From the Chair Abel Prize for John Nash *50 Fields Medal for Manjul Bhargava *01

16 Pages·2016·5.89 MB·English

Spring 2015 Issue 4
Department of Mathematics Princeton University
Abel Prize for John Nash *50 From the Chair
John Nash *50 received the 2015 Abel Prize This has been quite a year for
from the Norwegian Academy of Science and the Mathematics Department;
Letters for his work on partial differential however, space allows for mentioning but
equations. Nash shares the $800,000 prize a few of the highlights. To start with, we
with Louis Nirenberg, a professor emeritus are overjoyed to have Maria Chudnovsky,
at NYU's Courant Institute of Mathemati- Fernando Marques and Assaf Naor as new
cal Sciences. The prize recognized Nash and members of the senior faculty. Their pres-
Nirenberg for “striking and seminal contri- ence has already made a major impact on
butions to the theory of nonlinear partial the Department.
differential equations and its applications to
Manjul Bhargava *01 won the Fields medal
geometric analysis.” Nash’s name is attached
at last summer’s International Congress of
to a range of influential work in mathematics,
Mathematicians in Seoul, Korea. Manjul is
including the Nash-Moser inverse function
not only an extraordinary mathematician
theorem, the Nash-De Giorgi theorem (which stemmed from a problem Nash undertook
but also an unusually gifted teacher and
at the suggestion of Nirenberg), and the Nash embedding theorems, which the academy
tabla player.
described as “among the most original results in geometric analysis of the twentieth
century.” According to David Gabai, the Nash embedding/immersion theorems, which John Nash *50 and Louis Nirenberg from
required unusual insight as well as tremendous technical expertise, played an important NYU are this year’s Able Prize winners.
role in the development of young mathematicians who came in contact with Nash at While John is famous for winning the 1994
Princeton in the 1970s. Nobel prize in Economics for his Ph. D. the-
sis work on non-cooperative games, this is
the first major recognition for his extraor-
dinary work on isometric embeddings and
partial differential equations which most
mathematicians consider incomparably
deeper work. With Yasha Sinai winning the
Abel prize in 2014, this marks the first time
Fields Medal for
the Abel prize has gone to mathematicians
Manjul Bhargava *01
at the same institution in consecutive years.
Last summer saw the passing of two long
Manjul Bhargava is awarded a Fields
time professors, Harold Kuhn 50* and Ed
Medal for developing powerful new
Nelson. Harold and Ed were original and
methods in the geometry of numbers,
influential mathematicians who respectively
which he applied to count rings of small
changed the face of mathematical econom-
rank and to bound the average rank of
ics and constructive quantum field theory.
elliptic curves.
A special day was held on April 22, 2015 to
from the award citation commemorate Ed’s work.
Our finishing graduate students wrote mar-
Manjul Bhargava *01, the Brandon Fradd, sity). The prize comes with a monetary velous theses and obtained excellent first
Class of 1983, Professor of Mathematics, award of Canadian $15,000 as well. positions. Of the twenty Sloan Foundation
was awarded the 2014 Fields Medal on Bhargava’s Ph.D. thesis (written under fellowships in mathematics awarded this
August 13, at the opening ceremony of the the direction of Andrew Wiles, the James year, eight went to former Princeton grad-
2014 International Congress of Mathemati- S. McDonnell Distinguished University uate students; Richard Bamler, Boris Bukh,
cians in Seoul, Republic of Korea by South Professor of Mathematics, Emeritus), Vivek Shende, Andrew Snowden, Jacob
Korean President Park Geun-hye. provided a reformulation of Gauss’s law for Tsimerman, Melanie Wood, and Hau-tieng
For 2014, there were four Fields Medalists the composition of two binary quadratic Wu from Math and Lin Lin from PACM. In
(Artur Avila of the CNRS in Paris, Martin forms. He showed that the orbits of the addition, assistant professors Vlad Vicol and
Hairer of the University of Warwick in group SL(2,Z)3 on the tensor product Tasho Kaletha were also winners.
the UK, and former Princeton professor of three copies of the standard integral We have many excellent teachers among
Maryam Mirzakhani of Stanford Univer-
continued on next page continued on next page
....continued
Fields Medal for Manjul Bhargava (continued) Department Chair’s letter (continued)
representation correspond to quadratic Persi Diaconis, whose research incorpo- our faculty and students. Peter Sarnak won
rings (i.e., rings of rank 2 over Z) together rates decks of cards and coin-flipping with the University’s Phi Beta Kappa teaching
with three ideal classes whose product is other random problems. Bhargava thought award and grad student Thomas Beck won
trivial. This recovers Gauss’s composition they would be a good way to introduce stu- a teaching award from the Graduate School.
law in an original and computationally ef- dents to a field considered dry and daunt- Departmental teaching awards went to in-
fective manner. He then studied orbits in ing to many. “The Mathematics of Magic structors Jeffrey Case and Mihai Fulger
more complicated integral representations, Tricks and Games” was designed to show and graduate students Nathan Dowlin and
which correspond to cubic, quartic, and the artistic and creative side of mathemat- Thomas Beck.
quintic rings, and counted the number of ics, which Bhargava asserted is how math-
Departmental staff play the crucial behind
rings with bounded discriminant. ematicians approach their research. He
the scenes role that enables us to focus on
wanted to offer this seminar to freshmen
Bhargava next turned to the study of repre- our research, teaching and studies. Eszter
to capture their enthusiasm early in their
sentations with a polynomial ring of invari- Rudy joined the Department as Grants and
college careers while introducing them
ants. The simplest such representation is Business Manager, replacing Alberta Molnar
to the ‘correct’ and ‘fun’ side of math-
given by the action of PGL(2,Z) on the who got promoted to a managerial position
ematics. For this initiative, Bhargava was
space of binary quartic forms. This has two in the Sponsored Research office, and is off
awarded several grants from the University,
independent invariants, which are related to a great start.
including the 250th Anniversary Fund for
to the moduli of elliptic curves. Together
Innovation in Undergraduate Education Our Department Manager Kathy Apple-
with his graduate student, Arul Shankar,
and a grant from the University’s Council gate received the Presidential Achievement
Bhargava used delicate estimates on the
on Science and Technology. Award. Kathy has done tremendous work
number of integral orbits of bounded
for the Department and so we are delighted
height to bound the average rank of elliptic Students appreciated his enthusiasm and
that she has been recognized at the highest
curves. Generalizing these methods to outstanding commitment to his classes.
university level.
curves of higher genus, he recently showed His availability to the students and dedica-
that most hyperelliptic curves of genus at tion to providing interesting topics and Coming full circle, Scott Kenney has an-
least two have no rational points. visiting lecturers was unsurpassed in the nounced his pending retirement. To many
Department. of us Scott was the embodiment of the Math
Bhargava’s work is based both on a deep
Department. During his 25 years as De-
understanding of the representations of Sharing his love of mathematics extends be-
partment Manager, chairs came and went,
arithmetic groups and a unique blend of yond the university. He recently returned
but from day visitors to long-time faculty he
algebraic and analytic expertise. from a tour of India where he traveled to
was there as a constant, welcoming and ap-
a large number of high schools to discuss
Bhargava joined the Mathematics Depart- proachable soul always ready to tackle prob-
the beauty of mathematics with students.
ment as a full professor in 2003. In addi- lems from the complex to the mundane.
He is also head of a committee devoted to
tion to the Fields Medal, he has received
bringing scientists from all over the world While members of our faculty, students and
numerous other awards including the 2012
to visit schools throughout India. staff have received high profile recognitions
Infosys Prize, the 2011 Fermat Prize (pre-
for their research, teaching and service,
sented by the Toulouse Mathematics Insti- Bhargava was born in Ontario, Canada but
their awards reflect but a small fraction of
tute in France) and the Packard Foundation raised in New York on Long Island with
the tremendous productivity, energy, and
Fellowship in Science and Engineering in frequent trips to Jaipur, India, to visit fam-
enthusiasm that permeates Fine Hall.
2004. He was elected to the U.S. National ily. His interests include Sanskrit poetry
Academy of Sciences in 2013. and Tabla drumming. Considered a tabla Finally, it is my pleasure to thank Bob and
expert, he has given numerous free tabla Luisa Fernholz, Wei-Tong Shu and the Class
Bhargava is an outstanding teacher on both
performances at student cultural programs, of 1971 Fund for their very generous and
the graduate and undergraduate levels. In
international fairs, and charity benefits on ongoing support of the activities of our De-
recent years, he developed a very popular
both the Harvard and Princeton campuses. partment.
freshman seminar called “The Mathemat-
ics of Magic Tricks and Games,” which had Thank you for reading this newsletter and
the maximal enrollment of 15 students reconnecting with the Department. I’d love
in Spring 2013 and Spring 2015. He also to hear your thoughts and views.
Amazing. Everyone was engaged and it was always so much
taught “The Magic of Numbers” in the
fun. I don’t know how this course could be improved. It was
Spring 2007 and Spring 2010, an under-
the best experience ever, and even swayed me to consider David Gabai *77, *80, Chair
graduate course he developed that included being a math major! I don’t really know how Professor
guest lecturers, card games, and drumming Bhargava does it, but he’s able to explain with incredible [email protected]
to capture the attention of the class whose clarity very complicated ideas and make them extremely
interesting. He seriously deserves a medal or some honorary
enrollment neared 160 students.
award for the work he’s done with the class.
As an undergraduate at Harvard, Bhargava
Excerpt from a student evaluation
was exposed to magic from his adviser,
of a class taught by Manjul Bhargava
page2
Faculty news: we’ll miss them
Edward Nelson
Professor Emeritus Born in Decatur, Georgia, Nelson lived in ability theory to attack the hard analytic
Edward Nelson, 82 Italy as a child, under the dictatorship of questions of constructive quantum field
died of complica- Benito Mussolini. He moved to New York theory,” as stated on the award citation. The
tions from lympho- City before the start of World War II but latter paper “fired one of the first shots in
ma on September later returned to Italy to attend high school. what became known as the Euclidean revo-
10, 2014 in Prince- As a graduate student at the University of lution,” according to the AMS. Among his
ton, where he lived Chicago, he studied under Irving Segal and other honors, Nelson was elected to the
with his wife, Sarah received his M.S. in mathematics in 1953. American Academy of Arts and Sciences in
Jones Nelson. He came to Princeton after an appointment 1975, the National Academy of Sciences in
as an NSF Postdoctoral Fellow from 1956- 1997, and the American Association for the
Nelson received
1959 at the Institute for Advanced Study. Advancement of Science in 2003.
his Ph.D. from the
University of Chi- Although accomplished in many areas of Nelson enjoyed teaching and taught very
cago in 1955. He was appointed Assistant mathematics, Nelson was perhaps especially successfully on both the graduate and un-
Professor at Princeton University in 1959 well known for his successful application of dergraduate levels. (He had looked forward
and was promoted to the rank of associ- probability to quantum field theory. He re- to teaching a junior seminar called, “Radi-
ate professor in 1962 and full professor in ceived the Steel Prize for Seminal Contribu- cally Elementary Mathematics,” in the Fall
1964. He became Professor Emeritus in tion to Research in 1995 from the American semester, 2014.)
2013 upon his retirement. Nelson’s re- Mathematical Society (AMS) in recognition
In addition to his wife, Nelson is survived
search inspired further research and ad- of this work. The AMS also recognized two
by a son and daughter, three grandchildren,
vancement in the fields of analysis, prob- of Nelson’s papers (respectively published
and two great-grandchildren. He was pre-
ability, and mathematical logic. in 1966 and 1973) that “showed for the first
deceased by his first wife, Nancy Wong
time how to use the powerful tools of prob-
Nelson.
Harold W. Kuhn *50
Professor Emeritus of Mathematical Eco- Division of Mathematics for the National forever. He is par-
nomics Harold W. Kuhn *50 died peacefully Research Council from 1957-60, Mem- ticularly renowned
in his sleep on July 2, 2014 in New York ber of the National Research Council from for the “Kuhn-
City where he lived since 2005. He would 1961-64, and Senior Consultant and Board Tucker Theorem,”
have been 89 years old on July 29, 2014. Member for MATHEMATICA, Inc., from (in collaboration
1961-83. He also served as a co-Director with Albert W.
Kuhn was appointed at Princeton jointly in
of the NATO International Summer School Tucker), which is
the Mathematics Department and the Eco-
in Varenna, Italy for 1967 and 1970 and as considered a ma-
nomics Department as an Associate Profes-
co-Director of the NATO Advanced Study jor contribution to
sor of Mathematical Economics in 1959 and
Institute in Capri, Italy, for 1987. the development
was promoted to the rank of Professor in
of nonlinear pro-
1963. He became a Professor of Mathemati- Among his many honors were a Guggen-
gramming. He also
cal Economics upon his retirement in 1995. heim Fellowship for 1982-83 and Honorary
made many impor-
Kuhn was considered a world-leader in the Membership in the Hungarian Operations
tant contributions to general equilibrium
fields of linear and nonlinear programming, Research Society (1992). He was a Fellow
theory and the treatment of information in
game theory, combinatorial problems, and of the Econometric Society (1961) and Fel-
extensive form games.
the application of mathematical techniques. low of the American Academy of Arts and
Sciences (1992). He shared the John von Kuhn was a gifted teacher on both the un-
Kuhn was born in Santa Monica, CA in
Neumann Theory Prize with David Gale dergraduate and graduate levels. During his
1925. He served in the United States Army
and A.W. Tucker in 1980. tenure at Princeton, he also served diligent-
from 1944 to 1946. He received his B.S.
ly on a number of University committees
from CalTech in 1947, and his M.A. (1948) He edited the first two volumes of “Contri-
that had a profound impact on the Univer-
and Ph.D. (1950) from Princeton. He butions to the Theory of Games” with the
sity community.
joined the faculty at Bryn Mawr between late Professor Albert W. Tucker of the Math-
1952 and 1959. ematics Department. He was a member of Kuhn is survived by his wife, Estelle (nee
a prominent group of economists who in- Henken), whom he married while a gradu-
Kuhn served as President for the Society for
troduced sophisticated mathematical tools ate student at Princeton in 1949, three sons,
Industrial and Applied Mathematics (SIAM)
into economic analysis and changed the field six grandsons, and a granddaughter.
for 1953-54, Executive Secretary of the
page 3
Faculty appointments- professors
Maria Chudnovsky *03 Assaf Naor Fernando Codá Marques
returned to Princeton as a full professor joined our department as a full professor joined our department as a full professor on
jointly appointed in the Mathematics De- on September 1, 2014. Prior to coming September 1, 2014 after being a professor
partment and the Program in Applied and to Princeton, he was appointed Professor at IMPA—Associacão Instituto Nacional
Computational Mathematics on January 1, of Mathematics at the Courant Institute of de Matemática Pura e Aplicada in Rio de
2015. She comes from Columbia Univer- Mathematical Studies, New York Univer- Janeiro, Brazil. His field of research is in
sity, where she was appointed as Liu Family sity. His field of research includes Analy- Geometric Analysis.
Professor of Industrial Engineering and Op- sis, Probability, Quantitative geometry, and
Marques received his Ph.D. in Mathematics
erations Research and Professor of Mathe- their applications to combinatorics, math-
from Cornell University in 2003 studying
matics. Her field of research is in Discrete ematical physics, and theoretical computer
with Jose Escobar. He was the recipient of
Mathematics and, specifically, in the areas of science. His work on the Lipschitz Exten-
the 2012 Academy of Sciences for the De-
graph theory and combinatorial optimiza- sion Problem is an example of his very sig-
veloping World (TWAS) Prize, cited “for his
tion. nificant contributions.
contributions to the field of differential ge-
Chudnovsky received her Ph.D. in Math- Naor received his Ph.D. in Mathematics ometry, particularly for his work on varia-
ematics from Princeton University in 2003 from the Hebrew University in Jerusalem tional problems in conformal geometry and
working with Paul Seymour as her thesis ad- in 2002, where he also received an M.Sc. in applications of the theory of Ricci flow.” He
visor. She received a M.Sc. from Technion 1998. His awards include Bocher Memorial also was awarded the 2012 International
Israel Institute of Technology in 1999. Prize in 2011, the Salem Prize in 2008, and Centre for Theoretical Physics’ (ICTP) Ra-
the European Mathematical Society prize manujan Prize for Young Mathematicians
Her awards include the MacArthur Foun-
in 2008. He has been a prominent speaker from Developing Countries (It is supported
dation Fellowship in 2013, and the D.R.
at the University of Chicago (Zygmund- by the Norwegian Academy of Science and
Fulkerson Prize in 2009, which she shares
Calderón Lectures in 2011), International Letters through the Abel Fund, with the co-
with collaborators Neil Robertson, Paul
Congress of Mathematicians in Hyderabad, operation of the International Mathematical
Seymour, and Robin Thomas. She was also
the Indian state of Andhra Pradesh (2010), Union.) Fernando gave a plenary address
awarded a five-year Clay Mathematics Insti-
and was the plenary speaker at the annual at the International Congress of Mathemati-
tute Research Fellowship in 2003. She was
meeting of the Israel Mathematics Union cians in Seoul Korea, in 2014.
an invited speaker for the Combinatorics
and the Clay Research Conference, both in
Section of the International Congress of Marques is one of the world’s young leaders
2008. He also served as our Minerva Lec-
Mathematics held in Seoul, South Korea in in geometric analysis. He has made several
turer in October 2013 and gave a series of
2014. She was appointed jointly at Princ- fundamental contributions to a broad range
talks in our department as part of that spe-
eton and the Institute for Advanced Study of problems in geometric analysis, includ-
cial program.
as a Veblen Research Instructor from 2003- ing the very recent solution to the long-
2005 and was promoted to assistant profes- standing Wilmore conjecture (with André
sor for 2005-2006. Neves).
NOTICE: STAFF OFFICE CHANGES
LeeAnn Coleman, our Undergraduate Administrator, has moved her office to 315, along
the central third floor corridor of Fine Hall. Her office is now next to that of Graduate
administrator Jill LeClair, so that students can readily receive the administrative support-
they need and have a ready, friendly face during difficult times.
page 4
Faculty appointments/promotions
A
Mykhaylo Zsolt Patakfalvi Fabio Pusateri
S
Shkolnikov
Algebraic Geometry Analysis of PDEs: Dis- S
Probability theory, (with connections to persive and Wave Equa- IS
its applications to Complex and Arithmetic tions. Fluid Dynamics: T
A
mathematical finance, Geometry and to Com- Euler Equations and
N
queueing theory, and muta- tive Algebra). Water Waves. Harmonic
T
statistical physics. Analysis and applica-
Ph.D. in Mathematics, University of Wash-
P
tions to PDE. Hamiltonian Dynamics and
Ph.D. in Mathematics, Stanford Uni- ington, Seattle, 2011; Masters in Math- R
Small Divisors.
versity, 2012; Diploma in Mathematics, ematics (summa cum laude) Eötvös Lorand O
Ludwig-Maximilians Univeristy in Munich, University, Budapest, Hungary, 2006; Ph.D. in Mathematics, New York Uni- F
Germany, 2007; Vordiplom in Mathematics Masters in Computer Science, Technical versity, 2011. Masters in Mathematics , E
S
(passed with distinction; minor in comput- University of Budapest, Budapest, Hun- University of “Roma Tre”, 2006.
S
er science), Ludwing Maximans University gary, 2004.
Previous positions: Simons Postdoctoral O
in Munich, Germany, 2006.
Previous positions: Instructor, Princeton Fellow, Princeton University, Department R
Previous positions: Postdoc Department of University, Department of Mathematics. of Mathematics. S
Statistics, UC and MSRI, Berkeley.
Patakfalvi also serves as our junior Director Co-organizer of the Analysis Seminar and
Shkolnikov will be moving to ORFE next of Graduate Studies. the Analysis of Fluids and related topics
academic year. We wish him well in his Seminar.
new position.
I
Lucas Culler Chun-Hung Liu N
S
Gauge theory, invariants of smooth 4-mani- Graph Theory, combinatorics, and algo-
T
folds, mirror symmetry. rithms. R
U
Ph.D. in Mathematics, MIT, 2014; B.S. in Ph.D. in Mathematics, Georgia Institute of
C
Mathematics, University of Chicago,2009. Technology, 2014; M.S. in Mathematics,
T
National Taiwan University, 2009; B.S. in O
Mathematics (with minor in Computer R
Michaela Ignatova
Science and Information Engineering), S
Partial Differential Equations, Mathemati- National Taiwan, 2007.
cal Fluid Dynamics, Harmonic Analysis.
Ph.D. in Mathematics, University of South- Jonathan Kommemi
ern California, 2011; M.Sc. in Mathematics
50% Instructor 50% NSF Postdoc
and Mathematical Physics, Sofia Uiversity
General Relativity.
“St. Kliment Ohridski” in Sofia, Bulgaria,
2006; Maitrise de Mathématiques, Uni- Ph.D. in Applied Mathematics and Theo-
versité de Nates in France, 2004; B.Sc. in retical Physics, University of Cambridge
Mathematics, Sofia University “St. Kliment 2013; M.A.St. Part III of the Mathematical
Ohridski,” in Sofia, Bularia, 2004. Tripos, University of Cambridge, 2009;
B.A. in Mathematics (with Highest Distinc-
Previous positions: Postdoc, Stanford
tion), University of California, San Diego,
University; Visiting Assistant Professor,
2008.
University of California, Riverside.
Daniel Ketover Ana Menezes
Geometric Analysis, specifically Min-Max Differential Geometry.
techniques and their use in producing
Ph.D. in Mathematics, Assciação Instituto
embedded minimal surfaces in Riemann
Nacional de Mathemática Pura e Aplicada
3-manifolds.
(IMPA) 2013; M.S. in Mathematics, Uni-
Ph.D. in Mathematics, MIT, 2014; A.B. in versidade Federal de Alagoas (UFAL) 2009;
Mathematics (Magna Cum Laude), Harvard B.S. in Mathematics, Universidade Federal
College, 2007. de Sergipe (UFS) 2008, all in Brazil.
page 5
Faculty Awards
Manjul Bhargava *01 Emeritus Professor John H.
Conway
Foreign Fellow of the Indian National Sci-
ence Academy Doctor Honoris Causa of Alexandru Ioan
Cuza University, Iasi, Romania
The election, effective from 1 January 2015,
cites Bhargava’s “spectacular work with his The award was presented at a ceremony
discovery of composition laws of higher de- held on June 24, 2014.
gree, originally discovered by CF Gauss in
The awarding of this degree and attendant
the nineteenth century for quadratic forms.
conference in Iasi marked the official open- Vlad Vicol
His work in algebraic number theory is pro- ing of the Grigore Moisil Institute, a joint J
found and extraordinarily original. It has u
initiative of Alexandru Ioan Cuza University n
revolutionized the way in which number Ph.D., University of Southern California
of Iasi and the University of Bucharest. i
fields on elliptic curves are counted.” (2010); M.A., University of Southern Californiao
(2007); B.Sc., Jacobs University Bremen, Ger-r

many (2005). L.E. Dickson Instructor at thef
The Padma Bhushan award, one of the Sergiu Klainerman University of Chicago (2010—2012); Assistanta
highest civilian awards in the Republic of Professor of Mathematics, Princeton Univer-c
Simons Fellow in Mathematics u
India sity, since September 2012.
l
The Simons Foundation Division for Math- t
Manjul Bhargava was contacted by the Pres- y
ident of India to return to India to receive ematics and the Physical Sciences offers the Vicol hails from the beautiful city of Ora-
the Padma Bhushan award at Rashtrapati Simons Fellows Programs in both Math- dea, in Transylvania, Romania. pr
ematics and Theoretical Physics, providing o
Bhavan (the President’s House). The award, His research lies at the intersection of par-
funds to faculty for up to a semester long fi
confered by the president, is offered for tial differential equations and probabilityl
research leave from classroom teaching and e
“distinguished service of high order” and theory, with an emphasis on problems aris-
administrative obligations.
this year’s recipients include Bill and Melin- ing in fluid dynamics. His work focuses
da Gates as well as the famous Indian actor on the analysis of equations describing in-
Amitabh Bachchan. Amit Singer compressible Newtonian fluids, such as the
Navier-Stokes and Euler equations. These
Moore Investigator in Data-Driven Dis-
models account for interactions between a
covery
broad range of space and time scales (in a
The five-year awards, offered by the Gor-
highly nonlinear fashion) and the accuracy
don and Betty Moore Foundation will en-
needed to fully resolve the underlying phe-
able the recipients to make a profound im-
nomena via numerical computations is out
pact on scientific research by unlocking new
of reach for the foreseeable future. Two of
types of knowledge and advancing new data
the questions that drive Vicol’s work are:
science methods across a wide spectrum of
Do singularities in the fluid equations ex-
disciplines.
ist? If they do, what do they teach us about
turbulence?
Tasho Kaletha The mathematical tools he uses in his re-
search come from different areas in analysis,
and
such as harmonic analysis, regularity theory
Vlad Vicol
(elliptic and parabolic), spectral theory,
Sloan Fellows in Mathematics stochastic analysis, infinite dimensional dy-
namical systems, convex integration, and
The Sloan Research Fellowships seek to
integro-differential equations, among oth-
stimulate fundamental research by early-
Chair: David Gabai ers.
n career scientists and scholars of outstanding
o Associate Chair: János Kollár promise. They are awarded in recognition Both his graduate-level research and his
i
t Directors of Graduate Study:
a of distinguished performance and a unique graduate teaching were recognized with
Alex Ionescu and Zsolt Patakfalvi
r potential to make substantial contributions prizes: the 2009 Dennis Ray Estes Graduate
st Dept. Representative: János Kollár to their field. Research Prize and the 2009 Theodore Ed-
ni Associate Dept. Representative: Jennifer Johnson
ward Harris Graduate Teaching Prize, both
mi Senior Advisor: Paul Yang
from the University of Southern California.
Junior Advisor: Mark McConnell
d He was also awarded a Center for Applied
a Placement Officer: Vlad Vicol
Mathematical Sciences’ Graduate Student
Dept. Manager: Congratulations to Fields Medal winner Prize by USC in 2010. And, recently, he
Kathleen Applegate
Maryam Mirzakhani
who was on received a Sloan Research Fellowship in
Graduate Administrator: Jill LeClair
our faculty from 2004 to 2008. Mathematics for 2015.
page 6
Teaching Awards
Junior Faculty Teaching Graduate Teaching
This is the second year of the Department of This is the third year of the Department of
Mathematics Junior Faculty Teaching Award. Mathematics Graduate Teaching Award.
Jeffrey Case has been described by Teaching awards recognize excellence in Nate Dowlin was nominated for this
teaching at the undergraduate level. Selec-
his students as helpful and caring, a superb award because of his obvious commitment
tion for both awards was made by a commit-
and masterful lecturer who is able to pres- to teaching and dedication to his students.
tee of senior faculty members.
ent complex material in a way that is easy He is an innovative teacher who brings his
to understand. His students range from love of mathematics to the classroom, in-
math majors to non-majors and they have troducing new ways to keep his students
found his classes to be a valuable learning engaged. His students commented that he
experience while being highly enjoyable at stimulated their curiosity and independent
the same time. He has worked as a course thinking through daily puzzles, through ex-
head as well and has proven himself to be planation that revealed hidden connections,
well-organized and thoughtful, taking his and through lectures that were always both
duties quite seriously and serving as a valu- illuminating and engaging. One of his stu-
able mentor to his teaching colleagues and dents said, “He opened every class with a
to novice instructors as well. math riddle, and I looked forward to it ev-
ery MWF!”
Mihai Fulger’s students have referred Thomas Beck’s student evaluations
to him as ‘a great teacher with a terrific per- were overwhelmingly positive—with 17
sonality’ and ‘the perfect preceptor.’ He has out of 19 students attending his calculus
been exceptionally attuned to how his stu- class giving him the highest rating of “excel-
dents think and what they find challenging, lent.” His quiet and serious teaching style
always able to respond to their questions served as an inspiration to his students. In
with both clarity and insight. Students have his student nominations, one student said,
also described him as clear and methodical “Tom was a great teacher. His teaching was
while displaying a sense of humor that al- clear and organized, and he always made
ways kept his classes interesting. Teaching sure we understood what was going on be-
colleagues have found him to be insight- fore moving on to the next concept. He
ful, judicious, and generous as well. He has was patient with our questions, and able
served well as course head, taking those to explain things in a way that made sense,
duties seriously and creating supplemental which I think is very valuable for a math
handouts for an introductory course in lin- teacher.” Another student wrote, “I could
ear algebra, which was of great use to both not have asked for a better teaching for my
students and instructors alike. first math course at Princeton.”
MINERVA PROGRAM - Year 4 Through the generosity of the Minerva Foundation, the Mathematics
Department hosted another special lecture series during the Fall term.
Barry Mazur *59 Diego Cordoba *98
This year’s Minerva Lecture series was giv- Our Minerva Distinguished Visitor was Di-
en by Barry Mazur of Harvard University in ego Cordoba of the Instituto de Ciencias
mid-October 2014. The topics of Professor Matemàticas of Madrid. He spent the Fall
Mazur’s three lectures were: Logic, Elliptic semester at Princeton working on ongoing
Curves, and Diophantine stability. projects with our faculty and gave a series
of talks on “interface dynamics for incom-
pressible flows.”
Cordoba remained in our department as
a ‘visiting research scholar’ for the spring
term.
Videos of the lectures are now available at https://www.math.princeton.edu/media/videos
page 7
Events
Summer Undergraduate Research Program: 2014.
Once again, the Math Department was search topic that interests them, provided is felt that the experience of participating
pleased to be able to offer an eight week they can find a faculty member who agrees in an REU as an undergraduate student will
summer program for undergraduate math to serve as the supervisor over the summer. provide that student with the opportunity
majors to conduct on-campus research to focus on a single mathematical research
In addition to our own on-campus summer
and/or guided independent study. Over problem while the Princeton program in-
research program, undergraduate majors
the past three years, the program has pro- troduces students to the idea of indepen-
may apply for financial support to partici-
vided $4,000 stipends to approximately 10 dent research while providing the student
pate in an off-campus NSF-funded Research
math majors each year. Although rising ju- with a strong foundation of knowledge in a
Experience for Undergraduate Program
niors and seniors are given preference, ris- specific area of mathematics, which would
(known as an REU) at another institution.
ing sophomores are also accepted. be useful for pursuing other research topics
(REUs generally focus on mathematical ar-
in the future.
Undergraduate majors are encouraged to eas that are considered somewhat outside of
apply for this summer research opportu- the mainstream with problems that require
nity. Students are asked to choose the re- relatively little specialized knowledge.) It
The following students received support from the Mathematics Department and the Jaywood Lukens ’30 Scholarship Fund.
Student Faculty mentor Topic of research
Arka Adhikari ’16 Paul Yang General Relativity and Cosmic Censorship.
nKubrat Danailov ’15 Jon Fickenscher Properties of Symbolic Dynamical Systems and the S-adic Conjecture.
o
etBilly Fang ’15 Jon Fickenscher Toward the S-adic Conjecture.
c
nJack Jenkins ’15 Paul Yang Summer research on the S-adic Conjecture.
At PriMonica Marinescu ’15 Mihai Fulger Algebraic Geometry.
Clayton McDonald ’15 Jeffrey Case Riemannian Geometry and Applications to Topology.
Alexander Payne ’16 Paul Yang Optimal Transportation and the Isoperimetric Inequality in the Heisenberg Group.
Paul Rapoport ’15 David Gabai Knot theory and Homological Algebra
of
sity sota Bumsoo Kim ’16 Joseph Gallian The Cross Number of Zero-sum Free Sequences in Finite Abelian Groups
At the UniverMinne Marya Sardarli ’15 GPyrelagv sMkuysyi,k Veirc, RPeaivnloe r , Quivers of Period 2
Dennis Stanton,
Rising juniors and seniors were also invited to apply for funding made available by the NSF to Sucharit Sarkar, Assistant Professor of Math-
ematics, for a research project in low dimensional topology. Daniel Dore ’16 and Yuval Wigderson ’16 received $4,000 stipends and were
required to be on campus for the months of July and August. They studied two modern (and fairly important) invariants of knots: Khovanov
homology and knot Floer homology. Both invariants could be studied combinatorially; the former via a cube of resolutions of a knot diagram
and the latter via grid presentations of knots.
Geometry and Topology Conference

The conference was in honor of the 70th birthday of Martin Bendersky, professor at Hunter College,
CUNY, and in memory of Sam Gitler *60 , who passed away this year. It took place at Fine Hall, and
was co-sponsored by our department and the CUNY Graduate Center. It was organized by Tony Bahri
from Rider who is a visiting research scholar here this term.
Martin Bendersky Sam Gitler,
page 8
Events
ANALYSIS, SPECTRA, AND NUMBER THEORY:
A Conference in Honor of Peter Sarnak
By Michael Rubinstein, co-organizer of the conference
The conference was held at Princeton Uni- matrix theory, to shed light on number theory. These areas have seen a flurry of ac-
versity and the Institute for Advanced Study, theory, for example in his statistical analy- tivity in recent years, including: the resolu-
December 15 - 19, 2014 on the occasion of sis with Rudnick and Katz on distribution tion by Lindenstrauss of Rudnick and Sar-
Peter Sarnak’s 61st birthday. of zeros of L-functions. Sarnak’s knack for nak’s quantum unique ergodicity conjecture
recognizing connections between seemingly for arithmetic surfaces; spectacular break-
The conference was well attended, with
disparate areas of mathematics, and for pos- throughs by Bhargava and his colleagues
around 350 participants. These included
ing essential and fundamental questions that concerning the statistics of number fields
many of Sarnak’s students, postdocs, co-
lie at the interface between the difficult and and elliptic curves; detailed models and
authors, colleagues, and friends. The large
the impossible, has inspired colleagues and predictions for the zero and value distribu-
turnout is a testament to the far reaching
students alike and has changed the land- tion of L-functions that were inspired via
influence and importance of Sarnak’s work.
scape of mathematics. connections with random matrix theory;
While L-functions and automorphic forms
construction and the analysis of highly effi-
have played a central role in Sarnak’s re- The talks of the conference reflected Sar-
cient expander graphs; the development of
search, his broad view of mathematics has nak’s broad impact on mathematics. It fo-
additive combinatorics based on the work
allowed him to bring ideas from number cused on analytic number theory, with
of Green and Tao. The conference empha-
theory to bear on other areas, such as in his emphasis on its many relationships with
sized these developments, with many lead-
construction of Ramanujan graphs and also analysis and spectral theory. Highlighted
ing speakers in these areas.
quantum gates. Reciprocally, he has brought topics included arithmetic quantum chaos,
insights and techniques from other areas, analysis of families of L-functions, arithme-
such as mathematical physics and random tic statistics, and connections with ergodic
SPEAKERS
Nalini Anantharaman, Orsay Alex Eskin, Chicago Elon Lindenstrauss, Hebrew U.
Manjul Bhargava, Princeton Ben Green, Oxford Alexander Lubotzky, Hebrew U.
Alice Chang, Princeton Henryk Iwaniec, Rutgers Philippe Michel, EPFL
J. Brian Conrey, AIM Nicholas Katz, Princeton Werner Muller, Bonn
Bill Duke, UCLA Jon Keating, Bristol Jonathan Pila. Oxford
Matthew Emerton, Chicago Xiaoqing Li, SUNY-Buffalo Ze’ev Rudnick, Tel Aviv
Freydoon Shahidi, Purdue
ORGANIZERS
Percy Deift, NYU Richard Taylor,IAS
Stephen D. Miller, Rutgers Akshay Venkatesh, Stanford
Michael Rubinstein, Waterloo Shouwu Zhang, Princeton
Kannan Soundararajan, Stanford
videos of the lectures are available at:
https://www.youtube.com/user/princetonmathematics
Peter and his wonderful families
page 9
Our graduate students
Naser Talebi Zadeh
I work in analytic number theory. Specifi- Princeton is a heaven for mathematicians.
cally, I am interested in the topics related Before coming to Princeton, I had heard
to the limit multiplicity theorem and the great things about Professor Sarnak and
applications of the Ramanujan conjecture Princeton. Professor Sarnak is a phenom-
in geometry and graph theory. As an under- enal advisor and he is always inspiring and
graduate at Sharif and later at Cambridge full of energy. He introduced me to impor-
university, I explored different fields of tant problems and different projects from
mathematics such as probability theory, dif- computer science to Iwasawa theory. Sar-
ferential geometry, topology and analysis. I nak is certainly gifted in guiding students
found the questions in number theory deep and making graduate school seem easier for
and fascinating; one needs to apply tech- his students.
niques and ideas from other branches of
I am applying for postdoctoral positions
mathematics to understand them.
next year and I plan to pursue a carrier in
I am very fortunate to have great parents academia.
who always encouraged me and gave me
I certainly grew up a lot by interacting with
interesting books to read. I remember my
the diverse and highly intellectual com-
Nasser is in his fourth year of Ph. D. studies.
mother gave me some brainteasers as a
He grew up in Kerman, in the southeast of munity of Princeton university. I definitely
child. I realized that I was good at them!
Iran. He completed his undergraduate degree recommend international students to check
Later, in high school, I began training for
at Sharif University, and received a Master’s out the Davis international center program.
and participating in math Olympiads, and I
of Mathematics from Cambridge University. There is always something interesting go-
won a gold medal in the IMO.
ing on on campus. The best years of my life
have been spent in Princeton.
Heather Macbeth
Heather is finishing her Ph.D this year. with a I fell in love with differential geometry as an
thesis on “Kahler-Einstein metrics, Bergman undergraduate in New Zealand, when I en-
metrics, and higher alpha-invariants” super- countered the oldest and most fundamental
vised by Gang Tian. classification theorem in differential geom-
Starting in September 2015 she will be a etry: the classification of constant-section-
Moore Instructor at MIT. al-curvature manifolds according to their
universal covers. The things that delighted
Heather is originally from New Zealand
me about that theorem are still what ap-
where she completed her undergraduate
studies obtaining a B.Sc. in Mathematics, peal to me now about my field of research:
with First Class Honors, from the University the satisfaction and solidity of a good uni-
of Auckland. formization/classification theorem, and the
intricate interplay of topology, analysis and
She obtained a Master’s in Mathematics
(“Part III”), with Distinctio,n from Trinity Col- algebra.
lege, University of Cambridge, UK.
Heather’s international experience extends
The graduate admissions open house.
to many continents: she spent a semester
in Peking at the Beijing International Center
for Mathematical Research in 2013, and
a semester at Albert-Ludwigs-Universitat
Freiburg, Germany.
page 10