MATHEMATICS NEWSLETTER

Contents Letter from the Chair 2 Graduate News 12 New Academic Staff 4 Life After Davis 14 Research: Crinkled Spacetime 6 Galois Group 14 Research: Popular Books 7 Emeriti 15 Undergraduate News 8 AWM Update 15 Department Awards 10 Staff News 15 Letter from the Chair by , Department Chair

We had a great year for hiring in 2017-18, Among the honors collected by our De- We are very grateful for the support we with three new Assistant Professors (Laura partment this year, Jesús De Loera will be giv- get from our alumni and friends. Gifts make Starkston, Roger Casals, and Rishidev Chaud- ing an invited address at the Joint a critical contribution to our students and to huri) and three Krener Assistant Professors Meeting this January, and Anne Schilling has the mathematical environment. I hope that (Annalaura Stingo, Tair Akhmejanov, Martin been elected a Fellow of the American Math- you consider adding a gift to the Department Gebert) joining our Department. Two long- ematical Society. Tudor Dimofte won a pres- to your giving plans. Gifts can be designated time members of the faculty retired this June. tigious National Science Foundation CAREER towards scholarships, research, lecture series We hope that Emerita Professor Angela Cheer award. Postdoctoral fellow Anastasia Chavez or general uses. More can be found on dona- and Continuing Lecturer Emeritus Lawrence added to her achievements by winning an tion in the center of this newsletter, page 9, Marx will continue to contribute their valuable NSF Postdoctoral Fellowship. Nicholas Sher- or please contact us to learn about donation experience and expertise to the Department. A man, who wrote a senior with Professor possibilities. celebration of Angela Cheer’s research career in Bruno Nachtergaele as an undergraduate at October featured two members of the National UC Davis, won the American Physical Society Academy of Sciences in a fascinating afternoon LeRoy Apker Award for his work in mathemat- of talks describing applications of mathematics ical physics. Nicholas is currently in the grad- to everything from fluid flows in cells to how, uate program in physics at UC Berkeley. Dr. exactly, lobsters smell. Edward Tavernetti’s TEDx talk on the beauty of mathematics https://youtu.be/VIbjHIGMjQM has garnered over 100,000 views. One of our former Krener Assistant Professors, Moon Jesús De Loera Duchin (now a Professor at Tufts University) won a Guggenheim Fellowship, in part for her work on the geometry of gerrymandering.

Anne Schilling Angela Cheer and Lawrence Marx are both retiring

Last spring the Department hosted several exciting events. The Thurston Lectures, our endowed annual lecture series, were given by Thomas Hales, Thurston Lecture Professor Thomas Hales, who described his Tudor Dimofte work on the Kepler conjecture and on its for- mal (computer) verification. Associate Dean Motohico Mulase gave an inspiring lecture to honor the work of the late - ist , and Professor Janko Gravner conducted a fascinating symposium on Mathematics and Music (joint with the UC Edward Tavernetti Davis Music Department). We continue to struggle to accommodate Motohico Mulase on Mihzakhani our burgeoning undergraduate student popu- Seminars on Mathematics lation. Our faculty and staff have really risen to the challenges this has brought us, from The Department of Mathematics has seminars on a wide range of topics, which are focused on a diverse audience. Regular mentoring more students to streamlining ad- weekly seminars are usually focused on emergent math in that vising. We’re hoping that the campus is able area. Regular weekly seminars change as research evolves, and to provide us more resources so we can main- a new seminar was started last year in the Mathematics of Data tain the high standards we set for our teaching and Decisions. Special Events are a mix of special speakers as mission. well as talks intended to be more accessible. You can view upcoming seminars on our web page: https://www.math.ucdavis.edu/research/seminars/ Janko Gravner, Math & Music 2 Incoming Academic Staff Roger Casals • Assistant Professor Roger Casals received a B.S. in Mathemat- sets of polynomials) in any dimension. Figure ics from the Universitat Politecnica de Catalu- 1 gives an instance of how a 6-dimensional nya, a M.S. from the Universidad Complutense space with a 5-dimensional contact structure de Madrid and a Ph.D. in Mathematics (2015) on its boundary can be described and effec- from the Universidad Autonoma de Madrid tively understood via his planar colored dia- and the Instituto de Ciencias Matematicas. grams. This work featured this year in the Ge- His thesis research started with the con- ometry Section at the International Congress struction of contact structures in 5-dimension- of Mathematics 2018. al spaces. Contact structures are the geometric His work is known for providing new con- objects that underlie the physical principles in structions. He strongly follows the principle optics and thermodynamics. In recent years, that any geometric space that can a priori exist, the study of contact structures has become a must actually exist. This perspective is called central part of pure mathematics, especially the study of h-principles. In his research, Rog- in geometry and topology. R. Casals’s thesis er has proven several h-principles and used showed that contact structures always exist in them to give new applications, including new 5-dimensional spaces. results on contact structures, Engel structures Following his Ph.D., Casals was a CLE (in 4-dimensions) and complex geometry. Moore Instructor at the Massachusetts Insti- Recently, he has been actively developing a tute of Technology, a time during which he connection between contact geometry and the developed a calculus for studying the contact combinatorics of planar graphs. structures coming from affine varieties (zero

Laura Starkston • Assistant Professor Laura Starkston studies , par- geometry classifying (singular) plane , ticularly 4-dimensional spaces, which have and Laura looks for differences and similarities additional geometric data called a symplectic between these two geometric settings. form which gives a way of measuring areas of A running theme in Laura’s approach to surfaces inside the . Depending on geometric questions, is to use topology to en- the angle and orientation of the surface, its code the geometric structure. An example of symplectic area can be positive, negative, or this in her recent and current work is to en- zero. When every part of the surface contrib- code the symplectic topology of an open Stein utes zero to the area, it is called a Lagrangian manifold, using a core skeleton of the mani- surface, and when every part of the surface fold. The skeleton is built from gluing polyg- contributes positively to the area, it is called a onal objects along their boundaries and cor- symplectic surface. ners, and the data of how the edges are glued Many people have studied properties of onto other polygons completely determine the Lagrangian submanifolds, but very little is on the manifold which known about symplectic submanifolds. Stark- surrounds this skeleton. ston is working to understand symplectic sur- Although spaces in high dimensions can be faces in one of the most fundamental examples very complicated and their geometric informa- of a symplectic 4-manifold: the complex pro- tion can be difficult to access, Laura looks for jective plane. The classification of these surfac- settings where these spaces can be explored es has been open for decades and she is work- with pictures and broken up into simpler ing on this open problem as well as singular pieces that can be understood individually and generalizations. It is particularly interesting to then put back together to get a global under- compare this problem in symplectic geome- standing of the space. try with the analogous problem in algebraic 3 Incoming Academic Staff

Tair Akhmejanov Martin Gebert Annalaura Stingo Krener Assistant Professor Krener Assistant Professor Krener Assistant Professor

Tair Akhmejanov was born in Aktau, Ka- Martin Gebert studied in the beautiful city Annalaura Stingo started her study of zakhstan, later growing up in the Boston area. of Munich and received his Ph.D. at the end of Mathematics at University Federico II and He received his undergraduate degree from 2015 from Ludwig-Maximilian University Mu- earned her Ph.D. at the University of Paris Boston College, and a M.A.S. degree (Part III) nich. After a short intermezzo at ETH Zurich 13, under the supervision of Jean-Marc Delo- from Cambridge University. He received his he held Post-Doc positions at King’s College rt. Her thesis, Problems of global existence for Ph.D. from Cornell in 2018 under the super- London and Queen Mary University of Lon- critical non-linear evolution equations with small vision of Allen Knutson. He joined the Math don before joining UC Davis in the fall quarter data and semi-classical analysis, studies the Department in Fall 2018 and will be working 2018. global existence problem and asymptotic be- with Professor Greg Kuperberg. Martin is interested in Analysis and his havior of solutions for quasi-linear Klein-Gor- Tair’s research is in algebraic combinator- research is located between Operator Theory, don equations in one space dimension with ics, in particular, the interplay between com- Mathematical Physics and Probability. A special cubic non linearities, when small initial data binatorics, representation theory, and algebra- focus is on random operators and many-body are not compactly supported but only mild- ic geometry. This includes Schubert calculus, quantum systems. At UC Davis, he will work- ly decaying at infinity in space. With the use geometric representation theory, and combina- ing with Professor Bruno Nachtergaele. of the Klainerman vector fields method and a torial representation theory. He has also had When not doing mathematics, Martin en- semi-classical micro-local analysis of the prob- a long-standing interest in complexity theory joys playing soccer, hiking and the Californian lem, she showed that solutions are global, pro- and quantum computation. sun. vided that the data is succiently small and that His hobbies outside of math are playing a structure condition, introduced by Delort, is basketball, watching sports, and reading. satisfied by the non-linearity. She then studied systems formed by a cou- pling between a Klein-Gordon equation and a wave equation in two space dimensions (again in the quasi-linear framework). The goal was again to prove global existence and to develop a robust theory that could apply also to more general non-linearities. In 2017 she was awarded the “Fellow- ship For ” by Fondation L’Oréal-UNESCO, together with Academie des 4 Sciences. Research Highlight Finding Connections in Math

Is there really a separation between pure Understanding the exact central path is im- and applied mathematics? The great mathema- portant. How “curvy” can the central path re- tician Lobachevsky is attributed with saying ally be? Our intuition is that curves with small “there is no branch of mathematics, however curvature are easier to approximate using abstract, which may not some day be applied fewer segments and fewer Newton steps. to phenomena of the real world.” There are Recently, using exciting new methods from plenty of examples of how this is evidently tropical algebraic geometry, X. Allamigeon, P. true for algebra (broadly including number Benchimol, S. Gaubert, and M. Joswig showed theory too), geometry, and topology. that the total curvature of the central path can Here is one way in which algebraic geom- grow exponentially with the input data. This etry, sometimes mistakenly considered a pure implies a major breakthrough, that some in- and non-applicable part of mathematics, has terior-point methods cannot run in strongly helped us understand a well-known algorithm polynomial time! Tropical algebraic geometry in Optimization. Optimization deals with find- is a method to go from a polynomial system ing the best solution or best choice among to a simpler combinatorial version (see figure multiple valid solutions. right). These techniques are fresh and unex- by Jesús De Loera The concrete challenge in question is to pected, and there are many other examples maximize a linear functional under linear in- like this with novel applications of algebraic equality and equation constraints. A very sim- and geometric techniques in Optimization. ple example is to find two numbersx 1 and x2, Here at UC Davis we have a thriving research with xi ≥ 0 and so that 2x1 +3x2 is as large as group on this subject. possible. In matrix form we can write this as

Maximize cTx subject to Ax = b and x ≥ 0.

Here A is a real m × n matrix, and c, b are n and m vectors respectively. Despite its simplic- ity this is engine used in solving other optimi- zation problems. To solve the problem, Interior point meth- ods follow a piecewise-linear approximation to the central path using Newton methods steps (see left figure). In reality, the central path is an algebraic , given by the following system of quadratic and linear polynomial equations. When l = 0, we obtain the optimum solution

T Ax = b, A y − s = c, and xisi = l for i = 1, 2, …, n.

Above, a view of the entire central curve of a linear program projected to primal variable space (credit C. Vinzant). Below, on the the left and right, a cartoon of the tropicalization of a three (credit M. Joswig) 5 Crinkled Spacetime

In the early 20th century, Einstein pro- out map from the original, it is necessary and posed a set of equations that related the grav- sufficient to solve the RT-equations. In their itational force to the curvature of space time. final paper, they establish the general theory Understanding the mathematical theory of by proving solutions of the RT-equations al- these questions is a central challenge that is ways exist for wrinkled maps at least one order far from complete. Recent work in this area by smoother than the shock wave case. In other Professor Blake Temple with coauthor Moritz words, for wrinkled maps above a threshold by Blake Temple Reintjes has attracted attention in the Math and smoothness, the lack of smoothness is never Physics communities. They have developed a caused by the nature of spacetime, but always Blake Temple is a Distinguished Profes- new theory of “metric smoothing” in General by the way it is being modeled. As they put sor of Mathematics at UC Davis. Relativity, based on what they call Regularity it, “a crinkled map of spacetime can always Transformation Equations, or RT-equations. be smoothed out by a coordinate transforma- Their studies began by investigating wheth- tion.” The theory still leaves open the problem er the interaction of shock waves in General of regularity singularities at GR shock waves, Relativity (GR) could create a new kind of but reduces it to the problem of finding solu- regularity singularity where spacetime itself is tions of the RT-equations at the lowest level of not smooth. Earlier work on shock waves was smoothness. only able to prove existence of shock wave In fact, their methods apply beyond Ein- solutions for metrics that are Lipschitz con- stein’s theory of relativity, to the general prob- tinuous. A more regular spacetime, one order lem of smoothing the spaces that arise in smoother, is required to make the correspon- analysis and differential geometry. A rather dence between Einstein’s theory of General surprising aspect of their argument is that it Relativity and the physics of Special Relativity, relies on the theory of elliptic partial differential the case when there is no gravitational curva- equations to find coordinate systems which ture. What was unclear was whether the lack smooth out solutions to the equations of Gen- of smoothness was inherent in the spacetime eral Relativity, which are hyperbolic. This is itself, or in contrast, whether it was a feature unexpected because hyperbolic PDE’s, which of the way that space was being modeled, or govern sound waves and give rise to shocks, Moritz Reintjes completed his Ph.D. parametrized. That is, was the lack of smooth- behave very differently than elliptic PDE’s, with Professor Temple at UC Davis. After- ness due only to a bad choice of map, or coor- which typically apply to more regular settings wards he was a postdoc at the University dinate system, used to describe the spacetime? like electric fields or the distribution of heat. Regensburg, at the Max Planck Institute Reintjes and Temple set out to investigate this The RT-equations reduce the problem of regu- phenomenon. larity singularities at shock waves in GR, to the for Gravitational Physics in Potsdam and In a series of five papers (two of which existence of well-studied Calderon-Zygmund at the University of Michigan in Ann Ar- have appeared), they have now succeeded in type singularities in elliptic PDE theory, es- bor. From 2013 until 2016 Moritz was a characterizing the mechanism for smoothing tablishing a connection between two different postdoc at IMPA in Rio de Janeiro, Brazil. out the wrinkles in a wrinkled map. Specifi- kinds of singularities from two (apparently) Since 2017 he is a postdoc at the Instituto cally, by a wrinkled map, they mean a map in different subjects. Superior Tecnico in Lisbon, Portugal. Mori- which the gravitational metric is one, not the The new theory enlarges the space of tz received a “Research Scholarship” from usual two derivatives more regular than the solutions to the Einstein equations, puts the the German Research Foundation (2013- curvature; and unwrinkling the map means problem of regularity singularities at GR shock lifting the regularity of the metric up one or- waves on a solid mathematical foundation, 2014), a “Postdoc of Excellence” scholar- der, to two full derivatives above the curvature. and introduces a new direction for geometri- ship at IMPA (2015-2016). His research They prove that to construct a new smoothed cal analysis. concerns General Relativity, Shock Waves, Fluid Dynamics and the Dirac equation of 6 Quantum Mechanics. Research Highlight How popular are the books in your library? HowAnne Popular Schilling Are Your Books?

Suppose your library has one shelf with n books. If someone checks out book i and returns it, this book gets placed at the beginning of the shelf. After a while, the popular books accumulate at the front of the bookshelf. Suppose your library has one shelf with n This library is called the Tsetlin library. It is a Markov chain Tn, where books. If someone checks out book i and re- the states are the n! permutations of the n books. The Tsetlin library T3 is 2 213 turns it, this book gets placed at the beginning depicted in Figure 1, where an arrow labeled 1 i n from permutation of the shelf. After a while, the popular books π to permutation π means that book i is moved to the front. The question accumulate at the front of the bookshelf. 1 2 is now, what will be the distribution of booksHow if we popular wait for a are while? the In books in your library? This library is called the Tsetlin library. It mathematics, this is called the stationary distribution, which is the right is a Markov chain T , where the states are the 1 123 2 eigenvector with eigenvalue 1 of the transition matrix ofn the Markov chain. n! permutations of the n books. TheAnne Tsetlin Schilling li- If book i is picked with probability xi, then the transition matrix for T3 is brary T3 is depicted in the figure at the left, 3 where an arrow labeled 1 ≤ i ≤ n from permu- Supposex1 0 yourx1 libraryx1 has00 one shelf with n books. If someone checks out book i and returns1 it, this book gets tation π to permutation π’ means that book placed0 at thex beginning00How ofx the popularx shelf. After are a while, the the books popular3 books in your accumulate1 library?3 at3 the12 front of1 the32 bookshelf.1  1 i is moved 1to the1 front. The question is now, Thisx libraryx x is called000 the Tsetlin library. It is a Markov chain Tn, where 3 M = 2 2 what2 will be the distribution, of books if we T3 the states are the n! permutations of the n books. The Tsetlin library T is  000waitx for2 a xwhile?2 x 2In mathematics, Annethis is called Schilling 3 2 213 depicted in Figure 1, where an arrow labeled 1 i n from permutation 2 x3 x3 00the stationaryx3 distribution0  , which is the right ei- π to permutation π means that book i is moved to the front. The question  00x3 x3 0 x3 2 231 11 2 is now, what willgenvector be the distributionwith eigenvalue of 1 books of the if transition we wait for a while? In Suppose your library has one shelf with n books. If someone checks out book i and returns it, this book gets mathematics, thismatrix is called of the theMarkovstationary chain. If distributionbook i is picked, which is the right where we have orderedplaced the 6 at permutations the beginning of as the (123 shelf., 132 After, 213, a231 while,, 312 the, 321). popular books accumulate at the1 front123 of the bookshelf.2 eigenvector withwith eigenvalue probability 1 of x thei, then transition the transition matrix matrix of the Markov chain.3 2 For example, the entry inThis the column library is associated called the toTsetlin permutation library. It 312 is a and Markov the chain Tn, where If book i is pickedfor with T3 is probability x , then the transition matrix for T is row associated to permutationthe states 132 are (which the n! permutations is the entry in of row thei 2n andbooks. column The Tsetlin 5) library T3 is 2 213 3 depicted in Figure 1, where an arrow labeled 1 i n from permutation3 321 is x , which is the probability of transitioning from 312 to 132 by moving book 1 1 π to permutation π means thatx1 book0 ixis1 movedx1 00 to the front. The question by Anne Schilling 3 1 1 2 3 312 132 1 1 to the front. Using thatis now,x1 + whatx2 + willx3 = be 1 the (since distribution they0 x are1 ofprobabilities),00 booksx if1 wex1 wait one for a while? In   Figure 1: Tsetlin library T3 3 can compute the eigenvaluesmathematics, 1,x1,x2 this,x3 isand called 0 with thex2 multiplicitystationaryx2 x2 distribution000 2. Hendricks, which is the right MT3 = , 1 123 2 computed the stationaryeigenvector distribution withfor eigenvalue the permutation 1 of000 the transitionπ forx2 general matrixx2 x2n of the Markov chain.   Can we compute the stationary distribu2 - If book i is picked with probabilityx3 xx3 , then00 the transitionx3 0  matrix for T is n  i  3 3  00x3 x3 0 x3 tion of a general nite Markov2 2chain?31 The an-1 xπi   ψπ = i 1 x.1 0 x1 x1 00(1) swer is Yes, using new techniques from semi- 1 − where wei=1 have1 orderedj=1 x theπj 6 permutations as (123, 132, 213,group231, 312 theory., 321). In fact,3 this means1 that3 one3 1can2 132 1  −where we have0 orderedx1 00 the 6 permutationsx1 x1 as 3 2 For example, the entry in the column associated to permutation 312 and the 3 (123; 132; 213;x2 x231;2 x312;2 321).000 For example, compute an eigenvector of a matrix without Can we compute the stationaryrow associated distribution toM permutationT3 of= a general 132 (which finite Markov is the entry chain? in, row 2 and column 5)  000x x x  any linear algebra! 3 321 the entry in the column associated2 2 to 2permu - 2 The answer is Yes usingis x new1, which techniques is the probability fromx semigroup of transitioningx 00 theory. fromx In 3120 fact, to 132 this by means movingthat book one can compute an tation 312 and3 the3 row associated3 to permu - eigenvector of a matrix1 without to the front. any linear Using algebra!that x100+ x2 + xx3 =x 1 (since0 theyx are probabilities), one 1 tation 132 (which is the3 entry3 in row3 2 and Figure2 23 1:1 Tsetlin library T3 can compute the eigenvalues 1,x1,x2,x3 and 0 with multiplicity 2. Hendricks column 5) is x , which is the probability of wherecomputed we have the orderedstationary the distribution 6 permutations1 for the as permutation (123, 132, 213π, for231, general312, 321).n transitioning from 312 to 132 by moving book 3 2 For example, the entry in the columnn associated to permutation 312 and the row associated to permutation1 to the front. 132 Using (which that x isx1 π+ thei x2 entry+x3 = 1 in (since row 2 and column 5) ψπ = i 1 . (1) 3 321 they are probabilities), one −can compute the is x1, which is the probability of transitioningi=1 1 j=1 fromxπj 312 to 132 by moving book  − 1 to the front. Usingeigenvalues that x1 +1,x x21,+ x2x, 3x3= and 1 (since0 with theymultiplicity are probabilities), one  Figure 1: Tsetlin library T3 canCan compute we compute the eigenvalues2. the Hendricks stationary 1,x computed1,x distribution2,x3 and the 0stationary of with a general multiplicity distri finite- Markov 2. Hendricks chain? computedThe answer the is stationaryYesbutionusing for distribution newthe permutation techniques for the π from for permutation general semigroup n π for theory. general Inn fact, this means that one can compute an eigenvector of a matrix without any linear algebra! n xπi ψπ = i 1 . (1) − i=1 1 j=1 xπj  − Can we compute the stationary distribution of a general finite Markov chain? The answer is Yes using new techniques from semigroup theory. In fact, this means that one can compute an eigenvector of a matrix without any linear algebra!

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1 Updates from the Undergraduate Program Undergraduate by Monica Vazirani, Vice Chair for Undergraduate Affairs Research

This past year, the Department of Math- The Math Department places great impor- student chapter of the Association for Women ematics awarded 167 undergraduate degrees tance in providing our students with a support- in Mathematics (AWM) held a Mentorship So- (141 majors and 26 minors) — up by 15 from ive and encouraging environment throughout cial on October 26 for not only undergradu- the previous year. Of these, 65 students grad- their time with us. We began the 2018-2019 ates, but also graduate students, post-doctoral uated in Mathematics, 33 students graduated academic year by inviting all our students to scholars and faculty. in Applied Mathematics, 11 students gradu- attend our Undergrad Welcome Event, which Throughout the 2017-18 year they host- ated in Mathematical and Scientific Compu- took place on September 28th. At the event, ed several social events such as Game Night tation, and 32 students graduated from our we discussed the great things that one can do and Ice Cream Social, as well as outreach new Mathematical Analytics & Operations with a major in mathematics. We also talked events such as a visiting local middle and high Research (LMOR) major, up by 33% from last about the importance of starting early to plan schools and an interactive knot theory work- year, showing its growing popularity. At last an individual program of study in concert with shop at STEM for Girls. count, we have 118 LMOR majors, and a to- the staff and faculty advisors. We stressed that Several of our math majors participated in tal of 887 math majors, which has set a new we are here to help all our students succeed, mathematically based internships, for which record. and we described the multiple sources of sup- some received degree credit. The companies Among our graduates, 9 received Depart- port that are available when needed. our students worked at in past summers in- mental Honors awards for their senior theses A variety of activities are designed to foster clude banks, industries in China, and Kai- and for outstanding performance. Details are this atmosphere. All students are welcomed to ser Permanente. The activities they engaged provided in the Departmental Awards article the Math Club, which meets weekly (Thurs- in included cyber-security, marketing, and in this newsletter. days 5:10-6:00pm in the Mathematical Scienc- data analysis, implementing techniques they Several of last year’s graduating students es Building). The Math Club is dedicated to learned in their mathematics classes at Davis. went on to graduate school at prestigious in- advancing mathematics by building a strong The Department of Mathematics continues to stitutions, such as UCB, UCLA, UCSC, UCSD, community between and expand our course offerings and to hone its University of Michigan, Columbia University, people who enjoy math. They host guest lec- curriculum to enhance the experience of our Duke University, Cornell University. Many turers that range from professionals to profes- undergraduate students and to attract more other graduates went on to jobs in industry sors and provide a network of opportunities students to mathematics. This year, we will such as Financial Advisors, or as K-12 teach- for our members, as well as tasty snacks. Our offer three special topics courses for under- ers. These achievements testify to the commit- undergraduate lounge just had a make-over; graduates (MAT 180): “The Mathematics of ment and dedication of our students. come check out the new space! The UC Davis Theoretical Physics” (Professor Andrew Wal- dron) in Fall quarter, “Invitation to Classical Analysis” (Professor Naoki Saito) in Winter, and “Introduction to Analytic Number The- ory” (Professor Craig Tracy) in Spring. Last Spring, approximately 40 students took our second annual one-unit career seminar “Get the Maximal Value out of your Math Degree.” Led by Tim Lewis and Malina Gillies-Doherty, the course included a presentation by the In- ternship and Career Center, a graduate school panel, and visits from alumni who now work as data scientists, network engineers, web de- velopers, digital marketing analysts, and math teachers.

Undergraduates working in the newly furnished Undergraduate Study Lounge 8 Undergraduate Research

Undergraduate research helps students thrive in graduate education and in industry. Students enrolled in research programs ex- pand their skills in a subject matter, learn to think independently, and solve problems out- side the standard class environment. Students learn to present their research results at local and international conferences and some of them become co-authors in scientific papers. The UC Davis Deparment of Mathematics has been providing undergraduate students with research opportunities for many years. Undergraduate Research Conference Students doing research in our Department are introduced to the latest problems in math- ematical research and work directly with our faculty members and their graduate students. to a large audience of undergraduate students students nationwide know about our research Undergraduate advisor Malina Gil- and faculty members; and vivid discussions opportunities. lies-Doherty and Professor Javier Arsuaga are followed during the poster session. These in- Undergraduate research is a great way to starting a new effort to increase research op- clude Kyle Chickering, Michelle Flanner, Po- jump start a mathematics career! portunities for our students. The new program lina Khapikova, Aparna Komarla, Yuanbo Li, allows students to choose among different Diwen Lu, Lingyun Ye, Ruicong Zheng, and projects proposed by faculty members, and re- Zihao Zhu. To see samples of the research that search programs have grown from mostly sum- our students have done and to get informa- mer experiences to year-round opportunities. tion on how to get involved in undergradu- This Fall, the Department hosted the first ate research visit http://math.ucdavis.edu/ mathematics undergraduate research confer- undergrad/research. ence for UC Davis students. On a Friday after- Malina and Javier are working to expand noon, students presented their research orally this program further so that prospective

Mathematics for the Future The Department of Mathematics wishes Give Online We appreciate the many donors who dou- to thank all alumni, parents, students, faculty, If you would like to give, please go to the ble or triple the impact of their gifts through staff and friends who support the Department UC Davis secured giving site at: their employers’ matching gift program. For each year. For a list of our endowed funds, more information about matching gifts, you please see our web site: https://give.ucdavis.edu/Go/MathGift can go to: http://www.math.ucdavis.edu/about/donation/ Please click on “Donate to this Fund” and fol- http://matchinggifts.com/ucdavis/ low the prompts. Your gift to the Department is tax deduct- A list of donors can be found at the end of For additional questions please contact the ible as allowable by law, and you can choose this newsletter. Thank you for your continuing Development Office at (530) 752-3429. For to have your name published or remain support. your reference, disclosures can be viewed at: anonymous. http://giving.ucdavis.edu/ways-to-give/dis- Your gift can be used towards undergradu- closures.html. ate and graduate support, faculty and research support, and/or Departmental priorities. Your gifts ensure our future success. 9 Sallee Teaching - Allison Moore Schwarze - Nathaniel Gallup Schwarze - “Karry” Wong Ruliffson - Katharine Scott

Department Awards for 2018 Ruliffson - Michael Venturino G. Thomas Sallee Mathematics Teaching Award William K. Schwarze Scholarship in Mathematics Robert Lewis Wasser Memorial Scholarship The G. Thomas Sallee Mathematics Teach- William Karl Schwarze was born in 1942 Robert Lewis Wasser was born in 1973 in ing Award honors Professor Emeritus Tom Sal- in San Francisco. He excelled in mathemat- Sacramento. He excelled in many areas—he lee’s 40-year career with the Department, his ics in high school and at UC Davis, where he was selected as a National Merit Scholar in dedication to being an excellent teacher, and received a bachelor’s degree. He went on to 1991 and participated in the Academic De- his life goal of developing and supporting tal- graduate school at Berkeley and a career as a cathlon. Robert began at UC Davis in 1991. ented mathematics educators. mathematics teacher in San Francisco. Perhaps His academic achievements were numerous An endowment was established in his due to his mathematical insights, Bill also be- and impressive. He was one of the few stu- name that allows the Department to recognize came a successful investor in real estate. After dents in our Department who had already tak- the best teaching of lower-division mathemat- his death in 1988, a trust he established with en as a sophomore some of our most challeng- ics courses on an annual basis. the SF Foundation has donated to a variety of ing courses, such as Math 127. His instructor Recipient – Allison Moore humanitarian purposes, in particular to the in that course, Professor Don Chakerian, said Schwarze Scholarship to be presented today. how much he was inspired by their discus- G. Thomas Sallee Mathematics Prize This award is given to graduate students in sions and that Robert’s presence made the This award is also given in recognition of Mathematics who have demonstrated out- whole class much more lively and spirited. Af- Professor Emeritus Tom Sallee, and reaffirms standing mathematical scholarship and excep- ter his tragic death in an automobile accident his life goal of developing and supporting tal- tional promise of making a strong professional in 1993, prior to his Junior year, his grand- ented individuals in mathematics. This prize contribution as a mathematics teacher and ed- mother, Vera May Wasser, initiated the Robert recognizes exceptional undergraduate students ucator at the pre-college or college level. Lewis Wasser Endowment in his memory, with of junior or senior standing who competed in Recipients – Nathaniel Gallup and Ka Wai contributions from family and friends. Its goal this year’s Spring Mathematics Competition. “Karry” Wong is to benefit promising mathematics students Recipient – Zhenyi Chen at UC Davis. McCurdy Family Scholarship Recipients – Mengzhu Yuan, Henry L. Alder Award The McCurdy Family Scholarship is to be runner up Bohan Yang Professor Henry L. Alder received his Ph.D. made to undergraduate student(s) in the Col- from UC Berkeley in 1947. After spending a lege of Letters and Sciences at UC Davis. As year on the faculty in the Department of Math- a scholarship, selection of recipients is based ematics at Berkeley, he joined the Davis faculty on academic merit and promise, therefore a as an Instructor of Mathematics. He advanced minimum cumulative GPA is required; at the to the rank of Professor in 1965, and officially time of this pledge agreement, the minimum retired in 1992. He then served as Department cumulative GPA for scholarships is 3.25 or Chair from 1992 to 1994. After his retirement, better. The Scholarship should be restricted to Professor Alder continued to teach in the De- students with junior or senior class standing, partment for many years. and may include all undergraduate majors of- Wasser - Mengzhu Yuan Professor Alder was also active in other fered in the Department of Mathematics, with campus programs and was always a strong ad- a preference for females. vocate for quality teaching. In 1999, Professor Recipient – David Williamson Wasser - Bohan Yang Alder gave a gift to the UC Davis Foundation to establish an endowment. This provides sup- port to mathematics graduate students at UC Davis through the Henry L. Alder Prize for Ex- cellence in Teaching, an award given each year to the graduate student who is deemed to be the top teacher among all graduate students in mathematics. Recipient – Andrew Gallatin

10 Alder - Andrew Gallatin Sallee Prize - Zhenyi Chen McCurdy - David Williamson Leung - Subhadip Dey Lin - Beibei Liu Lin - Alec Todd Silvia - Yuk Shing Lam Galois Service - Tina Denena Eric C. Ruliffson Scholarship in Mathematics Evelyn M. Silvia Scholarship for Galois Group Service Award Eric Canady Ruliffson attended UC Da- Future Mathematics Teachers The Galois Group is “the official voice of vis from 1964-1968, loved the study of math The Evelyn M. Silvia Scholarship for Fu- the graduate students in Mathematics.” All and excelled in it. He was first and foremost a ture Mathematics Teachers was established by graduate students in the Department of Math- problem solver, which helped him to achieve generous donations from family and friends ematics are members of Galois; this is how life-long personal and professional success. of the late Professor Evelyn Silvia. Evelyn was graduate students in mathematics collective- While attending UC Davis, Eric worked as a hired by the Department in 1973 after receiv- ly communicate with Department faculty and summer intern in the actuarial department ing her Ph.D. from Clark University. The focus staff. The group also coordinates and facili- of Pacific Mutual Insurance in Los Angeles of Evelyn’s passion and unwavering commit- tates various activities, such as Monthly Game and was hired by them upon graduation. Af- ment was to develop talented mathematics Nights and New Student Welcomes. ter serving in the Navy, Eric attended gradu- teachers at the K-12 grade level. She was ex- Every year, the Galois Group presents an ate school in demography at UC Berkeley. In tremely generous with her time, whether it award to recognize outstanding service and/or 1973 he resumed his actuarial career at Pacific was as a campus committee member or as an sustained commitment to the graduate group. Mutual Insurance. He became a partner at the adviser assisting students. Recipient – Tina Denena San Francisco office of Coopers & Lybrand This scholarship honors Professor Silvia’s and named a Fellow in the Society of Actuar- memory by encouraging students who aspire Departmental Citation Awards ies. He was subsequently elected to the Board to be future mathematics teachers. It recognizes The Department recognizes undergraduate of Partners for Coopers and Lybrand, the first a junior or senior with a major in mathemat- students of exceptional ability who have tak- actuary to be so honored, and later served on ics, applied mathematics or statistics who has en both a very strong selection of mathematics the Board of Partners for PricewaterhouseCoo- shown an interest in teaching mathematics. courses and have made substantial contribu- pers, the world’s largest consulting firm. The tions to the Department or their program. In Recipient – Yuk Shing Lam Eric C. Ruliffson Scholarship in Mathematics addition, they have all received strong recom- is awarded annually to students of junior or Yueh-Jing Lin Scholarship in Mathematics mendations from the faculty. senior standing majoring in mathematics. Yueh-Jing (Jean) Lin and Chau-Hsiung Recipients – Sophie Jean Quynn, Shengwei Recipients – Katharine Scott (Mike) Chuang created the Yueh-Jing Lin Fund Huang, Gu Wu, Jacqueline Xiao Sun, Alon- and Michael Venturino in 2009. This endowment provides scholar- dra Garcia Horta, Zachary Spaulding ship support to one or more mathematics stu- Alice Leung Scholarship in Mathematics dents each year. The scholarships are available Departmental Honors Awards Every year, undergraduate students have Alice Siu-Fun Leung received a Master’s de- to high-achieving mathematics students, either the opportunity to participate in mathematical gree in Mathematics in 1975 from UC Davis. undergraduate or graduate. Mr. and Mrs. Ch- research, culminating in a senior thesis. Stu- She later worked as a global property manage- uang are alumni of UC Davis who met while dents typically work under the guidance of a ment accountant in Hong Kong. She remem- they were graduate students on campus. Jean faculty mentor to complete original research. bered with fondness her days at UC Davis. She received her Master’s degree in mathematics in The results are reviewed, and pending on the enjoyed gardening and working as a volunteer 1971, and Mike received his master’s degree in quality and substance, the student can receive helping animals. agricultural education in 1969. In her will, Ms. Leung generously provid- Departmental high or highest honors. Recipients – Beibei Liu and Alec Todd ed funding to award scholarships annually to Recipients – Yuzhe Bai, Dominic Tianli graduate students in Mathematics. This award Yang, Joel Ryan Barnett, Nicholas Edward is given to students who have shown excep- Sherman, Alec Lin Todd, Zachary Spauld- tional promise in all aspects of mathematics, ing, Madeline Ashley Chen, Franklin James including research, scholarship and teaching. Kerstetter, Jake Parkhurst Recipient – Subhadip Dey

11 Citation - Spaulding, Quynn, Horta, Huang, Sun Departmental Honors - Spaulding, Sherman, Parkhurst, Kerstetter, Chen, ?, Barnett, Todd Updates from the Graduate Programs by John Hunter, Acting Vice Chair for Graduate Affairs by Matthias Köppe, Chair of the Graduate Group in Applied Math

The Graduate Program in Mathematics In Fall 2018 the Graduate Program in Ap- continues to thrive, with a diverse group of ex- plied Mathematics welcomed an incoming cellent and committed students. The program class of 14 new Ph.D. students, selected from awarded 9 Ph.D.s in mathematics in 2017- a highly competitive pool of applicants. The 2018, whose recipients went on to various ac- total number of graduate students in the Ap- ademic, postdoctoral, and industry positions, plied Mathematics program is 64. John Hunter, Acting Graduate Vice Chair and 14 new graduate students are entering We are proud of our program graduates, the program, including a Gates Millennium who go on to impressive careers in academia Scholar. The total number of students in the and industry. Here is a small selection. Tom program is now 71. Chartrand, who wrote his dissertation on “The Several of our graduate students were rec- Role of Subthreshold Phenomena in Synchro- ognized in the annual Department Awards cer- nization by Electrical Synapses” joined the Al- emony, featured in this newsletter. len Institute for Brain Science as a Scientist. The Department and its graduate programs Jamie Haddock, who wrote a dissertation on hosted several distinguished visitors during topics in optimization, started a postdoctoral the year. In particular, Thomas Hales gave the position at UCLA. Steffen Docken joined the second Thurston Lecture, an annual lecture Kirby Institute, UNSW Australia, as a postdoc. series named after Fields Medalist and former The GGAM faculty keeps growing, giving UC Davis our graduate students new opportunities for that was recently endowed by Ian Agol, and research interactions. Within the last year, two spoke on computer assisted proofs of mathe- faculty joined: matical theorems. Javier Arsuaga, professor in the Dept. of Molecular and Cellular Biology and in the Dept. of Mathematics. His research concerns the analysis of data in molecular biology and in particular in the field of DNA, 3D chromo- Matthias Köppe, Chair of GGAM some structure and genetics of chromosome aberrations. His methods include random Are You a Graduate? knotting, topological data analysis and numer- ical methods in statistical physics of polymers. We want to hear from you! Please send us Krishnakumar Balasubramanian, newly information about yourself so that we can stay appointed assistant professor in the Depart- in touch and share in your experiences out- ment of Statistics, works in the intersection side of UC Davis. of theoretical statistics, optimization and ma- Please complete our Alumni Questionnaire: chine learning with a focus on addressing the- http://www.math.ucdavis.edu/news/alumni_quest oretical issues arising regarding inferential and or send e-mail to: computational aspects of analyzing large scale [email protected] heterogenous datasets. We will do our best to include it in the next The academic activities of GGAM during newsletter. the last year included: The GGAM Annual Meeting, held in the afternoon of October 18, 2017, with a lecture by a distinguished external speaker and a short talk by a new GGAM faculty member. The GGAM Mini-Conference, held in the afternoon of February 15, showcased the breadth of research that GGAM offers, with 6 12 talks by Applied Mathematics faculty, as well Graduate Degrees Awarded Hagemeyer, Colin • Ph.D., Math • Spiders and Generalized Confluence, Kuperberg Bassett, Robert • Ph.D., Math • Stochastic and Convex Optimization in Statistical Estimation, Wets Post Degree Placement: Assistant Professor, Naval Postgraduate School Berrian, Alexander • Ph.D., Applied • The Chirped Quilted Synchrosqueezing Transform and Its Application to Bioacoustic Signal Analysis, Saito Post Degree Placement: Audio Research Engineer, Gracenote Chartrand, Thomas • Ph.D., Applied • The Role of Subthreshold Phenomena in Synchronization by Electrical Synapses, Lewis Docken, Steffen • Ph.D., Applied • Mechanisms Underlying Functional Effects of Drugs on Car- diac Dynamics (Insights from Idealized Models), Lewis Haddock, Jamie • Ph.D., Applied • Projection Algorithms for Convex and Combinatorial Optimi- zation, De Loera Post Degree Placement: Postdoc, UCLA He, Xiang • Ph.D., Math • Lifting Properties of Tropicalization and Their Connection to Brill-Noether Theory, Osserman Post Degree Placement: Postdoc, Hebrew University of Jerusalem Lamb, Kevin • Ph.D., Math • A Distance for Circular Heegaard Splittings, Thompson Post Degree Placement: Assistant Professor of Applied Mathematics, University of the Pacific The GGAM miniconference Liu, Wen • Ph.D., Math • Limit Linear Series on Cycle Curves, Osserman Paramonov, Kirill • Ph.D., Math • Essays in Combinatorics: Crystals on Shifted Primed Tableaux, Brigraded Fibonacci Numbers and Data Mining on Social Graphs, Schilling as a lively poster session, in which graduate Post Degree Placement: Software Engineer (Machine Learning), YouTube students and postdocs explained their recent Samperton, Eric • Ph.D., Math • Computational Complexity of Enumerative 3-Manifold Invariants, research. On February 15 and 16, a group of Kuperberg prospective Ph.D. students visited our campus, Post Degree Placement: Visiting Assistant Professor, UCSB and our mini-conference contributed to their Shin, Gicheol • Ph.D., Math • The rectangular representation of the rational Cherednik algebra of impression of our Department and campus. type A, Vazirani The conference ended with a reception and Post Degree Placement: Lecturer, Korea National University of Education Lunar New Year celebration held jointly with the Department of Mathematics. Smothers, Evan • Ph.D., Math • Self-Similar Solutions and Local Wavefront Analysis of a Degener- In Spring 2018 we continued our series ate Schrodinger Equation Arising from Nonlinear Acoustics, Hunter of Ph.D. exit seminars, established in 2017, Post Degree Placement: Data Scientist, Uber each with a reception to celebrate the re- Tam, Patrick • Ph.D., Math • Nearly Finitary Matroids, Babson search achievements of our graduating Ph.D. Xu, Yuanyuan • Ph.D., Applied • On several problems in Random Matrix Theory and Statistical students. Mechanics, Soshnikov Fall 2018 began with a well-attended inaugural event of the new seminar on the Haley, David • M.S., Applied Meyer, Alexander • M.S., Applied Mathematics of Data and Decisions at Davis Blaine, Alexander • M.A., Math Parker, Joshua • M.S., Applied (MADDD) on October 1. Gallatin, Andrew • M.A., Math Ponce, Michael • M.A., Math Gibbons, Alaina • M.S., Applied Rose, Adam • M.S., Applied Gorman, Kara • M.S., Applied Sheng, Stephen • M.A., Math Jarvis, Katelyn • M.S., Applied Sheu, Norman • M.A., Math Kim, Albert • M.S., Applied Sumpter, Joshua • M.A., Math

13 The Galois Group by Jennifer Brown, President Varied as ever, this Fall Quarter’s main graduate seminar featured student talks rang- ing from discovering low dimensional behav- ior in presumably high-dimensional dynami- cal processes to generalizing spin geometry to infinite dimensional loop spaces. Speakers in the Geometry/Topology sem- inar have been holding introductory talks during its student run counterpart, and gra- ciously partaking in a pizza lunch organized by graduate students. Large reading courses, Life After Davis including ones in symplectic geometry and information theory, and numerous smaller Alex Berrain, Ph.D. 2018 reading groups have helped keep graduate students bustling. I’m an Audio Research Engineer at Gra- to UCD’s proximity to the SF Bay Area, which Math Circles, an entirely student-run vol- cenote, which is owned by Nielsen. I’ve been is a good place to find networking events in unteer-based organization, has continued doing work on audio fingerprinting and auto- audio signal processing and music technology. holding math classes each Saturday. Weekly matic music style classification, as well as some But the knowledge I gained through working attendance ranges up to 35 high school or other secret stuff that we’ll be presenting at the on a harmonic analysis dissertation was central middle school students, and sessions include a Consumer Electronics Show in Vegas this up- to my career progress. mixture of competition preparation and guest coming January. Most days I’m programming, Over my college years, I was first a pure lectures. generally in C or Python. I collaborate with math guy, then I switched gradually to applied On the social front, the Galois Group held my fellow audio and video research engineers math over time. I transferred to UC Davis from its traditional Fall Quarter BBQ at Slide Hill to design new algorithms, and I’ve also been the University of Iowa, and I was originally Park, provided light breakfast during the pre- brought onto projects midway through to help focused on fluid dynamics and PDE before I liminary exams and a celebratory atmosphere push them out into production. switched over to applied harmonic analysis. (and snacks) during its traditional “postlim” When I found out that audio signal pro- I’ve always been into math, though hon- party. All 28 incoming graduate students were cessing existed as a field (I really had no idea estly not as much as my fellow grad students paired with a mentor as part of the “dual pairs” until like February 2014, midway through my at UC Davis, whose passion for the study I al- program and presented with a set of the noto- second year at UCD), I fortunately was already ways admired. My biggest passion in life has riously bright-neon Hagomoro chalk. enrolled in Professor Naoki Saito’s class Ap- generally been music, and I didn’t think that plied and Computational Harmonic Analysis. I should combine my biggest passion with my I told him about a source separation problem I career path. I’ve never been so happy to be was interested in: given a mono or stereo song wrong about something. recording, how can you cleanly isolate the vo- I took classical piano lessons starting from cals from the rest of the track? He referred me when I was 5 until I was 18. I also sung a lot Alumni Updates to an article he had read about a related prob- of karaoke with my relatives growing up, and lem of melody extraction. Eventually it became dabbled only a small amount in composition. Karen W. Owen, M.A. 1978 clear that we were of very similar mind, being I generally play and sing pop and R&B music Karen Owen was a member of the techni- both musicians interested in how math can be nowadays. I play a lot of ultimate frisbee and cal staff at AT&T Bell Laboratories and Lucent used in music signal processing, and I became I captained the math ultimate intramural team Technologies. his student. Perpendiscular for two seasons. I’m a proud Karen is now retired and living in northern Through this time I realized I had to do a lot gay man, and I think that it’s important for us Illinois. of exploring on my own to tie this newfound as a community to take steps towards ensuring audio interest into my career path. Professor inclusivity of queer and trans mathematicians. Saito allowed me a lot of freedom to tread my I’ve always been into math, though hon- David F. Hayes, Ph.D. 1980 After graduation at UC Davis, David was a personal path of study, while also very help- estly not as much as my fellow grad students professor at College of Notre Dame de Namur fully connecting me with collaborators in the at UC Davis, whose passion for the study I al- for a year. He then joined San Jose State Uni- anthropology and neuroscience departments ways admired. My biggest passion in life has versity as part of their Mathematics faculty. In who helped me expand my projects out from generally been music, and I didn’t think that 2001, he served as chair for both Math and mathematical theory into fun, real-world ap- I should combine my biggest passion with my Computer Science Departments, after which plications. He also allowed me the time to career path. I’ve never been so happy to be he continued as faculty for both Math and pursue internships in the music technology wrong about something. Computer Science until 2006. industry that helped me get where I am now. David is retired and presently living in I was able to get these internships in part due Portland, Oregon. 14 Staff Update by Gladis Lopez, Department Manager The Department staff had a very good year. The administrative team is fully staffed. The newest member is Joann Pyon who joined the Department as Advising Coordinator. Joann filled the vacancy left by Stephanie My- ers who accepted a position in another UC Da- vis Department. Our chair, Abigail Thompson, was elected Vice President of the American Mathematical Society, the largest organization in the world for research mathematics, with 28,000 indi- vidual and 560 institutional members. She will serve a three year term from 2019 through Emeriti Update 2021. The past year saw 19 merit and promotion actions. The Department processed numer- Art Krener ous research proposals to funding agencies, Art Krener continues to teach and do re- The Winter AWM mentorship social of which twenty one proposals were awarded, search at Naval Postgraduate School. Last year producing a total of $3,390,403 in new re- two Army Captains and a Coast Guard Lieu- search funding. tenant Commander wrote their masters’ thesis Tina Denena received the Galois Group under his supervision. He gave talks at UCSB, AWM Update Service Award. Sarah Driver was a co-organiz- UCSD and University of Colorado. and a short by Katy Jarvis, Co-president er of the first Graduate Student Advisors con- course on computational issues in nonlinear This year, the UC Davis Student Chapter ference at UC Davis, an event that had over control at the University of Padua. of the Association for Women in Mathemat- 100 participants. Malina Gillies-Doherty has ics (AWM) has hosted events and workshops, been creative in coming up with programs with the goal of encouraging inclusivity and to enhance our undergraduate student sense supporting women in math. of community by organizing a new mentor- For the third year in a row, AWM hosted a ing program for transfer students and a cof- mentorship program. Undergraduate students, fee-with-a Prof program for Mathematics ma- graduate students, and faculty were paired jors and upper division students. into mentor/mentee groups to foster a sense of I thank all the administrative staff for all community and provide support to students. their great contributions and look forward to AWM also continued a local outreach pro- another productive year. gram. Members visit local schools and connect with young female students, teaching students to see the possibilities of mathematics and in- spiring them to continue learning about math. AWM is additionally starting a new math club for girls at Pioneer High School in Woodland. In the past year, AWM has also host- Join us on Facebook! Interested in the Past? ed quarterly workshops aimed at educating members. The Department of Mathematics is on Prior newsletters back to 1994 are available on In late 2017, our chapter was honored to Facebook! Visit us there to get updates on the Department of Mathematics website. be named by UC Davis as “The Inspirational current seminars, events and news. We’d be Aggies of the Year” at the 2017 Center for Stu- happy to include any memories or photos you https://www.math.ucdavis.edu/research/news/archive/ dent Leadership Awards. have of the Department on our wall. Finally, AWM has hosted speakers, pro- To “like” us, search for “Department of moting prominent women mathematicians to Mathematics - UC Davis” on the Facebook speak at Davis. web page: It has been a great year with AWM and we https://www.facebook.com/ are excited for what comes next!

15 Nonprofit Org U.S. Postage MATHEMATICS PAID 1015 Department of Mathematics UC Davis University of California, Davis One Shields Avenue Davis, CA 95616-8633

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Featured on cover: Many members of the Mathematics Depart- ment play musical instruments. The beautiful alternating link shown on the cover is inlaid on the back of a viola da gamba belonging to De- partment Chair Abigail Thompson, and was made by local luthier Devin Hough. Knots such as this one are studied in the mathematical area called Topology.

Featuring the 2017-18 Academic Year

Newsletter Committee: Joel Hass, Editor Gladis Lopez, Management Services Officer Marianne Waage, Designer

Thanks For Your Support The Department of Mathematics wishes to gratefully acknowledge the generosity of the following donors, who have contributed to its support over the past several years.

Ian Agol Herbert Holden Brent Schultz Rex & Mary Allen Donald Ichikawa & Jann Nakashima Bryan & Erica Schultz William & Laura Beattie Hazel Jacoby Jennifer Sharples James Boudinot Robert Jaffa Roy Simpson John & Joyce Boyland Jeffrey & Pamela Jarvis Sherman & Hannah Stein Ernest Tam & May Chau Edmond & Susanna Kong Seth & Jennifer Stevelman Richard Collins Juleen Lam Allan Thompson Bruno Nachtergaele & Marijke Devos Jack Latimer John & Ngangiang Thoo Sarah Donovan Eric Lee Julian Thurston Gennis Emerson Jeffrey Martell Ursula Van Dijk Daniel & Joy Faletti Nelson & Mika Max Ronald Vucurevich Maureen Keesey Fuentes Chareles Morris, III Carolyn Weist Gary Gruenhage Tan Nguyen James & Sybil Wells Fields & Carol Gunsett Shon & Carrie Prisbrey Andrew & Kathleen Williams Robert Guy Diana Rojek-Skonnord Dennis & Betty Winslow David Hall & Lauren Breon Dan Romik Earl Wong Joel Hass & Abigail Thompson Sandra Ruliffson Sidney Wong & Marion McCurdy Stephen Hennagin Amre Saadeh