Undergraduate/Research News Department News Faculty News Graduate News Alumni News VirginiaVirginia MathMath BulletinBulletin Issue 3 Volume 1 June 2016

Kerchof Hall . Last summer View from the Chair the front Kerchof was completely redone, The articles this newsletter Work onthis summer continueve manys offices being reflect the tremendous activity of had in the department while we ha

during academic year. It renovated.

wewas amazingin year for us. Our faculty sustains its excellence. Leonid Petrov The year the began by welcoming won the Moscow Math Prize, while Ben Webster thean department three has been promoted to Associate Professor, won

the Cory Family Teaching Award,um and was a Kavli Paul Bourdon, to Aseel Farhat. the winternew Fellow – the only pure mathematician invited edto spring we hadfaculty: an extremely Thomas activeKoberda, hiring toattend the Kavli Symposi at the National season. a result,and five facultyIn will be Academy of Sciences. Karen Parshall was elect joiningand the department - Jennifer the important Nominating Committee of they Ascomes a Fullnew Professor in American Mathematical Society and next year Combinatorics, Julia Bergnerin 2016 17. Associate putsanotherhaton,becoming ChairoftheHistor ProfessorMorse in Algebraicas Juraj Department. Foldes (PDEs), Francesco Plinioas an (Harmonic Analysis), Sara Maloni , - and Please enjoy reading about these successes and Geometry) join us as Di Professors. We changes, as well asadother articles on ”Citizen welcome newand post doctoral fellows: (Low Dimensional Axel - Science”, on John Berman’s experiences helping Rodriguez in Probability, Assistant and Ramanujan train the U.S. Olympi team last summer, about Santharoubane Topology. We also welcomeSaenz new the activities, ofd our Math Club, about ourr staff member Allison Boese. distinguished lecture series in the Institute of in Mathematics an about the activities of ou a c alumni. Craig Huneke This year marked the start of nticipated hanges Marvin Rosenblum Professor of Mathematics in our undergraduate program as w ell. Our Distinguished Majors Program, wasr reorganized and Supporting Us revitalized into a more robust experience. Under the direction of Paul Bourdon ou new Director of t is its a Lower Divisional courses, next year we will be The Mathematics Departmen grateful for the generous fts a y to its most u t ds, a beginning our movement to ward smaller and more support of lumni and friends. The Department wel- to t h pr interactive Calculus classes. Two of our graduate comes gi nnuall address rgen nee s ty. w y students, Peter Bonventre and Katelynn Kochalski, well as the endowmen whic ovides funding in per- t will be helping to change the wa y we teach our petui To learn about ho you can make a difference b iz Bl - o Math 1310 courses next Spring. Our major supporting the Mathematics Department, please contac t , program continues to be robust and challenging. L aine at [email protected] or (434) 924 6156. T This year we had what may be a record of nine of 1 make a gif online please visit http://giving.virginia.edu/ our majors being electedto Phi Beta Kappa. mathematics Student Awards

Edwin E. Floyd Prize in Mathematics E. J. McShane Prize in Mathematics April 2016 April 2016 The 2016 Edwin E. Floyd Prize in The 2016 E. J. McShane Prize in Mathematics was given to Peter Dillery. The prize Mathematics was given to Alexander Grieser is awarded to second- or third-year students who show exceptional promise in mathematics. for his achievements in mathematics.

William Lowell Putnam Mathematical Competition Award April 2016 The 2016 William Lowell Putnam Mathematical Competition Award was given to Sifan Ye, Juan Velasco, and Arun Kannan for their outstanding scores on the exam. Congratulations!

As the oldest and most distinguished honor society in the country, Phi Beta Kappa offers membership to less than one percent of all undergraduates. Many of the leading figures in American history and culture have begun their careers with election to the society, including Nine Majors have been elected seventeen presidents of the into Phi Beta Kappa United States. As a result, Congratulations to: membership is a remarkable accomplishment, both for the Peter Dillery, Stephanie Gulley, Ji Won student who achieves it and the Kim, Honglei Li, Hexuan Liu, Megan faculty and staff whose support Marcellin, Yingze Song, Qi Tang, and and guidance has led to this Boya Yang! milestone.

2 Department Transitions Benjamin Webster Associate Professor examples of his r w in e Ben We has b n ng h l k in ts whose f t to Particular ecent ork clud bster ee ch ics a e known p l k ot e P of constructi omologica not varian promoted rom Assistan conj es on the relat b n Ben comp Euler aracterist r olynomia n Associat rofessor the rep n t of q ions of the his PhD at U Ber invariants, ectur ionship etwee Mathematics. leted s an C b nches of cer p sical under the g e of resentatio heory uantizat C keley in e t s an g ng new pro s of a Nicolai Re He then held p ons at the Higg d oulomb ra tain hy 2007 uidanc d on of the a ues of ute for A M the U ty o gaug heorie d ivi of shetikhin. ositi - p ls f both C an Nor n U b e conjectured escripti nalog Instit dvanced Study, IT, niversi f L supe e co- a ng the f at UVa. H s be an Kazhdan Lusztig olynomia or herednik Oregon, d theaster niversity, efor in May 2 at UVA on r top C R g a S oan F an and ie ralgebras. H organized joini aculty e' en awarded has p or conf s in Pa s to travel to ce a A a conference 016 elated ics, NSF AREE rant, l ellowship, d l an Boston. B has serv as a ment r the C F Teaching A and reviously ganized erence ris, fellowship Fran nd ustralia, nd g stud ts in und - g oups UVA ( page 7 s r h is on the Montrea d en ed or recently eceived ory amily ward the U M I ute a f the ion b g algebra an for raduate en er represented r from see ). Ben' esearc ion for Wom in M H also ach of these f s has p in VA entoring nstit nd or intersect etween eometry, d es on the AM C on Pub ions ns in the othe so g ic i n Associat en athematics. e topology. E ield rofound A an is a b membe o lea to a c m w constructs serv S ommittee licat and applicatio rs, eometr ntuitio a succes ul - - er l invar Web dvisory Group, d oard r f can d lgebrai achinery hich e for r h m MathOverflow, sf question and answ topologica iants. Paul Bourdon relatedsit toesearc superdenseathematics. coding with partially Director of Lower Division entangled quantum particles. Courses and his research He has published has been supported through four grants and two mathemat w e p more than 50 papers and books, -opportunity awards from the National w in es a A ician hos ub- Science Foundation. In 2000, Bourdon received xt on har c f on t research lished ork clud graduate the John Smith Award for Distinguished Teaching a resea mo h on cy te moni uncti heory; of Mathematics, conferred by the MD-VA- DC f com on op an rch nograp clic Section of the Mathematical Association of articles in P sical Re the J l of the phenomena or positi erators; d Bourdon earned a Ph.D. in mathematics n M S an the J l of hy view, ourna from the University of North Carolina at Chapel l A Paul on will irect the America. America athematical ociety, d ourna Hill (1985) and a bachelor's degree in p am an s e as a men f the Functiona nalysis, Bourd d mathematics and physics from Washington and s g assi H calculus rogr d erv tor or Lee University (1981). He has held appointments h interests i e operator theor department' raduate-teaching stants. is at Michigan State University, W&L, and the com ope s act on sp ces researc nclud y University of Tennessee, an c f f on t ( c & (especially position rator ing a an q - on t Knoxville. of alyti unctions), uncti heory analyti 3 harmonic), d uantum informati heory DepartmentDepartment TransitionsTransitions Aseel Farhat Thomas Koberda Whyburn Instructor Assistant Professor

s a Z n P al as K a was a I Un the last l S e F ion A or ostdoctor Fellow Thom oberd y A l Fa hat al F at Yale at ndiana iversity Nationa cienc oundat ht cou ses on dif al f two y s three ears, see r Postdoctor ellow c linear e b ng aw a taug r ferenti University or ear a, sis, d uate l Willar Gib s A equations, alculus, befor ei arded l eq ons. he also w d as a in Yale s algebr analy an grad partia J. d b ssistant uate h assis nt at the Los Alamos of M ics in differentia uati S orke Professorship ' l La s C r of ar Kobe s r h f ses on geometric grad researc ta Department athemat s in 2 r ng her Ph.D. in oup t an low l top In Nationa boratory' ente Nonline 2014. rda' esearc ocu ics at the Un ersity of a, he is i in map class Studie 201 afte completi gr heory d -dimensiona ology. e that year. s r h interests oups of su in d hism g oups o mathemat iv Californi particular, nterested ping e n r al d l eq , A n gr an the t of Irvin Farhat' esearc gr rfaces, iffeomorp r f luid mics, sical models of s arr includ onlinea parti ifferentia uations manifolds, rti oups, d opology d the atmosphere, mical sy ms, data is p w s in e a p er in f dyna geophy ocean hyperplane angements. ion a s, d c an sis. Geometric an F l A - an dyna ste H ublished ork clud ap Her work has been published in the Journal of A n gr ups a a gene assimilat lgorithm an harmoni aly d unctiona nalysis ("Right Mathematical Physics, the Journal of hism pro lem f f g angled rti o nd ralized Communications in Mathematical Physics, the oups of map class g Decembe isomorp b or initely enerated Journal of Communications in Information and an a j p sched f subgr ping roups," r Systems, the Journal of Communications on on in G & Topolog ( - 2012) d oint aper uled or Pure and Applied Mathematics, Physica D: trees a r - A n sub oups of p ar publicati eometry y "Anti r a J l, d the J l g co- w h Sa - un nd ight angled rti gr lan of cal Fluid ics. er academic Nonlinea Phenomen ourna an ourna s in e the C lly d or braid roups," authored it ng hy Mathemati Mechan H a recei his Ph. in mathematics fr m ce in Re ch d Teaching (20 ) Kim). honor clud onne Awar f Un ( He also r his d a Gr uate s Dissertation F ship Koberd ved D. o Excellen sear an 12 s in mathemat s fr H ( ) at the U ersity of C a, e, s Harvard iversity 2012). eceived an ad Dean' ellow g h h s fr the U ersity ell as the M a Nasser Fellowship or master' ic om arvard 2008) (2011 niv aliforni Irvin a C o w h a B. in mathemat t P sics S ts ( - ) at t and raduated wit onor om niv w ous f y in e. at d her of hicag it S. ics. Excellen hy tuden 2002 05 Birzei s d ee in sics at Bi t ( , Universit Palestin Farh earne e she also r ived a master's d ee in bachelor' egr phy rzei 2005) ic com g . n a ion to her wher ece egr , at ed her . in s scientif putin (2007) I ddit at UC I Ph.D. Farh complet M.S mathematic 4 rvine. MathMath ClubClub

active und math clu is or ts a f lea that the st A ew Obus and L Pe This year, b method is in fact b n b Our ergraduate b ganized Studen nd aculty rned andard the club had an array o sp ers and other b that the dif o " by ndr eonid trov. airplane oarding eate y As e fr U. math p s ( in on e c es makes them f eak random oarding, ficulty f dividing und --- Zy suite f an that activities. id om Va. rofessor and by tegers" llipti curv ers came fr the U ersity o C o in the p - one ergraduate Bradley koski), ideally d or cryptography, d n S Un of Br ish ay US can be mea mathemat f m speak om niv f hicag "liberalness/conservativeness" resent a ( Br UC D ( Ke r s w h onl the sli (Aaro ilberstein), the iversity it d sured ically ro U ( Willia M ( Buf notion of what the te ms actually Columbi David ydges), S Todd mp), voting ecord it y ghtest he topics r f an ai JM Cassie ms), and IT Alexey etov). preconceived r tly (b ou v n Leo Pe to T anged rom boarding rplane mean!he math clu act es culm w h an c cu e cr ( J s C efficien y r ery ow trov), ion Be w h questions wr n b f - to what it m means fo T b iviti inated it ellipti rv yptography by MU' assie stud t Be in w f - to be the " th most liberal "Integrat e," it itte y irst Williams), athematically r stud t Arun Ka was cr " er ( J n K o f the U Polit year en njamin Keigwin hich irst someone 11 I year en nnan owned Mast senator” by o ropk rom .Va. ics of ntegrals." department).

Andrew Obus studies number theory

5 Virginia Mathematics Lecture Series

In 2014, the IMS established the Distinguished Lecture Series ``Virginia Mathematics Lectures.’’ This year, Ian Agol (UC Berkeley), and – most recently – Karen Smith (University of Michigan) presented the lectures. These lectures were given to an enthusiastic audience which included undergraduate and graduate students, faculty members, and guests from other departments and institutions.

Spotlight: Ian Agol means a new manifold made from M by unraveling a certain collection of loops) contains an essential In October 2015 Ian Agol (Professor of surface without self-intersections. The reason Mathematics at the University of California - (explained by German mathematician Wolfgang Berkeley and Visiting Distinguished Professor at Haken in the 1960s) why this is important is that the Institute for Advanced Study in Princeton) gave such surfaces may be used to cut the three- a series of three lectures, the Virginia Mathematics dimensional shape into smaller pieces which are Lectures, on his proof of the famous Virtual Haken easier to study. For his work on this conjecture Conjecture. This conjecture was formulated by Agol was awarded the 2013 Veblen Prize of the in 1982, and its resolution is a American Mathematical remarkable culmination of work by many Society and the 2016 mathematicians in the subject of 3-dimensional in topology. The goal of 3-dimensional topology is to Mathematics. These lectures classify 3-dimensional shapes, rigorously were accompanied by a mathematically defined as "manifolds". Agol's workshop on geometric theorem states that every 3-dimensional manifold group theory. M has a "finite cover" (a mathematical notion which

Spotlight: Karen Smith r the ts of these Smith is the ons mod p ime n ers in a suit le equations, educing coefficien Pro of then st thei sets of solu ons over Karen equati ulo r umb p ab cs at the e fields as one v s the p imes p The Keeler fessor sense, udying r ti of M us h hism taking elements to thei Mathemati finit arie r . he gave thr lectures th p ers pla s a fu l University ichigan. Frobeni omomorp r on the uses of Smith in the S ee p ow y ndamenta ic p methods in algebraic geom t of Fro ius sp s role. troduced on the classification of sin ty es sho ho it in s characterist etry, concep ben litting using numerical in ts coming f r ion the st of sin s an specifically gularity p and wed w fluence to char c p This in es be used to stud clu varian rom educt udy gularitie d the si es of alg c v s acteristi . method volv can y ster er the com lex num ers by r the studying ngulariti ebrai arietie algebras. s as the set of z oes of p l ov p b epresenting 6 varietie er olynomia Faculty Awards and Honors

Leonid Petrov Discusses his Series of Works, Combinatorics of Branching distributions of spectra of random matrices. Here Graphs and Probabilistic Models, for one starts from exact computations in the which he Won the 2015 Moscow Math Gaussian case, and then expands the asymptotic Society Prize results to general distributions of entries of the matrices. Systems I am interested in are similar to random matrix models, but are discrete, which In several past decades, leads to even stronger ties to algebraic structures. Probability Theory has Despite the specialty of the approach using exact been widely successful in formulas, above examples provide hope that the analyzing complicated asymptotic behavior observed via exact random systems modeling computations should be universal, i.e., it should numerous real-world phe- also occur in large classes of "similarly looking" nomena, from spectra of random systems which do not necessarily admit heavy nuclei to shapes of melted crystals and exact formulas. growing bacteria colonies. A significant part of Benjamin Webster Receives Cory Family these developments is made possible by Teaching Award applications in a probabilistic context of ideas and methods from more abstract areas of Congratulations to Associate Professor Benjamin Mathematics, such as Representation Theory or Webster. He was named as one of two recipients of Algebraic Combinatorics. Applying these ideas, I this year’s prestigious am exploring a rich zoo of complicated random Cory Family Teaching systems by means of concise exact distribution Award, and joins David formulas. These formulas allow to approach Sherman (2013) among asymptotics of these special random systems (as the award recipients time or size of the system goes to infinity). from the Mathematics A historically first example of applying exact department. The Cory formulas to study randomness is the De Moivre- Family Teaching Awards Laplace theorem from the 1700s, which states are designed to reward that the coin-tossing frequencies can be and incentivize excellence in teaching among junior approximated using the famous bell-shaped curve faculty. Since 2013 and continuing through 2017, (the normal, or Gaussian, distribution). More two junior faculty members are chosen as recipients than 100 years later, this exact computation was and honored at Fall Convocation. Each recipient is followed by the general Central Limit Theorem awarded $25,000 thanks to the generosity of Mr. allowing to use normal approximations in much and Mrs. Charles R. Cory. Well done, Ben! more general situations. In the recent 10 years, a similar program was completed (by two groups led by and Horng-Tzer Yau) for

7 FacultyFaculty AwardsAwards andand HonorsHonors

2016 Conferences Honoring Members of our Faculty

Algebraic Groups, Quantum Groups, and Geometry Workshop Honoring Brian Parshall his w w as part of the S n L Th series , as at the U ersity o V on May 2 ay 2 th of this year. The T orkshop, hich w outheaster ie eory w was sup b the Na l S nce F ion as well as held niv f irginia, 4th—M 7 the U ersity o V ’s I ute for M cal S May 2 th conference ported y tiona cie oundat as d as a sp al day in recog on of the wo ou own niv f irginia nstit athemati ciences. 6 Br n P w esignated eci niti rk of r professor, ia arshall. Dunkl Operators, Special Functions and Harmonic Analysis he M cs I ute at the Un of Pa n in Germany is to hold a conference in honor of C les Du T athemati nstit iversity derbor on the occ on of his 7 th bi The confe w will ta e Paderborn, har nkl lace Au ust 8 - th o this year, will center on cur t dev s asi 5 rthday. rence, hich k the man f s on w Du ’s st n the i n p g th 12 f ren elopment Du ope s in the 19 s has had an im The confer ce w ll in y ield hich nkl work – mo otably, nventio also in e relate topics such as harm c an sis on sy ic of nkl rator 80 – pact. en i s al fu an or l p volv d oni aly mmetr spaces, peci nctions, d thogona olynomials.

Conference at the University of Michigan to Honor Craig Huneke he Un of M at A A will h a ho C Huneke in r on of his 6 th T iversity ichigan nn rbor old This conference will take place J 7th to J 1 conference noring raig ecogniti 5 an is e “ e Alg a a its birthday. uly uly 2th, ons w h A c Geom Ti ht C 2016, d ntitled Commutativ ebr nd an S Interacti it lgebrai etry: g losure, Linkage, d yzygies.”

8 Graduate Experiences

John Berman Discusses Coaching the Team that top 6 students then attend the IMO. At the IMO, Won the International Mathematical Olympiad about 500 students from 100 different countries compete to solve 6 very difficult problems in 9 I first got involved in math competitions in 7th hours. grade. I was at a small middle school of 50 students, and my math teacher encouraged me to Technically, the problems require no background come to MATHCOUNTS meetings. At the regional beyond high school mathematics, but in practice, competition that spring, I surprised myself by competitors train for years before they can solve winning 1st place. I realize now that I came from a even one problem. This year, the US surpassed small region of Eastern North expectations by coming in 1st place for the first Carolina, and certainly would time since 1994, beating out China not have done so well even in and South and North Korea. Most Raleigh or Charlotte, but at importantly, everyone had a the time I was extremely great time and made new excited by this performance. I international friends. assumed it meant I could get I have enjoyed being a part of so in the top 10 at the state level many diverse mathematical competition. When the state communities, from Charlottesville competition came around, John Berman (right) with the IMO team and North Carolina to MIT and the I got 44th place. What I took international level. Here in Charlottesville, I try out of the back-to-back success and disappoint- to give back to the community in the ways that ment was an enthusiasm for math competitions meant the most to me as a student. Last year, I and a drive to improve. The next year, I got 2nd worked with local middle and high school math place in the North Carolina state competition, and clubs and math teams, and I volunteered at the by the summer after 12th grade, I was traveling to regional MATHCOUNTS competition, the same Germany to compete in the International Math competition where I got started back in middle Olympiad (IMO) as one of a six-person team from school. I have also been involved with Tai the US. Melcher in outreach to middle school classrooms. I have been closely involved in the IMO This year, I will be helping to run the Putnam training ever since then, returning to the IMO as training for UVA undergraduates. The Putnam is an observer in 2013 (Colombia) and 2014 (South the premiere college-level math competition in Africa). This year, the IMO was in Thailand, and for the US. In short, I'm looking forward to an the first time, I was able to go as Deputy Leader, exciting year for the UVA and Charlottesville-area the second-in-command of the US team. This also math community! involved helping the team leader, who is a math professor at Carnegie Mellon University, to run a month-long training program in Pittsburgh. At the For an example of one of the problems, see our training program, there are about 50 students, Problem Corner (page 13). taught by a collection of graders and instructors who have been through the program before. The

9 RecentRecent PhDsPhDs cott Alexander A on Dav S S tkins S s A to C*- [Advisor: id herman] Convex et ssociated Algebrasalo Bley Del o L ce Th as] Gonz gad s on l I als of Non- c [Advisor: awren om tum Fi Th h A ions to the Estimate Functiona ntegr Relativisti Nelson a Polaron M Quan eld eory, wit pplicat o De S i [Ad Cnd H odels l M Alessandr tefan visor: raig uneke] an Homologica ethods, l I Singularities, d Numerica nvariantsel E [A M l E the Re ual Fi ss of L Dani . Franz dvisor: ikhai rshov] Quantifying sid nitene inear Groups hen R H [A Dav S ct C*- Step . ardy dvisor: id herman] Pseudocompa Algebras Ko Br n P ] ( 1 Hankyung ns of quant g oups at [Advisor: ia arshall Sum 6) oots of unit an thei ons mod p to Representatio um r c g oup r r y d r reducti n Ju Lai [Ad W ng W algebrai r epresentations e Qu tum Sym tric Pa M n Chu visor: eiqia ang] las an C cal Base Affin an me irs: ultiplicatio Formu d anoni s ce A. Ter H C n Gro Bry williger em Queues w h I cal S [Advisor: . hristia moll] imes in H Tr Tand it denti ervice Joshua S T eavy affic A Rap ] 1 chwartz C le Z - [Advisor: ndrei inchuk (Sum 5) oups of A c Groups Define O er Weekly ommensurab ariski Dense s of Posi e Ch Subgr lgebrai d v 10 Field tiv aracteristic Alumni Activities

Turbulence Games In the fall of 2015, Rafner carried the project over the Turbulence—both `bad' and `good'—is omnipresent in Atlantic to Denmark, as a part of her Fulbright the world surrounding us. On one hand, understanding Fellowship research in collaboration with Rikke Schmidt the genesis and dynamics of a turbulent wake behind a Kjaergaard, the head of iNANO Visualization Lab at large plane is key in maintaining safety of the airspace in Aarhus University. An immersion in the science and art & the proximity of an airport. On the other hand, turbulent design communities of Aarhus and Copenhagen, and mixing may be desirable, an example being designing keeping in touch with Grujic, recently sparked the more efficient drug delivery systems. project Gamification of turbulent flow, A.K.A. the Turbulence Games. Various coherent vortex structures are observed at all scales, from spiral galaxies to solar wind phenomena to This project is best viewed as a part of a greater hurricanes and tornadoes to tea leaves spiraling in movement for citizen science-based research and will be a cup to quantized vortex motion in Helium II. in conjunction with the Niels Bohr Institute (NBI) and Some of the more famous artistic renditions of the vortex ScienceAtHome, a large-scale crowdsourcing project phenomena include Leonardo da Vinci's drawings of based in Aarhus University. ScienceAtHome transforms eddy motion in the study for the elimination of rapids in open science problems into games and invites citizens of the river Arno, a woodblock print The Great Wave off all possible backgrounds to play them. People worldwide Kanagawa by Katsushika Hokusai and a painting of spend three billion hours a week playing games. By Starry Night by Vincent van Gogh. turning science into games, researchers can tap into that resource; the gameplay ultimately translates into On the scientific side, large-scale computational scientific data, shining a new light on the problem in simulations of turbulent flows confirm that the regions of view. intense fluid activity organize in coherent vortex structures. Developing a rigorous theory of turbulence Turbulence Games are based on the recent mathematical consistent with the experiments, computational work by Grujic and collaborators on the interplay simulations and the phenomenology, and identifying the between the mechanisms of vortex stretching and locally role that the geometry of the flow plays in the theory of anisotropic diffusion as the main physical cause of the turbulent cascades and turbulent dissipation in 3D phenomenon of turbulent dissipation. Incidentally, this incompressible, viscous fluid flows, modeled by the 3D approach also provides a new avenue to better and more Navier-Stokes (NS) equations, has been a grand chal- geometric understanding of the problem of possible lenge in the mathematical fluids community since the formation of singularities in the 3D NS model (one of the foundational works of Kolmogorov, Onsager and Taylor Millennium Prize Problems). in the 1930s-1950s period. Richard Feynman described A key facet in this novel theory is the scale of local linear turbulence as “the most important unsolved problem of sparseness (LLS) of the regions of intense vorticity (RIV), classical physics.” and it would be very useful to have solid computational The seed for the Turbulence Games was planted in Fall results revealing the value(s) (in an appropriate average 2014 and Spring 2015 when then undergraduate Janet sense, as anything in turbulence) of its scaling exponents. Rafner took two semesters of MATH 4993, Independent Within the realm of the state-of-the-art of the Study, with math professor Zoran Grujic. computational fluid dynamics, simulating the RIV is feasible; unfortunately, a purely algorithmic After completing her study, Rafner was eager to test her identification of the scaling exponents of LLS does not design talents and scientific visualization skills, catalyzed seem to be. while she was on a summer internship with the French research team Le Physique Autrement (Physics Reimagined), lead by Julien Bobroff, within the realm of turbulent flows. In a summer 2015 REU-type project, under the guidance of Grujic, she produced a storyboard for scientific visualization of the two fundamental ways in which the coherent vortex structures emerge in turbu- lent flows: a flow past an obstacle and vortex shedding off the boundary. This was done with an eye on produc- ing detailed visualizations using Maya animation software, and with the end-goal of bringing the secret life of turbulent entities closer to the public. The great wave off Kanagawa by Hokusai 11 The computational barrier and human's innate abilities in pattern recognition is why the Aarhus-NBI-UVA research team proposed a gamification approach to the problem, based on visualization of the RIV via Maya animation software, within Unity development platform. The game Janet Rafner is a US Fulbright Fellow and visiting will utilize the data imported from the computational researcher at the Niels Bohr Institute, University of simulation of the RIV to be performed by the NBI group Copenhagen and at ScienceAtHome, a large-scale for modeling of complex phenomena, simulating a fully crowdsourcing project based at Aarhus University. She developed 3D NS turbulent flow on a periodic box with graduated in spring of 2015 from the University of the Reynolds number of the order of 1000. (This would Virginia and holds degrees in Physics and Studio Art. provide much higher resolution and accuracy compared While at UVA Rafner was an officer for both the Society of to the output that would have been generated using the Physics Students and Sigma Pi Sigma, the physics honor NS solver already incorporated in Maya.) society. Her current work bridges domains of physics, mathematics, design, science communication, simulation The main point of this approach is to replace the purely modeling, ‘gamification,’ didactics, and science, algorithmic identification of the scale of LLS of the RIV technology, and society (STS). with gathering the same information via the gameplay. Essentially, a player would traverse scenes of the At ScienceAtHome Rafner works on all things design turbulent world', each scene representing a visualization related, co-maintains the ScienceAtHome website, and is of an RIV, and identify the scaling exponents of LLS in currently developing physics visualizations. At the Niels process. Bohr Institute, Rafner, along with a fluid flow simulation group, is collaborating with UVA math professor Zoran This seems to be well within the capabilities of the Unity Grujic on a project to create an innovative, 3D game engine, as the main data set would be essentially computationally intensive video game to engage the static (the data imported from the computational public in the efforts of the mathematical fluids simulation of the RIV), and writing a dynamic script for community to solve one of the Millennium Prize verification of the correct choice of the scale with the real Problems: whether a singularity can form in a turbulent -time feedback should be feasible. The purpose of the flow. Rafner has also curated ‘physics + design’ initial levels (I III) of the game would be to test and train exhibitions at the Science Museum of Virginia and at the players in identifying relevant scales in the context of the Niels Bohr Institute for Copenhagen’s Culture Night. She progressively mor - e and more complex geometry (this intends to pursue a career that integrates the arts and the part is also of interest to cognitive scientists studying the sciences while continuing to find new ways to reimagine processes behind the reaction time and accuracy of a physics. player when confronted with this type of spatiotemporal challenges). Players completing Level III will gain access to Level IV, offering high resolution RIV scenes, where hard scientific data will be collected from every gameplay. The Level I is currently being developed by a game designer from the Aarhus group.

Janet Rafner

12 tt ni lat p s in thr - ( p Thets withProblem in coef Corner e that 1. Given ne tice oint ee space that is, SpotlighSpotligh onon AlumniAlumni there is an i lat ce p ( does not nine oin teger ficients), prov e to be one the n on at least one seg nterior ti oint which ng a p ir o them. hav of ine) ment joini a f O, 20 Dete all triples ( of p e i s such that each of the n ers ab- 2. (IM 15) rmine a,b,c) osi- - an ca- is a p of 2 ( = 2 is a tiv nteger umb0 c, bc a, d b ower 1 llowed). M Two p an ahead of time of the task they will be asked to do, 3. (From SRI) risoners, A d B, know he M h M s d r this S g and develop a strategy for They ed . n M e as our uest not e in y ay once the task as T at ajor inne prin 100% succeeding. er. . e received his PhD f m n. at ns is the foll A s a featur Dr Berrie oor g can communicat an w h UVa under M in . d room in which the 52 cards of an ordinary deck are speak Dr Moor ro begu Wh happe owing. enter to talk out his j y om a PhD in face up in a line on a table. A is allowed to take two arv Rosenblum He returne to his cur t p n at the of the cards and interchange them. A then leaves, ab ourne fr y of ma as the C e and the warden turns the cards face down without mathematics ren ositio y ion Ch r in e disturbing their positions in the line. B enters the Universit Oklaho hesapeak Dean of the Col e of Atmospheric The warden announces a card selected at Energ Corporat ai Climat d hic S s, or of the random. The task B must perform is turn the cards Studies, leg room. l Weather , d ice up one at a time (B can decide which card to turn an Geograp cience Direct t for her d e up at any given point on the basis of what B has Nationa Center an V ams. e sp e a out the cr on and already seen). If the card is among the first 26 that Presiden Weat an Climat ersion of in the e and B turns up, both prisoners go free. What is the Progr H ok b eati s. . e j d the U ersity of strategy? disp CO2 atmospher New e in 19 9 d ed there What are you Doing? ocean Dr Moor oine niv l 2 . ts to the s H We’d like to hear from you! Hampshir 6 an stay hic I ute p ed You may complete the form below and return it to us: unti 008 Visi Wood ole important role in his transition from Form [ctrl+click]: http://pi.math.virginia.edu/ Oceanograp nstit lay an pure mathematician to questionnaire.pdf interests in climate. He has published Facebook:[Ctrl+click].https://www.facebook.com/ his current UVAMath extensively on the global carbon cycle, FAX: 434-982-3084 biogeochemistry, remote sensing, Email: [email protected] environmental and space policy, and Department of Mathematics University of Virginia mathematics. P. O. Box 400137 Charlottesville, VA 22904-4137 13