll, Louis research, and is in fact a “highly Rossi and Tobin Driscoll. From the Editor cited” researcher in mathematics Supported by alumni donations, according to the respected our undergraduate students have Dear Department Alumni, Students, and “Web of Science” database. So taken part in the Putnam Exam Friends, it is not too much of a stretch (one team ranked 66th) and the to claim that President Harker It is my pleasure to distribute our Mathematical Contest in Modeling fourth edition of Reckonings. As in our continues the tradition of having (MCM). One interdisciplinary previous three issues, you’ll find an a mathematician as President of team in the MCM earned the University (both Presidents our first ever “Outstanding” update on the department from our Roselle and Trabant were trained award (one of 5 out of 568 chairman, a collection of news items as mathematicians). contestants) and another team highlighting the events and milestones of President Harker has initiated a earned a “meritorious” rating. the past year, and profiles of new faculty program to review and determine The Putnam and MCM contests and current students. In addition, you’ll strategic directions for the are two examples of enrichment find articles profiling our distinguished University. Significantly for our activities funded by donations alumni, and articles reporting on some Department, early indications are to the Department. These are of the exciting research being carried that graduate education is one very important to us and allow out by faculty in our department. direction that will be emphasized us to put a “Delaware Stamp” Professor Sturm has contributed a much more strongly in the future. on undergraduate and graduate The graduate program is of education. I would like to take fascinating article on her research in enormous importance to both our this opportunity to thank all probability. The possible implications of educational and research missions. our donors, particularly Kathy this work are profound and as you’ll see, Currently, our graduate program and David Hollowell, for their address questions that concern us all. has grown to 49 students, and generosity this year. In the article “Optimization of Density this year we expect to graduate no One of the goals when Ivar Functional Methods for Atomic Structure less than eight PhDs (4 in pure Stakgold was hired as chair was Calculations,” Professor Luke takes mathematics and 4 in applied to enhance the research level us on a tour of the atomic world and mathematics). and visibility of the Department. describes some of the neat experiments Some of our students graduate Building on the work of the he’s carried out in the department’s MEC and move to non-academic previous chair, Willard Baxter, he Lab. In this issue, you’ll also get to learn careers, but most remain in was extremely successful and our how mathematicians follow their family 2 academia. To help them prepare Department now has a thriving trees and ways in which mathematics is for their future teaching mission, research enterprise and graduate we are creating a small number of program. We continue to improve considered a competitive sport. “Stakgold Teaching Assistants”. with grant income up 13% last I would like to thank all of the Students in these positions will be year and the faculty publishing contributors to this newsletter, but drawn from our most experienced roughly 70 papers over the year. assistants, and will be assigned In addition the Department has especially Russell Luke, Anja Sturm, to teach classes in our regular established a collaborative research Peter Monk, Constantin Bacuta, Cristina semesters under the watchful program with Ecole Polytechnique Bacuta, and Fioralba Cakoni. I’d also like eye of faculty mentors. This in Paris, France (Professor Cakoni to thank Elizabeth Dunkle from UD’s will provide better preparation is heading the Delaware team). Office of Publications for all of her help for future teaching jobs, and This will facilitate visits of graduate with the design and layout of this and recognizes Ivar Stakgold’s students and faculty in scattering past newsletters. commitment to education. theory between Delaware and When Ivar Stakgold first came Paris. I’d like to encourage everyone to to Delaware, one important Looking forward, the regularly check the department’s home step forward was to revamp the Department will need to work page (www.math.udel.edu), where undergraduate calculus sequence inside President Harker’s vision you’ll find up-to-date news about the with the aid of a Sloan Grant. In to continue to improve the department and its activities. If you addition Discrete Mathematics scholarship, both teaching and have news you’d like to share, either on was added to the curriculum. research, in the Department to the web page or in future editions of Our undergraduate program enhance our global reputation in Reckonings, please feel free to send me an continues to evolve with two mathematical sciences. We hope email at [email protected]. I look new degree programs: a BS also to have a more active dialogue forward to hearing from you. in Quantitative Biology (in with alumni to help facilitate this cooperation the Department of growth. Best wishes, Biological Sciences) and a BS in To end these comments, I Mathematics Education. The would like to take this opportunity BS in Quantitative Biology is the to thank Ivar for everything that most obvious manifestation of he has done for the Department several years of cooperation with and University, and to wish him Biological Sciences by a team of the very best of good fortune in faculty led by John A. Pelesko and his new endeavors. John A. Pelesko methods for such PDEs and a new in my previous projects. The proposed New approaches in approach for Maxwell’s equations with work for solving saddle point systems solving Saddle Point practical applications to computing has scientific and technical applications modes for devices and to radar in optimization, optimal control, Problems scattering. computational fluid dynamics, linear elasticity, electromagnetism, electrical Constantin Bacuta My research for this project will focus on two areas: solving saddle networks, linear models in statistics Modeling the air flow near a plane point problems and discretization on and image restoration. A second or modeling the flow near immersible non-matching grids. To build new and area of research will be to investigate objects involves the solving of complex efficient algorithms, I will combine new multilevel discretizations and multi- partial differential equations (PDEs) ideas on solving saddle point problems level preconditioning techniques in including second-order elliptic with already known methods from the context of discretizations on non- problems, Stokes and Navier-Stokes distinctive fields of numerical analysis matching grids based on the Partition systems. such as iterative methods, multilevel of Unity method. The applications In September 2007, I was awarded methods and adaptive methods for are to modeling fluid and gas flow an NSF grant for my research on elliptic PDEs. The main technique will near complex objects and fluid flow in developing and implementing faster be based on the new spectral results porous media. and more efficient computational for saddle point systems that I found

due to inherent randomness (plain applications, the goal is to describe Where do we come “luck” or “bad luck”) or a selective the distribution of genetic variability from and where are advantage or disadvantage stemming one should expect to see in the sample from the genetic type of an individual, given these characteristic influences. we going? its location, or its surrounding Comparison with data then allows for environment (e.g. competing inference of the population’s history. Anja Sturm individuals). Recently, I have received On the level of individuals this answers My research interests lie in funding from the National Science to the question “Where did we come probability theory and its applications. Foundation to continue to develop from?” On the level of genes it also The main focus of my work has the mathematical theory on various sheds light onto the importance and been on probability models and aspects of such spatial models with function of particular parts of our 3 stochastic processes that describe varying offspring laws. genetic code. the evolution of interacting particle Backward in time the focus is on Forward in time one of the central systems and population models analyzing the genealogical tree of forward and backward in time. Many questions being addressed is to a small sample from a population determine parameter regimes for long- of these models have implications for and their diffusion limits – i.e. the applied sciences, especially for term survival without explosion of the as the population grows. These population size and -if multiple types Biology and Physics. My particular models of genealogies are also of particles are present initially- of interest has been on models in known as coalescent processes long-term coexistence of various or population genetics and ecology. because the ancestral lines forming all types. Stochastic particle models Here, realistic mathematical models of the genealogical tree of the sample that may exhibit such phenomena the underlying processes that govern coalesce as we follow them into the are generally spatial models with which genes are passed on from one past. Such coalescent processes an interaction mechanism between generation to the next are of ever connected to populations models particles that gives small populations increasing importance as they are with singular offspring distributions prerequisite to the correct quantitative - corresponding to potentially large (of a particular type) an advantage. analysis and interpretation of the individual families - have attracted Unlike these particle systems with unprecedented quantities of genetic much recent attention as several self-regulation those with independent data available today. deep connections to different classes reproduction of all individuals, which My own recent research in this of stochastic processes have been are mathematically simpler and have area has centered on suitably chosen discovered and exploited, albeit in been well-studied, do not have this models of populations (individuals or a non-spatial setting. On the other property and are known either to go genes) that realistically incorporate hand, spatial settings arising from extinct or to explode. The ultimate the influence of two factors which models with population subdivision goal is to determine whether there have a significant impact on genetic and migration (and small offspring are phase transitions in the parameter data: firstly, spatial substructure of variances) have been studied for some space that separate survival of the the population manifesting itself time. In my work, one aim will be to populations from extinction and through local reproduction and bring these two directions of research coexistence from dominance of single interaction as well as locally varying together by studying the genealogies types. This allows one to conclude environments; secondly, variations in of spatial population models with which mechanisms and forces lead to a reproductive success as they may arise larger offspring variances. For stable population with lasting diversity. If F is contractive, then, by Banach’s same techniques are used for solving Optimization of Fixed Point Theorem, the simple the inverse problem of determining Density Functional iteration the electron density from diffraction images. In some cases this problem Methods for Atomic ρ = F(ρ ) can be solved directly. Hauptman ν+1 ν (mathematician) and Karle won the Structure Nobel Prize in 1985 for solving this Calculations will converge to a fixed point. problem. Still, for large, nonperiodic Unfortunately, F is almost never molecules these direct techniques don’t Russell Luke contractive and seldom has even work, and projection algorithms start a closed-form representation. So to shine. Fundamental mathematical numerically, we expect the worst and questions about the behavior of We address the numerical challenges hope for the best. facing simulations and reconstructions proximal point and projection In particular we focus on algorithms of molecules from first principles algorithms in nonconvex, inconsistent for nonlinear (more to the point, models at atomic scales; these are: settings such as this remain open and nonconvex), nonsmooth fixed point dimensionality, nonlinearity, multiple must be addressed before further operators. We study regularized (for scales, and model inconsistency. In progress in algorithms is possible. stability), preconditioned (for multiple simplest terms, the problem is to Determining the weakest regularity scales), limited memory (for high determine the “locations” of the requirements for achieving linear rates dimensional problems) quasi-Newton electrons in a molecule given fixed of convergence of simple projection (for nonsmoothness) methods in a nuclei. The governing equation is algorithms is currently an active area trust region framework (linking local the Schroedinger equation and the of research in the variational analysis and global methods) for solving the electrons are described by vector- Kohn-Sham equations. We look to community and a topic that I am valued wavefunctions that minimize mathematical and physical insight working on with Adrian Lewis of the the energy of the molecule for a to determine scalings of quasi- School of Operations Research and given temperature and fixed nucleus Newton methods in order to avoid Industrial Engineering at Cornell locations. Due to the dimensionality of ill-conditioned matrices that slow University. This offers a rare marriage the problems, current methods can only convergence. of application and theory. So far, we determine wavefunctions for molecules can prove linear convergence of simple 4 with several hundred atoms. Density My first stab at the problem, alternating projections between a closed Functional Theory (DFT) addresses the together with Laurence Marks at the set and a so-called prox-regular set curse of dimensionality (by a factor of Department of Materials Science at (that is, a set for which the projector three) by exploiting the correspondence Northwestern University, has been is locally single-valued). This, to date, between the wavefunctions and scalar- included in the latest release of the valued electron density functions. DFT Wien2k computational chemistry is the most general statement on the was the beginning of a new field of software package out of the Technical matter. Whether this applies to the chemistry, computational chemistry, University of Vienna which has over more complicated algorithms that I use for which Walter Kohn and John Pople 1000 registered users. So far we’ve for my inverse problem is still an open won the Nobel Prize in 1998. One beaten the state of the art by, on question. of the first and most widely used DFT average, a factor of three, and in some The research project outlined here is approximations is due to Kohn and cases ours is the only method that integrated with graduate education and works. Sham. Under the Kohn-Sham model, offers young researchers an excellent the density one seeks is the fixed point There are some nice connections opportunity to combine fundamental of a mapping of the densities that to proximal point algorithms and mathematical research with high- approximates the Frechet derivative of operator splitting strategies that impact practical applications and the Schroedinger Hamiltonian with will be key to increasing the size of interdisciplinary work. Undergraduates respect to the electronic wavefunctions. systems that can be solved. Projection are also encouraged to get involved Mathematically, its “just” a fixed point algorithms (a special case of proximal through a hands-on diffraction problem: point algorithms) are a promising laboratory up and running in our MEC alternative to conventional path- Lab that allows students to create their find ρ such that F(ρ) = ρ following techniques and open the door to the possibility of tackling the exact own “crystals” on transparency film electronic structure equations without and measure the resulting diffraction where F is the Kohn-Sham operator resorting to the approximations of patterns created by illumination from and ρ is the electron density. density functional theory. These an ordinary laser. Brief News Items from the Math Department Professor Xiang receives NSF grant tion to study the optimization of density on biologically inspired wireless network- Professor Qing Xiang has received a functional methods for atomic structure ing and funding provided will allow grant from the National Science Founda- calculations. This grant will allow Profes- Professor Rossi and his collaborator, Dr. tion to study the invariants of incidence sor Luke and his collaborators at North- Chien-Chung Shen, to study new and matrices, difference sets and strongly western University’s Department of novel networks such as mobile ad hoc Material Science to address the numerical regular graphs. This grant will support networks, wireless sensor and actuator challenges facing simulations of mole- Professor Xiang and his collaborators in cules built upon atomic-scale physics and networks, and large grid and point to their efforts to develop the mathemat- chemistry. This work has the potential point networks. In this project, Professor ics underlying technologies such as CD to impact the design of nanostructured Rossi and Dr. Shen will take inspiration players, high speed modems, and cellular materials and efficient fuel cells. from biology, in particular, the behavior phones. Students speak at the department’s of swarms of biological organisms, to annual Undergraduate Symposium design adaptive network architectures for novel networks. Professor Wenbo Li named to editorial On April 7, 2007, the Math Department hosted its annual symposium for under- board of Journal of Theoretical Prob- graduate summer research students. This ability. year’s speakers were Donald Knieriem, Professor Cai has been selected as an Professor Wenbo Li has been named Lucero Carmona, Kyle Stern, Paul ACE Fellow to the editorial board of the Journal Parson, Peter Ucciferro, Van T. Lam, Professor Jinfa Cai has been selected of Theoretical Probability. The journal and Haozhu Wang. as one of the 37 American Council on publishes high-quality, original papers in These students were supervised by Pro- Education (ACE) fellows in 2007-2008 all areas of probability theory, including fessors Richard Braun, John A. Pelesko, academic year. Professor Cai will spend probability on semigroups, groups, vec- Louis F. Rossi, and Chien-Chung Shen. the academic year at Temple University, tor spaces, other abstract structures, and working directly with President Ann random matrices. This multidisciplinary Professor Bacuta receives NSF Grant Weaver Hart to observe and participate quarterly provides mathematicians and Professor Constantin Bacuta has re- in key meetings and events, and take on researchers in physics, engineering, ceived a grant from the National Science special projects and assignments while Foundation to study new approaches statistics, and computer science with a under the mentorship of President Hart in solving saddle point problems. This peer-reviewed forum for the exchange and other senior administrators. The of vital ideas in the field of theoretical grant will support his research in the areas of both saddle point problems and ACE Fellowship Program was estab- 5 probability. discretization on non-matching grids. lished in 1965 to strengthen leader- The new algorithms he will build have ship in American higher education by Professor’s Rossi, Driscoll and Luke applications to problems in optimization, identifying and preparing promising awarded grant to expand mathematics optimal control, computational fluid faculty and staff members for responsible dynamics, linear elasticity, electromagne- teaching software. administrative positions. tism, electrical networks, linear models in Professors Louis F. Rossi, Tobin A. statistics, and image restoration. Driscoll and Russell Luke have received Professor Roselle newest mathematics a grant from the University of Dela- Professor Emeritus Professor Sturm receives NSF grant ware’s Center For Teaching Effectiveness Professor Anja Sturm has received a Professor David Roselle, longtime to expand applications of the MapleTA president of the University of Delaware, software for use in pre-calculus, calculus, grant from the National Science Founda- tion to study spatial models for popula- and faculty member in the Department linear algebra and ordinary differential tions with variable offspring laws. This of Mathematical Sciences, has been equations courses. MapleTA is a web- grant will support Professor Sturm’s granted the status of Professor Emeritus based automatic problem generation research in spatial stochastic processes of Mathematical Sciences by the board tool that provides students unlimited that model self-regulation. The ques- of trustees of the university. In their opportunities to hone their problem tions explored in this work are of interest May 2007 meeting they also granted solving skills. The project is also support- in epidemiology, ecology, and genetics. Professor Roselle the status of President The applications range from reconstruct- ing a pilot program this summer to see Emeritus. if ALEKS (another automated learning ing the origin and history of humans to package) can improve the performance locating and identifying genes on the of incoming engineering majors who genome that are causative factors for Professor Rossi named to the editorial traditionally have trouble making the diseases. board of SIAM’s newest journal transition from high school pre-calculus Professor Louis F. Rossi has accepted topics to college level calculus courses. Professor Rossi receives NSF grant and a position as a founding editor for the Army SBIR grant Society of Industrial and Applied Math- Professor R. Luke receives NSF Grant Professor Louis F. Rossi has received two ematics’ newest journal, SIAM Under- grants, one from the National Science graduate Research Online (SURO). The Professor Russell Luke has received a Foundation, the other from the U.S. goal of SURO is to publish the best of grant from the National Science Founda- Army SBIR Program. These grants focus undergraduate research in applied and continued on page 6 computational mathematics. The new Prof. Driscoll named to the editorial Goldwater Scholarship. The scholar- journal will publish papers authored board of the SIAM Journal on Scientific ship program, honoring the late U.S. solely by undergraduate students or Computing Sen. Barry M. Goldwater of Arizona, is designed to encourage outstanding teams of undergraduate students. The Professor Tobin A. Driscoll has been students to pursue careers in the fields respected and experienced editorial named an associate editor of the SIAM of mathematics, the natural sciences and board is charged with applying profes- Journal on Scientific Computing. The sional peer review to the unique needs of engineering. The Goldwater Scholarship SIAM Journal on Scientific Computing is the premier undergraduate award of its undergraduates, including a fast turn- contains research articles on numerical type in these fields and students compete around time from reviewers and a rapid methods and techniques for scientific nationally for the award. acceptance-to-production time-line so computation. According to ISI journal that students will see their work pub- reports for 2006, SISC has the 6th- Mathematics Department Graduates lished before they graduate. highest impact factor among all applied Nine New Ph.D’s mathematics journals. In 2008, the Department of Mathemati- Professor Cook elected to second term cal Sciences graduated nine new Ph.D’s. as SIAM Secretary Professors Cakoni, Colton, and Monk Students receiving their doctorate are Professor L. Pamela Cook has been receive Air Force Grant Jon Regan Beckham, Craig Culbert, elected to a second term as Secretary of Professors Fioralba Cakoni, David Todd Gutekunst, Alfa Heryudono, the Society for Industrial and Applied Colton, and Peter Monk have been Derek Moulton, Zeying Wang, Noam Mathematics. Professor Cook will con- awarded a three year grant from the Air Zeev, Xinyi Zhang, and Junhua Wu. tinue in office for an additional two-year Force Office of Scientific Research. This Congratulations to all of our graduates. term: January 1, 2008 to December 31, project is concerned with problems in 2009. electromagnetic imaging where weak Prof. Bettyann Daley receives degree in Prof. Lou Rossi recognized as exem- scattering models and nonlinear optimi- education. plary assessment fellow zation techniques are inappropriate. The Professor Bettyann Daley has received specific problems to be considered are a Doctor of Education degree with Professor Louis F. Rossi has been named the non-destructive testing of dielectrics, as one of three faculty at UD named a major in educational leadership. the detection of caves and tunnels in the Her thesis was entitled: “A College Exemplary Assessment Faculty Fellows. earth and imaging problems associated The award recognizes Prof. Rossi’s Departmental Plan to Address the with anisotropic materials. activities working with his colleagues and Deficient Algebra Problem in College 6 the Office of Educational Assessment to Freshmen.” In her work she studied develop a comprehensive assessment plan the difficulties students have when Mathematics Student Chosen as Gold- transitioning from high school to college for our undergraduate programs and for water Scholar his efforts to apply the same rigorous mathematics for students in majors that thinking and analysis used in mathemati- Congratulations to mathematics major do not require more then one or two cal research to our teaching activities. Spencer Tofts who has won a prestigious semesters of mathematics.

Connections – Delaware. Many of the state’s students. In November, Cristina Bacuta, mathematics teachers have been trained along with Christine Ebert, organized The Department and in our department, some of our faculty a professional development day for Local High Schools teach advanced courses in local high the mathematics faculty of Newark schools, and over the last few years, High School. Professors Kay Biondi, Professor’s John A. Pelesko and Cristina Christine Ebert, and Gary Ebert, gave Bacuta have worked to provide novel presentations and led interactive sessions professional development training for for this group. Professor’s Peter Monk, in-service high school mathematics John A. Pelesko, and Joseph Pika, also teachers. This past year saw two such participated in the day’s activities. workshops hosted by the department. In October, the mathematics faculty In the coming years we hope to extend from McKean High School and the these type of activities and include the Charter School of Wilmington spent a mathematics faculty from other local day with faculty from the department Delaware high schools. If you or your exploring cutting edge research problems faculty are interested in this type of in mathematics. Professors Richard activity, I encourage you to contact Braun, Gary Ebert, Russell Luke, and either John A. Pelesko (pelesko@math. The Department of Mathematical Louis F. Rossi shared their expertise and udel.edu) or Cristina Bacuta (crbacuta@ Sciences enjoys a unique relationship worked with faculty to develop new math.udel.edu) to explore these with high schools in the state of ways to inspire high school mathematics possibilities further. Seminar on stochastic and young investigators in probability contributions to probability theory and stochastic processes alike. Apart and particularly to stochastic processes conference from informal sessions, in which in processes throughout his long research particular young Mathematicians career. Examples include the Ray and 2008 at UD had the opportunity to give short Knight compactifications as well as Anja Sturm presentations on their research and the introduction and development of From April 3-5, 2008 we have had present open problems, excellent talks prediction processes. The session, led by the pleasure to host the Seminar on were given by five invited speakers: Marc Yor and Ed Perkins (University of Stochastic Processes at the University Amarjit Budhiraja, University of British Columbia), summarized Frank of Delaware. These informal North Carolina Knight’s work and gave anecdote from conferences have been held annually his life. Xia Chen, University of Tennessee since 1981 and have become one of The conference was generously the most important regular conference Richard Kenyon, Brown University sponsored by the National Science series for probabilists in North Foundation as well as by our own Anita Winter, University of America. The event at the University Department of Mathematical Sciences. Erlangen-Nuernberg (Germany) of Delaware, organized by Dr. Anja This support contributed greatly to the Sturm and Dr. Wenbo Li, has been Marc Yor, Université Paris 6 success of the conference, not least by a great success attracting over eighty (France) providing funding and thus making it participants, accomplished researchers possible for many graduate students Topics ranged from and young researchers to attend. branched polymers over tree-valued processes with applications in genetics and stochastic games to large deviations of random walk intersection times and new interpretations of the famous Black-Scholes formula used in finance.

University of Delaware participants with Professor In addition, an afternoon 7 Marc Yor (Université Paris 6) who lectured on “An session commemorating Frank interpretation of the Black-Scholes formula in terms of last Knight’s life and work took passage”. From left to right, graduate students Liquan place. Frank Knight, who Professor Marc Yor (Université Paris 6) Huang, Ang Wei, Dr. Xinyi Zhang are followed by died March 19, 2007, has lecturing on “An interpretation of the Black- Professor Marc Yor and Professor Wenbo Li. made numerous creative Scholes formula in terms of last passage.”

The International Conference on Ph.D. from the University of Inverse Scattering Problems which is Edinburgh, Scottland and D.Sc. degree taking place in Sestri Levante, Italian from the University of Edinburgh. He Riviera, May 8-10, 2008, is organized held the Chair of Applied Analysis at in celebration of 65-th birthday of David Colton and in recognition of the the University of Strathclyde, Glasgow international leadership and outstanding before joining the University of scientific achievements of David Colton Delaware as a Professor of Mathematics and Rainer Kress in the area of inverse in 1978. He became Unidel Professor scattering problems. in 1996. We will gather at this occasion The research of D. Colton and R. researchers who have actively interacted Kress has essentially influenced the with D. Colton and R. Kress and those development of the mathematical who have been influenced by their achievements. The main sponsors of foundations of inverse scattering this event are the AFOSR London theory. Together, they have written Office and INRIA Paris, with some two research books that have become contribution from the University of classics in this area each cited over 1000 Delaware, the University of Göttingen, times. Germany and the University of Genova, Italy. Fioralba Cakoni David Colton received his B.S. degree On behalf of the Organizing form California Institute of Technology, Committee Donald Marquardt iterate on the path to the solution, the step is identical to the Newton Marquardt observed a characteristic step. This is one of the first instances (1929-1997) behavior for hard problems: methods of what are now known as trust- like steepest descent, which follow region strategies. The practical detail Russell Luke the gradient of the objective function, Marquardt added was a technique I was delightfully surprised to marched in a direction that was nearly to dynamically adjust the scaling of learn recently that one my favorite orthogonal to that of Newton-like the identity so that one gets robust algorithms is the namesake of one of methods, which generate sequences performance far from the solution our department’s very own. Donald W. based on a linearization of the first and quadratic convergence near the Marquardt was a native of New York derivative of the objective function. solution. This innovation was the City and earned a Bachelors degree in This behavior is symptomatic of long, product of a great deal of numerical mathematics and physics at Columbia narrow, banana-shaped valleys in the experimentation, which Levenberg had University in 1950. Drafted during the objective function (Rosenbrock’s not done (all available computers were Korean Conflict, he served in the U.S. function is the classical example). occupied with more pressing matters in Army Chemical Corps at Camp Detrick Ideally one would choose a descent 1944). -- later upgraded to Fort Detrick-- in direction between these two extremes. Levenberg’s work was ahead of its Maryland where he did statistical This, coupled with a strategy for finding time, but Marquardt’s work came analysis related to biological research. a reasonable step length in the given when the same idea appeared in This experience convinced the young direction would provide the means to many different forms. A year before Marquardt to pioneer a career in the quickly and robustly solve the nonlinear Marquardt’s work appeared, J. J. new field of statistics. After the Army optimization problems that Marquardt Moreau published in French a paper he took a job at DuPont as a research was faced with. on what he called proximal operators engineer and mathematician. He spent Some ideas are singular points like which have only recently gained evenings and weekends working towards a tree falling in the forest with no one the serious attention of numerical a Masters degree in mathematics and to hear. Others seem to be part of a optimizers, and from which Levenberg statistics at the University of Delaware, convergence of simultaneous discoveries and Marquardt’s method can be which he completed in 1956. like an inevitable avalanche that changes derived. Indeed, Marquardt extended At DuPont Marquardt worked the landscape. Marquardt’s algorithm his ideas to reinvent proximal operators on a wide variety of problems, for nonlinear optimization, published in from a statistical perspective, what 8 from nonlinear interpolation of 1963, was of the latter category, though was later called ridge regression. Also thermodynamic models to help with it was preceded 19 years earlier by the in 1963, the Russian mathematician plant design, to estimating heats of same idea due to Kenneth Levenberg Alexei Tikhonov published two works formation from laboratory data, to that landed without making a sound. on stable approximations of ill-posed the optimization of manufacturing The Levenberg-Marquardt algorithm is linear operator equations, again a special processes, and even safety statistics. so named to honor both its inventors. case of Moreau’s proximal operator Many of the problems he worked on, And though Marquardt arrived approach. Tikhonov regularization, while from very different applications, independently at the same conclusion as it is known today, is central to the boiled down to the same optimization many years later than Levenberg, field of inverse problems and is a problem: nonlinear least squares. Marquardt’s publication included two particular favorite in our department. Marquardt’s problems were tiny by critical features that created some noise: For whatever reason, regularization was today’s standards, only 2 or three a practical, though critical parameter an idea whose time clearly had arrived. variables, but the nonlinearity, together “tweak’’ that made the algorithm fly, What made Marquardt’s work rise above with primitive computers (46 word and, equally important, a free Fortran the others was the companion code that RAM and 3.75 floating operations per implementation. he made available to practitioners. second!) provided the necessity that In a nutshell, the idea is to add a Marquardt continued to make begets invention. scaling of the identity to the second valuable contributions to the field of derivative of the function one is trying At the time, the state of the art for statistics and in the last two decades to minimize. such problems was either the method of his life he focused on influencing of steepest descent with a line search For algorithms built on the second- beneficial changes in organizations. He or Newton-type methods. Gradient order Taylor series approximation to the was president of the American Statistical descent with an optimized step-length objective with such an adjustment to the Association (1986), co-architect of is extremely robust globally but it is second derivative term, international quality standards (ISO only asymptotically linearly convergent, the larger the scaling, the more the 9000), head of DuPont’s Quality so it can be very slow. Newton’s next iterate rotates in the direction Management and Technology Center, method, on the other hand, converges of steepest descent while at the same and in 1991 founder of his own quadratically near a solution, but is time becoming shorter; in the other company, Donald W. Marquardt & unstable globally. Looking at every extreme, as the scaling approaches zero Associates. (MCM) sponsored by the Consortium Outstanding designation for their work UD Math Students for Mathematics and its Applications on the “Take a Bath” problem. The Score Big in the (COMAP). The University of Delaware Outstanding designation was awarded has a close relationship with this special to only 9 teams, placing UD in the Putnam and MCM modeling contest. One of the past top 1% worldwide. Their report will be COMAP presidents is former University published in the UMAP journal next Competitions of Delaware President and Emeritus fall. Undergraduates Donald Knieriem Professor of Mathematics David Roselle. and Robert A Mitchell III earned a Sometimes mathematics is a For the last six years, Professor Louis F. Meritorious designation for their competitive sport, and this year, teams Rossi has organized and coached teams project report on the Sudoku problem. of University of Delaware students from the University of Delaware. This The Meritorious designation is the scored big in two of the sports biggest year, one of his teams took top honors, second highest and has been given to tournaments. The annual Putnam a truly amazing achievement. the top 13% of completed reports this Competition is organized by the year. Undergraduates Stephen Johnson Mathematical Association of America The MCM contest challenges teams of and Kyle Thomas earned a Successful and has been held annually for sixty- up to three undergraduates to solve an designation, reserved for those who seven years. Known as one of the most open-ended problem in four days. For enter a complete project report. 2008, more than 3800 teams registered challenging and difficult mathematics Congratulations to all students for the contest, but only 1162 submitted competitions in the world, the list of participating in the Putnam and MCM a complete solution. Student teams must past winners of the Putnam include competitions and to their coaches on a two Nobel Prize Winners and three propose mathematical models supported truly outstanding “math season.” Fields Medallists. This year, University by the latest scientific research and of Delaware team members Bobby present a comprehensive analysis of the DeMarco, Spencer Tofts and Alison resulting solution. Two problems are Gordon ranked 66th in the competition. posed during the contest, and students Stephen Johnson also participated and are free to choose either one. This served as first alternate for the team. year, the problems were “Take a bath” This year’s competition included 3753 asking teams to model the effects of contestants from 516 institutions. The the melting of the North Polar Ice Cap team was organized and coached by due to global warming, and “Creating Professors David Bellamy and K. N. Sudoku Puzzles” asking teams to devise 9 Ranganathan. algorithms for constructing Sudoku In the world of applied mathematics, puzzles of varying difficulties. the most prestigious tournament is the Undergraduates Matt Thies, Bob Mathematical Contest in Modeling Liu and Zachary Ulissi earned an

New Faculty degree in develop a network of connected mathematics mathematical concepts. He has education published over 120 articles and book The Department of Mathematical from The chapters in his field. He is an avid biker. Sciences continues to hire new Ohio State Dr. Dejun Xie joins us as a Unidel faculty to replace retirements and University. Postdoctoral Fellow. He is an expert in to add strength in new areas. In this His primary newsletter, we are pleased to introduce interest is the area of financial mathematics and our two most recent additions to the helping related fields. This includes ordinary department. students and partial differential equations, Dr. Alfinio Flores is our new and prospective and in service teachers functional analysis, asymptotic analysis, Hollowell Professor of Mathematics develop their conceptual understanding stochastic processes, and statistical Education. He received his Bachelor of of mathematics. He uses computers, modeling. Most recently, his work has Science and Masters of Science degrees calculators, and concrete materials to focused on the free boundary problems at UNAM, the National University make mathematical abstractions more that arise in mortgage contract of Mexico. He received his doctorate tangible and help students and teachers valuations. Featured Graduate Student: Derek Moulton is originally from “Mathematical Modeling of Field Littleton, Colorado. He attended the Driven Mean Curvature Surfaces,” and Derek Moulton University of Denver where he received is now extending his work to magnetic his Bachelor of Science in Mathematics soap bubbles. in 2003. Derek arrived at the University Derek has become known as an of Delaware in the fall of 2003 and excellent speaker. He has given began working towards his doctorate in numerous talks in the department’s applied mathematics. graduate student seminar series and For the last several years, Derek has has also given invited talks at the been working with his Ph.D. supervisor, University of Maryland, Dickinson Professor John A. Pelesko, on a University, and at an International variety of projects ranging from the Conference on Non-linear Dynamics study of heat transfer in coated bodies and Chaos. His speaking ability serves to the study of soap films subjected to him well in the classroom and two electric fields. His first paper, “Thermal year’s ago his excellence in teaching was Boundary Conditions – An Asymptotic acknowledged with the Baxter-Sloyer Analysis,” appeared in the journal Graduate Teaching Award. Heat and Mass Transfer last year. His Derek recently accepted the Hanno subsequent papers have all focused on Rund Postdoctoral Fellowship at the the behavior of soap films in electric University of Arizona and hence in the fields. His most recent paper, “Theory fall will be relocating to Tucson. We and Experiment for Soap-Film Bridge congratulate Derek on his outstanding in an Electric Field,” is due to appear achievements at the University of in the prestigious Journal of Colloid Delaware and wish him the best of and Interface Science this year. Derek luck in Arizona and with all his future recently successfully defended his thesis, endeavors.

2008 Student Award Recipients The Baxter-Sloyer Graduate Teaching The Carl J. Rees and Eleanor K. Rees The Mathematical Sciences Department 10 Award recognizing graduate teaching Scholarship which is awarded to Faculty Recognition of a Graduating assistants who have demonstrated superior undergraduate students majoring in Senior 2008 was given to Alison M. Gordon effectiveness in teaching and in the mathematics upon academic performance and Robin A. Prescott. performance of their responsibilities was this year awarded to Brian M. Rife. went to Rachel E. Bailine, Michele L. Giuliano, The William D. Clark Prize for a senior Stephen T. Johnson, Mark W. Mackey, Angela majoring in mathematics who has shown The Stephen J. Wolf Memorial M. Pollino, David J. Puliti, Leanna M. Shannon, unusual ability in the area was this year Scholarship awarded to a student entering and Spencer N. Tofts presented to Robert V. DeMarco.. the senior year majoring in mathematics who has demonstrated both love and The Outstanding Student Teacher Award talent for the subject was awarded to for an undergraduate student who has Spencer N. Tofts. demonstrated outstanding performance in student teaching went Caitlin M. Bogosta and Shannon D. Tingley.

Donor Support Mathematic Sciences Alumni Donors to the University of Delaware in Fiscal Year 2007 and Other Friends contributing to the Department of Mathematical Sciences. Dr. John F. Ahner Dr. Bayard O. Baylis Ms. Stephanie M. Carr Dr. Benjamin F. Esham, Jr. Mrs. Ann D. Augensen Mrs. Elaine H. Baylis Mrs. Joanne Heath Cheasley Mr. R. Nim Evatt Mr. Harry J. Augensen Mrs. Elizabeth H. Black Dr. David L. Colton Mrs. Susan Evatt Mr. David P. Bacon Dr. Robert G. Bowers Dr. L. Pamela Cook-Ioannidis Dr. Thomas E. Favinger Mrs. Lucia W. Bacon Dr. Richard J. Braun Dr. Fred D. Crary Mr. John E. Foskey Ms. Elinor L. Baker Mr. Richard S. BreMiller Mr. Peter A. Daunais Mrs. Alexandra S. French Dr. Karen L. Balasaygun Dr. Philip Broadbridge Mr. Eugene R. Davis Mr. Jonathan L. French Dr. David J. Barsky Mrs. Janice M. Burns Mrs. Gayle E. Davis Mr. James M. Frey Mrs. Martha C. Baumeister Bush Bros. Disposal Mrs. Arlene L. Dowshen Mr. Carl F. Geiszler Mr. Theodore Baumeister III Dr. Jinfa Cai Ms. Anna A. Ellis Mrs. Gail Ford Geiszler Dr. William J. Geppert, Jr. Mrs. Frances Bazela Katsuura Mrs. MaryAnn H. Peltier Mrs. Raymond R. Strocko Mrs. Rochelle Goren Dr. Hidefumi Katsuura Dr. John F. Porter Raymond R. Strocko, M.D. Mrs. Mary E. Grovola Dr. Stephen L. Koffler Dr. Kathryn F. Porter Dr. Lowell H. Tonnessen Mr. Michael J. Grovola Mrs. Ruth C. Krayesky Mrs. Jo Anne P. Pratt Mrs. Mary Lou Tonnessen Ms. Beverly K. Grunden Mrs. Laurie B. Krebs Mr. Marino A. Puliti Mrs. Denise C. Ucciferro The Reverend Larry A. Mr. William A. Krebs, Jr. Mrs. Mary Ann Puliti Mr. Joseph J. Ucciferro, Jr. Grunden Mrs. Nancy Lee Lese Dr. Jorge G. Punchin Mr. Andrew W. Urquhart Mrs. Barbara A. Haber Dr. William G. Lese, Jr. Mrs. Maria C. Punchin Mrs. Linda J. Vozzo Mr. Kenneth R. Haber Ms. Elizabeth A. Lincoln Ms. Judith G. Repp Mr. Thomas J. Vozzo Dr. Gene Sand Hall Ms. Hemei Liu Dr. Kathryn Rommel-Esham Dr. Joseph K. Wald Mr. Peter C. Hall Mr. Charles L. Mallon III Mr. Milton Rubin Mrs. Lindalee P. Wald Mr. Gary T. Hallenbeck Mrs. Regina B. Mallon Mrs. June B. Sacco Mr. Jian-Guo Wang Dr. Katarzyna Hallenbeck Dr. Alice L. Meissner Dr. William J. Sacco Dr. John W. Weaver Mrs. Marilynn Hallenbeck Arthur Milholland, M.D. Mrs. Phyllis R. Schott Mrs. Margaret R. Weaver Mr. Nicholas G. Hallenbeck Mr. Carl O. Miller Mrs. Mary E. Schreiber Mr. George A. Webber Mr. Charles L. Hammond, Jr. Mrs. Shirley P. Miller Mr. Alan E. Sefcik Mrs. Dian O’Connell Weddle Mrs. Karen A. Hammond Mrs. Ellen F. Monk Dr. Anthony Seraphin Mr. Timothy E. Weddle Dr. Dorothy J. Helm Dr. Peter B. Monk Mrs. Patricia Seraphin Dr. Joan Wyzkoski Weiss Mr. Douglas J. Hermann Mr. Peng Nie Mrs. Terry T. Shelton Dr. Ronald H. Wenger Mrs. Douglas J. Hermann Mrs. Diane M. O’Connor Ms. Debra L. Shenk Dr. Sherry L. Wenger Dr. Saul D. Hoffman Mrs. Patricia M. Overdeer Mr. Kenneth A. Skinner Mrs. Linda I. Woolson Mr. Joseph A. Horgan Mrs. Susan V. Pannell Mrs. Vichitra L. Skinner Dr. Robert F. Woolson Mrs. Sheila B. Horgan Susan L. Parker, Esq. Mr. Stuart L. Spinner Ms. Yihuan Xu Dr. Kirk E. Jordan Jay A. Peacock, M.D. Dr. Ivar Stakgold Mrs. Karen Yates Mrs. Lorraine H. Jordan Dr. Kenneth Pefkaros Dr. Robert M. Stark Mr. Michael Yates Mr. Harry J. Kamack Mr. Dennis F. Peltier Ms. Evelyn A. Strawbridge 11

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