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Growth & Excellence MATHEMATICS NEWSLETTER Growth & Excellence Contents Letter from the Chair 3 AMS Society Fellows 2-3 New Academic Staff 4-7 Colloquium: Schwarz 10 In Memorium: Edelson 11 Focus: Lecturers at Math 12-13 Graduate News 8-9 Undergraduate News 15 Department Awards 16-17 Life After Davis 8-9, 14, 18 Staff News 19 Fellows of Math: Recognition from the American Mathematical Society additional necessary conditions for optimality. This work has stimulated strong interest over the years, and been generalized and extended by many authors. With colleagues Krener gave conditions for the existence and construction of decou- pling and non-interacting control laws for nonlinear systems. This paper won the Best Paper of the Year Award of the IEEE Transac- Art Krener tions on Automatic Control. He also has been Jesus De Loera a leader in the development of software tools Arthur Krener joined the faculty of the for nonlinear control. His Nonlinear Systems Jesus De Loera has made many notable Mathematics Department at Davis in 1971, Toolbox is a suite of MATLAB routines that contributions to discrete mathematics and its immediately after receiving his Ph.D. from implement a variety of the latest methods of applications, as well as to the education of our Berkeley. He spent his entire career at Davis, nonlinear control. students at UC Davis. retiring in 2006 as a Distinguished Professor Art’s work has earned him many honors. He started his career working in the area of Mathematics. In addition to being named a Fellow in the of discrete and computational geometry. His Art’s mathematical interests focus on non- American Mathematical Society, he also is a Ph.D dissertation solved an outstanding prob- linear control theory, where he did founda- Fellow of the Society for Industrial and Applied lem posed by Gelfand, Kapranov and Zelevin- tional work. With Hermann, Krener gave the Mathematics (SIAM), the Institute of Electrical sky concerning the structure of the space of definitive treatment of controllability and ob- and Electronic Engineers (IEEE) and the In- triangulations of a product of simplices, a servability for nonlinear systems based on dif- ternational Federation for Automatic Control topic started by J. Stasheff and Milnor in the ferential geometric tools. The importance of (IFAC). He has won numerous awards includ- 1970’s. Later, in joint work with Below and this paper was recognized immediately. It was ing a Guggenheim Fellowship, the SIAM Reid Richter-Gebert, he solved another longstand- cited by the IEEE Control Systems Society as Prize, the IEEE Bode Lectureship and an IFAC ing problem by showing that finding a trian- one of Twenty Five Seminal Papers in Control Certificate of Excellent Achievements. gulation of a convex 3-polytope with the mini- published in the twentieth century. It forms Krener held a variety of administrative mum number of simplices is NP-hard. the basis for many of the seminal advances in posts while at UC Davis, including Chair of He also has made important contributions control theory that have followed. the Department of Mathematics, and member in other areas of discrete geometry, in particu- Around 1960 the well-known Pontryagin of the Committee on Academic Personnel. lar on computational problems involving lat- Maximum Principle was developed for opti- He began and endowed the Krener Assistant tice points, volumes, and integrals of polyhe- mal control problems. These are the first order Professorships. This program brings several dra. His work in this area has been applied necessary conditions that a control must satis- excellent young mathematicians to UC Davis in many fields of mathematics, including al- fy to be optimal. But they are not always deter- each year. He also was founding Chair of the gebraic geometry, representation theory and minative, particularly for problems where the SIAM Activity Group on Control and Systems algebraic combinatorics. Together with others control enters affinely. The High Order Maxi- Theory. at UC Davis he has developed the highly suc- mum Principle that Krener developed gives cessful software package LattE that provides many useful computational methods for dis- 2 Fellows of Math: Letter from Recognition from the American Mathematical Society the Chair by Dan Romik This has been a great year to be a math- ematician. A ranking of U.S. occupations published last April by the job search website CareerCast and quoted in the Wall Street Jour- crete geometry problems. nal, Forbes and other notable media outlets, In recent years Jesus’ research interests declared ‘mathematician’ to be the top job in have extended to encompass more applied the United States in 2014. (Lumberjack was areas of mathematics, including integer and ranked as the worst job, in case you were combinatorial optimization. An Integer Linear wondering.) Color us unsurprised: Here in Program (ILP) problem is this: given a matrix the UC Davis Mathematics Department we A, vector b and linear function f(x), find the have always known how much fun and how maximum value of f(x) over all integer vec- rewarding math is! Of course we are delighted tors x that satisfy Ax = b and every compo- that the rest of the world is catching on, as this nent of x is non-negative. In pioneering work enables the Department to enjoy an exciting with Hemmecke, Koeppe and Weismantel, De wave of growth. the past year the Department graduated ten Loera proved the first theoretical results for In the past year we have hired four excel- doctoral students. Our incoming class of grad- the generalization of this problem in which lent new faculty members: Javier Arsuaga, Mi- uate students comprises 20 students. We are f(x) is a non-linear objective function. To put chael Friedlander, Mariel Vazquez and Eugene proud of our continued ability to attract tal- this results in context, recall the celebrated Gorsky (who will arrive later this year). Also, ented graduate students, which form an essen- result by H.W. Lenstra: When the number of Niels Grønbech-Jensen has joined us by tran- tial part of any successful research program, variables is fixed there is an algorithm to solve sitioning into a joint appointment with Me- and wish them luck in their work. ILPs in polynomial time on the input size. De chanical and Aeronautical Engineering. And Our undergraduate program is growing in Loera et al. extended this to the case when f this year we have appointed Andrew Sorn- size and prominence. This is due both to the is non-linear. Although they showed that the berger to be our first Research Scientist. growth in undergraduate enrollments at UC problem becomes NP-hard, even in dimen- In the coming year our growth will con- Davis, and to the increasing recognition of the sion two, they designed an approximation tinue unabated, with a recruitment for one value and importance of STEM (Science, Tech- algorithm to maximize an arbitrary integral tenure-track position at the Assistant Profes- nology, Engineering and Mathematics) educa- polynomial over the lattice points of a convex sor level, and no fewer than four additional tion. This year our undergraduate program rational polytope with a fixed dimension. faculty positions in a joint recruitment effort includes 568 math majors, the most ever. And The excellence of Jesus’ De Loera’s work with the Physics Department. we are launching a new major, Mathematical has been recognized by all the mathematical The Department also has been successful Analytics and Operations Research, which al- societies. He has been a plenary speaker for in many other ways. Two of our members, Pro- ready is attracting significant interest. the AMS, the MAA, and SIAM. In 2010 he was fessor Jesus De Loera and Professor Emeritus The excellence of our instructors’ teaching co-winner of the computer society award from Arthur Krener, were elected as Fellows of the continues to be recognized at the national lev- The Institute for Operations Research and the American Mathematical Society. They join five el. This year, our popular lecturer Dr. Duane Management Sciences. of our faculty who were recognized with this Kouba was awarded the 2014 Golden Section De Loera is an outstanding mentor and prestigious honor in 2012. In May we hosted Distinguished Teacher Award by the Math- teacher. While at UC Davis he has supervised a large conference held to honor the research ematical Association of America. eight Ph.D students, five postdocs, and over achievements of Professor Albert Schwarz. En- I’ll conclude with a note of thanks to our 30 undergraduate honors theses. More than titled “The Mathematics of Quantum Theory,” outgoing chair, Joel Hass. His four years of sig- 45 undergraduates have conducted research this highly successful event featured talks by nificant accomplishments as chair have left the with him. He received the 2003 UC Davis Fields Medal-winner Andrei Okounkov of Co- Department in great shape. Joel now is focus- Chancellor’s fellow award, the 2006 UC Davis lumbia University and several other luminaries ing on research activities, with a quarter-long award for diversity, the 2007 Award for Excel- from mathematics and theoretical physics. In visit to the Hebrew University in Jerusalem. lence in Service to Graduate Students by the the present academic year we have scheduled We are immensely grateful to our many UC Davis Graduate Student Association, and talks and visits by other famous mathematical contributors for their generous donations, the 2013 Chancellor’s award for mentoring scientists, including the Fields Medalists Ed- which support and make possible many of our undergraduate research. But the success of his ward Witten and Charles Fefferman. activities. If you are considering joining this many students is his greatest reward, and one We have had impressive success in teach- select group, see the back of the newsletter for he receives every day.
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