Asia Pacific Mathematics Newsletter

1

The SASTRA
Ramanujan
The Sastra
RamanujanPrize — ItsPrize
Origins∗and
Its
Winners— Its Origins and Its Winners
Krishnaswami Alladi

Krishnaswami Alladi
The SASTRA Ramanujan Prize is a $10,000 annual award given to mathematicians not exceeding the age of 32 for path-breaking contributions
in areas influenced by the Indian mathematical genius Srinivasa Ramanujan. The prize has
been unusually effective in recognizing extremely
gifted mathematicians at an early stage in theircareers, who have gone on to accomplish evengreater things in mathematics and be awarded
prizes with hallowed traditions such as the Fields
Medal. This is due to the enthusiastic support
from leading mathematicians around the world
and the calibre of the winners. The age limit of 32
is because Ramanujan lived only for 32 years, andin that brief life span made revolutionary contributions; so the challenge for the prize candidates
is to show what they have achieved in that sametime frame! The way the prize was conceived
and launched is an incredible story which I will
relate here. I will then briefly describe some major
aspects of the works of the winners, and a few of
their biographical highlights.
The Origins
The district of Tanjore (=Tanjavur) in the state ofTamil Nadu in South India, has been a seat of culture for several centuries. Tanjore has produced
some of the greatest composers and performers
of South Indian classical music. Tanjore is wellknown for art in various forms and has the greatest concentration of Hindu temples. Ramanujan
was born in Erode on Dec 22, 1887, but it was in
the Tanjore region steeped in culture that he lived
in the town of Kumbakonam until he completed
high school.
During the second half of the 20th century,
Ramanujan’s humble home in Kumbakonam from
where a thousand theorems emerged, was ina dilapidated condition. Even though in India∗ This is the original and slightly expanded version of anarticle under the same title that appeared in The Notices of
the American Mathematical Society 66 (2019) 64–72. Permission
granted by the AMS is gratefully acknowledged.

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many events and programs were held regularly
in Ramanujan’s memory, including the grandRamanujan Centenary celebrations in December
1987, nothing was done for the renovation of thishistoric home. One of the most significant developments in the worldwide effort to preserve andhonor the legacy of Ramanujan is the purchase in2003 of Ramanujan’s home in Kumbakonam by
SASTRA University to maintain it as a museum.
This purchase had far reaching consequences because it led to the involvement of a university
in the preservation of Ramanujan’s legacy for
posterity.
The Shanmugha Arts, Science, Technology andResearch Academy (SASTRA), is a private university in the town of Tanjore after which the
district is named. SASTRA was founded in 1984
and has grown by leaps and bounds. Admission isvery competitive, and SASTRA has succeeded in
attracting some of the brightest students in India.
SASTRA has renovated Ramanujan’s home
beautifully without altering its structure or design. The only modification was to add a bust of
Ramanujan in the living room. In connection withthe purchase of Ramanujan’s home, SASTRA University opened a branch campus in Kumbakonamin 2003, called the Srinivasa Ramanujan Center.
SASTRA has a museum there in which several
important letters, photographs and documents
related to Ramanujan are displayed. A visit to
Kumbakonam just to see Ramanujan’s home andthis museum will be worthwhile and inspiring.
One afternoon in September 2003, I received aphone call from S Swaminathan, then a graduate
student at the University of Virginia (now a Dean
at SASTRA). He introduced himself as the son ofVice-Chancellor R Sethuraman of SASTRA University, gave me some background about SASTRA
and said that to mark the occasion of the purchase of Ramanujan’s home, SASTRA would be
conducting an international conference that year
in December at the Kumbakonam campus. The
President of India, Dr Abdul Kalam, had agreed

Asia Pacific Mathematics Newsletter2

Krishna Alladi being introduced to the President of India Dr Abdul Kalam during the First Ramanujan Conference at SASTRA University
on Dec 20, 2003. To the left of Krishna are George Andrews (Penn State) and Noam Elkies (Harvard).

to inaugurate this conference on Dec 20, 2003 anddeclare Ramanujan’s home as a national treasure.
Swaminathan invited me to bring a team of mathematicians from abroad to the conference, andsaid that SASTRA would cover all their expenses
including international travel. I felt that what
I heard over the phone was incredible becauseinternational airfare is rarely paid for participants of mathematical conferences in India. But
on checking I realized that something important
was taking place. So I called George Andrewsof The Pennsylvania State University, the world’s
foremost authority in the theory of partitions andon Ramanujan’s work, told him about SASTRA,
and invited him to come to the conference. He
said that based on my assurance, he would come.
In fact Andrews gave the opening lecture of theconference as well as the concluding Ramanujan
Commemmoration Lecture on December 22, Ramanujan’s birthday. At the valedictory function,
the participants suggested that SASTRA should
conduct conferences annually around Ramanujan’s birthday on different areas of mathematics
influenced by Ramanujan. Dean Vaidhyasubramaniam of SASTRA agreed to this suggestion
and invited me to help organize these annual
conferences. I have done this annually since 2003,
and so have also had the pleasure of being in
Ramanujan’s hometown each year in December
thus making it an annual pilgrimage for me (seearticle 25 in [1], pp. 153–160).
For the second SASTRA Ramanujan Conference in 2004, the Vice-Chancellor invited me toinaugurate it and also deliver the concluding

Ramanujan Commemmoration Lecture. I was
honored to receive such an invitation and I accepted it happily.
Conference inaugurations in India are usually
elaborate and grand ceremonies starting with thetraditional “lighting of the lamp” by the Chief
Guest, with the lamp representing enlightenment
through knowledge. There was a large gatheringin the auditorium, and as we walked up to thestage to be seated before the official start ofthe ceremony, the Vice-Chancellor whispered tome and said “I wish to give $10,000 annuallyfor a worthy cause in the name of Ramanujan.
You please decide how it should be used andannounce it in your inaugural speech.” I was
pleasantly shocked by this and said “This isvery generous of you, but are you asking me toannounce this in the next few minutes without
consulting anybody?” He said “Yes, consulting
people, or going through a Committee, will cause
unnecessary delays, and so I want you to come todecision right now and announce it.” Fortunately,
my inaugural speech was preceded by the lamp
lighting ceremony and the customary elaborate
welcome of the audience and the introduction of
the Chief Guest (me) as is common in India, andso I had at least 15 minutes to think about it as
all this was going on! When I got up to speak,
I mentioned this very generous offer from theVice-Chancellor, and suggested that a SASTRA
Ramanujan Prize be created and that $10,000 begiven to a mathematician not exceeding the ageof 32 for outstanding contributions to areas influenced by Ramanujan. I pointed out that theDecember 2018, Volume 8 No 1

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Asia Pacific Mathematics Newsletter

Fields Medal is given only to those under 40 yearsof age, and the SASTRA Prize would be given
to even younger mathematicians, some of whom
may later win the Fields Medal or other well established major prizes. The Vice-Chancellor liked
this suggestion very much, and at the conclusionof the inaugural ceremony, in thanking me, he
confirmed that the prize would be launched thenext year. He then turned towards me and said
“I request you to be the Chair of the Prize Committee.” So that is how the SASTRA Ramanujan
Prize was conceived and launched, and how I got
involved with the Prize. All this happened within
the span of an hour on Dec 20, 2004 during theinauguration.
Upon return to the United States, I called
George Andrews and told him this incredible
story of the launch of the prize and said that forthis to be a success, I would need the supportof the mathematical community. In particular, I
wanted his presence on the Committee for the
first year. He was suprised and happy to hear
this and agreed to serve on the Prize Committee.
Over the years, eminent mathematicians havesupported the prize by either serving on thePrize Committee, making nominations, or writing
letters evaluating the work of the nominees. The
prize is given annually at SASTRA University,
Kumbakonam, during an international conference
held around Ramanujan’s birthday, except in theyear 2012 when it was given in New Delhi (seethe 2012 Prize below).
The Prize Committee consists of six mathematicians besides me. They all vote, and I serveas the non-voting chair. I vote only to break a tie.
Three of the six step down each year, and three
new members join. Thus each voting member on
the Committee serves a two year term.
The Winners
The 2005 Prizes: Manjul Bhargava of Princeton University and Kannan Soundararajan of the
University of Michigan came out on top as thestrongest young mathematicians in the areas ofalgebraic number theory and analytic number
theory respectively, and were equally ranked 1 by
the Committee.
One of the pioneering discoveries of Gauss
was the composition law for binary quadratic
forms. Introducing several new and unexpected

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ideas, Bhargava broke an impasse since the timeof Gauss, and established in his 2001 PhD thesis
written under the direction of Andrew Wiles ofPrinceton University, composition laws for higher
degree forms. Bhargava applied these to solve
new cases of one of the fundamental questionsof number theory, that of the asymptotic enumeration of number fields of a given degree. This had
far reaching consequences on various problems inalgebraic number theory. He published the resultsin his thesis in a series of papers in the Annals of Mathematics. Bhargava’s lecture at SASTRA
University upon accepting the prize was on adifferent topic; he announced his joint work with
Jonathan Hanke on the solution of the problem
of determining all universal quadratic forms —a problem whose origin can be traced back to
Ramanujan.
Kannan Soundararajan had made spectacular
contributions to many parts of analytic number
theory, most notably pertaining to the Riemannzeta function and Dirichlet L-functions — especially on the distribution and location of theirzeros. He also established deep results in random matrix theory, which has fundamental connections with prime number theory. With HughMontgomery of the University of Michigan, heshowed that prime numbers in short intervals
are distributed normally, but with a variance thatdiffers from classical heuristics. In his PhD thesis
written under the direction of Peter Sarnak at
Princeton University, he showed that 7/8ths of thequadratic L-functions have no zeros at the criticalpoint s = 1/2 which provided strong evidence fora certain conjecture of Chowla. Along with Brian
Conrey, he had shown that a positive proportionof Dirichlet L-functions have no zeros on the real
axis within the critical strip.
The Prize Committee felt that both candidates deserved the full award. The SASTRA
Vice-Chancellor generously agreed to the recommendation of the Committee that Bhargava andSoundararajan be awarded two full prizes, andthat it should not be split. Thus the SASTRA
Ramanujan Prize could not have had a better start(see Ken Ono’s article [3] on the award of thefirst SASTRA Ramanujan Prizes, and mine ([1],pp. 161–166) as well.)Two years prior to winning the SASTRA Prize,
Bhargava was appointed Full Professor at Princeton at the age of 29, the youngest at that rank.

Asia Pacific Mathematics Newsletter
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Kannan Soundararajan (then at Michigan) receiving the First SASTRA Ramanujan Prize on Dec 20, 2005 from Dr Arabinda Mitra, Director,
Department of Science and Technology, India. (Second from Left) Manjul Bhargava (Princeton) who had received the same prize a few minutes
earlier, looks on. Next to Dr Mitra is SASTRA Vice-Chancellor R Sethuraman, and next to Soundararajan is Krishna Alladi.

Bhargava had graduated from Harvard in 1996
with the highest honors and received the Hoopes
Prize. That year he was awarded the Morgan
Prize of the AMS for undergraduate research. For
his revolutionary PhD work, he was awarded theBlumenthal Prize of the AMS in January 2005. Justprior to coming to SASTRA, he received the ClayPrize at Oxford University. Bhargava continued
producing fundamental work after receiving the
SASTRA Ramanujan prize, especially relating to
the average rank of elliptic curves. He was recognized with the AMS Cole Prize in 2008 and theFields Medal in 2014.
Soundararajan hails from Madras (now Chennai), India, where he began his research in number theory while in high school. He won a
Silver Medal in the International Mathematics
Olympiad in 1991. As an undergraduate at the
University of Michigan, he received the First Morgan Prize of the AMS in 1995. After obtaining
his PhD from Princeton, for outstanding contributions to analytic number theory he was awarded
the Salem Prize in 2003. When Soundararajan
received the SASTRA Prize, he was a tenured
faculty member at Michigan, and in the next year,
was appointed Full Professor at Stanford. He hascontinued to produce work of outstanding quality
and subsequently, he was recognized with theInfosys Prize and the Ostrowski Prize, both in2011.

The 2006 Prize: Thirty one-year old Terence Taoof UCLA had made far reaching contributions todiverse areas of mathematics such as number theory, harmonic analysis, partial differential equations and ergodic theory. He is widely regarded
as one of the most influential mathematicians ofour times.
One of Tao’s most notable contributions wasfor the Kakeya Problem in higher dimensions.
One aspect of the problem is to determine thefractal dimension of a set obtained by rotating aneedle in n-dimensional space. In a joint workwith Nets Katz, Isabella Laba and others, he
improved all previously known estimates for thefractal dimension with ingenious combinatorialideas. Another of Tao’s seminal contributions was
his joint work with Ben Green on long arithmetic
progressions of prime numbers. One of the deepest results in this area is due to the Hungarian mathematician Szemeredi who showed thatany set of positive density will have arbitrarily
long arithmetic progressions. Subsequently, Tim
Gowers of Cambridge University gave a very
different proof of Szemeredi’s theorem. This resultof Szemeredi does not apply to the set of primes
which is of zero density. By combining the ideas
of Gowers along with tools from ergodic theory,
Green and Tao proved the sensational result that
there are arbitrarily long arithmetic progressionsof primes.

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Krishna Alladi reads the citation before the 2006 SASTRA Ramanujan Prize is presented to Terence Tao (standing, middle) of UCLA.

Yet another fundamental contribution of Taoconcerns the sum-product problem due to Paul
Erdös and Szemeredi. Roughly speaking, thisproblem states that either the sum set or the
product set of a set of N numbers must be large.
Tao was the first to recognize the significanceof this problem in combinatorial number theory and harmonic analysis. In collaboration with
Nets Katz and Jean Bourgain, Tao made important generalizations which led to breakthroughs
in harmonic analysis and number theory. Tao
has also made inroads into physics through his
study of wave maps that occur in Einstein’s theory of relativity, and his work on Schrödinger
equations.
Tao was born in Adelaide, Australia in 1975
and lived there until 1992. He did his BSc (Honors) and MSc at Flinders University in South Australia. He went to Princeton in 1992 for his PhD
which he completed in 1996 under the direction ofElias Stein. Honors have been awarded to him in a
steady stream. Prior to winning the Fields Medaland the SASTRA Ramanujan Prize in 2006, he
was awarded the Salem Prize (2000), the Bocher
Prize of the AMS (2002), the AMS Conant Prize(2005), and the Fields Medal in August 2006. Morerecently, he received the 2014 Breakthrough Prize.
He currently holds the James and Carol Collins
Chair at UCLA.
The 2007 Prize: Ben Green of Cambridge University had made phenomenal contributions toseveral fundamental problems in number theory
by himself and in collaboration with Terence Tao.
Green’s PhD thesis at Cambridge is a collection ofseveral outstanding papers. In one of these papers
he solved the Cameron–Erdös conjecture which
is a bound on the number of sum-free sets of28

December 2018, Volume 8 No 1

2007 SASTRA Prize Winner Ben Green (then at Cambridge University) seated on the windowsill of the bedroom at Ramanujan’shome. The cot there was the only one for Ramanujan’s family. As aboy, Ramanujan used to sit on the windowsill and do his “sums”
watching the passers-by on the street.

positive integers up to a given number N. Prior tocollaborating with Tao, Green had also establishedan important result that any set of primes withrelative positive density would contain infinitely
many arithmetic progessions of length 3. It was
this paper of Green’s in the 2005 Annals of Mathematics that caught the attention of Tao and which
led to their collaborative and definitive resulton arbitrarily long arithmetic progressions among
the primes. Subsequently Green and Tao alsocollaborated in extending the Hardy–Ramanujan–
Littlewood Circle Method by bringing in methods
from ergodic theory.
Green was born in Bristol, England in 1977.
He went to Cambridge University to do his BA(1995–98) and continued to do his PhD there(1999–2002) under the direction of Fields Medalist
Tim Gowers. He received the 2001 Smith Prizefor his PhD work. In 2005, Green was appointed
Hershel Smith Professor at Cambridge University,and was awarded the Salem Prize and the Whitehead Prize that year. He was elected Fellow of
the Royal Society in 2010 and was awarded theAsia Pacific Mathematics Newsletter
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Akshay Venkatesh (Stanford), 2008 SASTRA Prize Winner, garlanding the statue of Ramanujan at SASTRA University.

Sylvester Medal in 2014. He is currently Waynflete Professor of Pure Mathematics at Oxford
University.
The 2008 Prize: Akshay Venkatesh of Stanford
University was creating waves in the mathematical world, by making powerful contributions todiverse areas, by himself and with a host ofcollaborators. His 2006 paper with H Helfgottcontained striking and original ideas, and provided the first non-trivial upper bound for the
3-torsion in class groups of quadratic fields. His
joint work with Jordan Ellenberg on representing
integral quadratic forms by quadratic forms had
its roots in the work of Ramanujan.
An important and difficult problem in number theory is to asymptotically count number
fields according to their discriminant. This is a
generalization of the classical problem of determining the relation between the number ofrational or integral solutions of a polynomial
equation in several variables and the coordinatesof the solutions. The case up to degree 5 hadbeen solved by Manjul Bhargava. For large degrees, Ellenberg and Venkatesh provided the firstmajor improvement over bounds in the earlier
work of Wolfgang Schmidt and thus broke animpasse of 30 years. Also of great importancewas Venkatesh’s work on sub-convexity of automorphic L-functions, and his joint work withE Lindenstrauss which settled a famous conjecture of Peter Sarnak’s concerning locally symmetric spaces. One of Venkatesh’s most impressive
achievements was his individual work on subconvexity of automorphic L-functions. The problem of subconvex bounds at the center of thecritical strip for L-functions is very important.
Venkatesh provided a novel and more direct

2009 SASTRA Prize Winner Kathrin Bringmann (University of
Cologne) lighting the ceremonial lamp to mark the opening of theRamanujan Conference.

way of establishing subconvexity in numerous
cases that went beyond the foundational workof Hardy–Littlewood–Weyl and of current leading
researchers as well.
Venkatesh who is of South Indian descent, wasborn in New Delhi, India in 1981 but was raised in
Perth, Australia. He showed his brilliance early bywinning medals in both the International Physics
and Mathematics Olympiads at the age of 12. His
entry into research began in 1998 when he joined
Princeton for his PhD under the direction of Peter Sarnak. On completing his PhD in 2002, hebecame Moore Instructor at MIT and then a Clay
Research Fellow. He received the Salem Prize in2007 and was appointed Full Professor at Stanford
the next year. After the SASTRA Ramanujan Prize,
he has been awarded the Infosys Prize in 2016
and the Ostrowski Prize in 2017. In 2018 he wasawarded the Fields Medal and appointed to thepermanent faculty at the Institute for Advanced
Study, Princeton, New Jersey.
The 2009 Prize: The 2009 Prize was awarded toKathrin Bringmann for work related to Ramanujan’s mock theta functions. Ramanujan’s discovery of the mock theta functions and the identities
he communicated about them in his last letter
to G H Hardy in 1920 just a few months before
his death, are among his deepest contributions.
Mock theta functions are objects which are likethe classical theta functions in their shape, but
are not modular forms, yet their coefficients canbe calculated with a degree of precision comparable to what can be done for functions thatcan be expressed in terms of theta functions. No
one knew the exact relationship between theta
functions and mock theta functions, and indeed

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determining this relationship was one of the tantalizing puzzles of mathematics. Following a leadprovided by Sander Zwegers, Kathrin Bringmann
and her post-doctoral mentor Ken Ono provided
the key to unlock this mystery by showing how
mock theta functions are intimately connectedwith harmonic Maass forms.
Bringmann was led to the investigation ofmock theta functions when she did her postdoctoral work under Ken Ono at the Universityof Wisconsin. Bringmann and Ono, inspired by
the work of Zagier and Zwegers, wrote a fundamental paper that appeared in the Annals of
Mathematics, in which they showed that Ramanujan’s 22 mock theta functions are special casesof infinite families of Maass forms of weight
1/2. This and other works by Bringmann, Ono,and their collaborators, has resolved the puzzle
surrounding mock theta functions and led to anunderstanding of their fundamental role in themathematical landscape.
Kathrin Bringmann was born in 1977 in Muenster, Germany. She obtained a Diploma in Mathematics with top honors from the University ofWuerzburg, Germany, in 2003. She then went to
the University of Heidelberg where she received
her PhD under the direction of Winfried Kohnen
in 2004. Following that, she became Van Vleck
Assistant Professor in Wisconsin, where her collaboration with Ken Ono began. After a brief
period in Minnesota, she joined the Universityof Cologne, Germany, as Professor. In 2009, prior
to receiving the SASTRA Prize, she was awarded
the prestigious Krupp Prize, which provides her
support at the University of Cologne to conduct
a comprehensive program in number theory withseveral PhD students, post-docs and visitors.
The 2010 Prize: Wei Zhang, who did his
doctoral work under Professor Shouwu Zhang
at Columbia University, had made seminal contributions by himself and in collaboration withothers to a broad range of areas in mathematics including number theory, automorphic forms, trace
formulas, L-functions, representation theory andalgebraic geometry.
In 1997 Steve Kudla constructed a familyof cycles on Shimura varieties, and conjectured
that their generating functions are actually Siegel
modular forms. The proof of the Kudla conjecture
for cycles of codimension-1 is a major theoremof Fields Medalist, Richard Borcherds. In his PhD

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72010 SASTRA Prize Winner Wei Zhang (then at Harvard) seated(on the right) along with his former PhD advisor Shouwu Zhang(Columbia) at the entrance to Ramanujan’s home in Kumbakonam.

thesis, Zhang established conditionally, among
other things, a generalization of Borcherds’ result for higher dimensions and in that processessentially settled the Kudla conjecture. Zhang’s
thesis opened up major lines of research and led
to a significant collaboration with Xinyi Yuan andShouwu Zhang. The three established an arithmetic analogue of a theorem of Waldspurger thatconnects integral periods to values of L-functions.
In addition, Wei Zhang by himself had done
outstanding work on relative trace formulas, andon Shimura varieties.
Wei Zhang hails from the People’s Republic ofChina where he was born in 1981. After obtaining
his Bachelor’s degree from Peking University in
2004, he joined Columbia University to do his
PhD. When he heard of the Kudla Conjecture asa first year graduate student, he started working
on it, and in one year, had mastered the techniques needed to attack it. After his PhD, hebecame Post-Doctoral Fellow at Harvard. When
Zhang received the SASTRA Prize, he had become

Asia Pacific Mathematics Newsletter
8

Benjamin Pierce Instructor at Harvard. In 2017he was awarded the New Horizons Prize inMathematics. He is currently a Full Professor atColumbia University.
The 2011 Prize: Roman Holowinsky of Ohio
State University had made significant contributions at the interface of analytic number theory
and the theory of modular forms. Along with
Kannan Soundararajan (winner of the SASTRA
Ramanujan Prize in 2005), he solved an important case of the famous Quantum Unique Ergodicity (QUE) Conjecture. This was a spectacularachievement.
In 1991, Zeev Rudnick and Peter Sarnak formulated the QUE Conjecture which in its generalform concerns the correspondence principle forquantizations of chaotic systems. One aspect ofthe problem is to understand how waves are
influenced by the geometry of their enclosure.
Rudnick and Sarnak conjectured that for sufficiently chaotic systems, if the surface has negative
curvature, then the high frequency quantum wave
functions are uniformly distributed within thedomain. The modular domain in number theory
is one of the most important examples, and forthis case, Holowinsky and Soundararajan solved
the holomorphic QUE Conjecture.
The manner in which this solution came about
is amazing. By a study of Hecke eigenvalues andan ingenious application of the sieve, Holowinsky
obtained critical estimates for shifted convolution sums and this almost settled the holomorphic QUE Conjecture for the modular domain
except in certain cases where the corresponding
L-functions behave abnormally. Simultaneously,Soundararajan who approached the problem froman entirely different direction, was able to confirm
the conjecture in several cases, and noticed thatthe exceptional cases not fitting Holowinsky’s
approach were covered by his techniques. Thusby combining the approaches of Holowinsky andSoundararajan, the holomorphic QUE Conjecture
was fully resolved in the modular case.
Holowinsky also wrote two fundamental papers — on a sieve method for shifted convolution
sums, and on sieving for mass equidistribution.
Holowinsky was born on July 26, 1979. He
obtained his Bachelors degree from Rutgers University in 2001, where he continued to do his
PhD under the direction of Henryk Iwaniec. Already in his PhD thesis he made major advances

2011 SASTRA Prize Winner Roman Holowinsky (Ohio State)delivering the Ramanujan Commemmoration Lecture on Dec 22,
Ramanujan’s birthday.

towards the QUE Conjecture. He held postdoctoral positions at the Institute for Advanced
Study, the Fields Institute and the University ofToronto before joining the permanent faculty at
Ohio State University. In 2011, in addition to the
SASTRA Ramanujan Prize, he was awarded a
Sloan Fellowship.
The 2012 Prize: Zhiwei Yun of Stanford University had made fundamental contributions toareas that lie at the interface of representation theory, algebraic geometry and number theory. Yun’s
PhD thesis on global Springer theory at Princeton
University written under the direction of Robert
MacPherson of The Institute for Advanced Study,
opened up new vistas in the Langlands program.
Springer theory is the study of Weyl group actions
on the cohomology of certain subvarieties of theflag manifold called Springer fibers. Yun’s global
Springer theory deals with Hitchin fibers insteadof Springer fibers which he used to determine theactions of affine Weyl groups on cohomology.
Bao-Châu Ngô was awarded the 2010 Fields
Medal for his proof of the Fundamental Lemmain the Langlands Program. Yun made a breakthrough in the study of the Fundamental Lemma
formulated by Jacquet and Rallis in their programof proving the Gross–Prasad conjecture on relative
trace formulas. Yun’s understanding of Hitchin fibrations enabled him to reduce the Jacquet–Rallis
Fundamental Lemma to a cohomological propertyof the Hitchin fibration. In addition, Yun’s workon the uniform construction of motives with exceptional Galois groups is considered to be very
fundamental.
Since 2012 was the 125th Birth Anniversaryof Ramanujan, Yun was awarded the SASTRA
Prize in India’s capital, New Delhi, at a conference

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Zhiwei Yun (MIT and Stanford) receiving the 2012 SASTRA Ramanujan Prize from Minister of State Jitin Prasada at the Universityof Delhi on December 22. SASTRA Vice-Chancellor Sethuraman
and Krishna Alladi are looking on. [Photo courtesy: SASTRA
University.]

organized by the National Board for Higher Mathematics (of India), and co-sponsored by SASTRA
University and Delhi University. That was the
only year when this prize was not awarded in
Kumbakonam.
Zhiwei Yun was born in Changzhou, China, in1982. He showed his flair for mathematics earlyby winning the Gold Medal in the International
Mathematics Olympiad held in Korea in 2000.
He obtained his bachelor’s degree from Peking
University in 2000 and joined Princeton University where he received his PhD in 2009. WhenYun received the SASTRA Prize, he had just been
appointed to the permanent faculty at Stanford
University after having completed his term asa Moore Instructor at MIT. In 2018 he was arecipient of the New Horizons in Mathematics
Prize.
The 2013 Prize: Peter Scholze of the Universityof Bonn had made revolutionary contributions toarithmetic algebraic geometry and the theory of
automorphic forms. Already in his Masters thesis
at Bonn, Scholze gave a new proof of the Local
Langlands Conjecture for general linear groups
based on a novel approach to calculate the zetafunction of certain algebraic varieties. While thiswas groundbreaking, his PhD thesis at Bonn under the direction of Michael Rappoport was amuch bigger breakthrough: he developed a new
p-adic machine called perfectoid spaces and used
it brilliantly to prove a significant part of theweighted monodromy conjecture due to Deligne,
thereby breaking an impasse of more than 30
years. Scholze extended his theory of perfectoid spaces to develop a Hodge theory for rigid

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(L to R) 2013 SASTRA Prize Winner Peter Scholze (Universityof Bonn) and his former PhD Advisor Michael Rappoport (Bonn)standing next to the statue of Ramanujan at SASTRA University.

analytic spaces over p-adic ground fields, generalizing a theory due to Faltings for algebraic
varieties.
Scholze was born in Dresden, Germany, in
1987. He was a winner of three gold medals andone silver medal at the International Mathematics
Olympiads. He was made Full Professor in Bonnsoon after his PhD. Scholze was the youngest
winner of the SASTRA Prize at the age of 25. Following that, he has been recognized with the AMS
Cole Prize (2015), the Fermat Prize (2015), theOstrowski Prize (2015), the Liebniz Prize (2016),
and the Fields Medal in 2018.
The 2014 Prize: James Maynard of Oxford
University, England, and of the University ofMontreal, had made outstanding contributions tosome of the most famous problems on prime
numbers. He obtained the strongest results at thetime on the celebrated prime twins conjecture byshowing that the gap between consecutive primes
does not exceed 600 infinitely often. Not only did
he significantly improve the path-breaking workof Goldston, Pintz, Yildirim, and Zhang, but heachieved it with ingenious methods which were
simpler than those used by others.
A generalization of the prime twins conjecture is the prime k-tuples conjecture which statesthat an admissible collection of k linear functions
will simultaneously take k prime values infinitely
often. In the last 100 years, several partial results towards the k-tuples conjecture were obtained by replacing prime values with “almost
primes”, namely numbers with a bounded number of prime factors. Another major achievementof Maynard in his doctoral thesis and in his postdoctoral work in Montreal was to significantly

Asia Pacific Mathematics Newsletter
10James Maynard (Oxford University), the 2014 SASTRA Prize Winner, standing next to the Ramanujan statue at SASTRA University.

improve on the work of earlier researchers on
k-tuples of almost primes.
Just before receiving the SASTRA Prize, Maynard announced the solution to the famous$10,000 problem of Erdös on large gaps between
primes. This was simultaneously announced by
Kevin Ford, Ben Green, Sergei Konyagin, andTerence Tao, but Maynard’s method was different
and simpler. Maynard’s results and methods have
led to a resurgence of activity worldwide in prime
number theory.
Maynard was born in Chelmsford, England,on June 10, 1987. He obtained his BA and Masters from Cambridge Unibersity in 2009, and his
PhD from Oxford in 2013 under the direction of
D R Heath-Brown. Following that, he became apost-doctoral fellow at the University of Montreal
in 2013–14 under Andrew Granville. After the
SASTRA Prize, he received the Whitehead Prize in2015 and the EMS Prize in 2016. He is currently aprofessor at Magdalen College, Oxford University.
The 2015 Prize: Jacob Tsimerman of the University of Toronto had made deep and original contributions to diverse parts of number
theory, most notably to the André-Oort Conjecture, which states that special subsets of Shimuravarieties that are obtained as Zariski closures of
special points, are finite unions of Shimura varieties. Shimura varieties are special algebraic varieties (such as moduli spaces of abelian varieties)
that arise as quotients of suitable complex domains by arithmetic groups. Yves André initiallystated this conjecture for one-dimenional subvarieties, and subsequently Frans Oort proposed thatit should hold more generally. A major achievement of Tsimerman in his Princeton PhD thesis of2011 written under the direction of Peter Sarnak2015 SASTRA Prize Winner Jacob Tsimerman (University ofToronto) standing outside Ramanujan’s home. The majestic Gopuram (= entrance tower) of the Sarangapani Temple, where Ramanujan and family regularly worshipped, is seen in the background.

was to obtain certain unconditional bounds up
to dimension 6. Another important result in histhesis was to answer in the affirmative a questionof Nick Katz and Oort’s whether there exists anabelian variety over the set of all algebraic numbers which is not isogenous to the Jacobian of astable algebraic curve over the algebraic numbers.
Just before receiving the SASTRA Prize,
Tsimerman gave a proof of the André-Oort Conjecture for the moduli spaces of principally polarized abelian varieties of any dimension — a resultthat was sought after for a long time.
Tsimerman was born in Kazan, Russia, on
April 26, 1988. His family first moved to Israel,
and then to Canada in 1996 where he particpatedin mathematical competitions from the age of 9.
In 2003 and 2004 he represented Canada in theInternational Mathematics Olympiads and won
gold medals both times. After completing his PhD
at Princeton in 2011, he was conferred an AMS
Centennial Fellowship. He held a post-doctoral
position at Harvard and in 2014 joined the permanent faculty at the University of Toronto where
he is presently.
The 2016 Prize: This was shared by Kaisa
Matomaki of the University of Turku, Finland,and Maksym Radziwill of McGill University,
Canada, and Rutgers University. Their revolutionary collaborative work on multiplicative functions in short intervals shocked the mathematicalcommunity by going well beyond what could be
proved previously even assuming the RiemannHypothesis, and opened the door for a seriesof breakthroughs on some notoriously difficult
questions such as the Erdös discrepancy problem

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Maksym Radziwill (McGill University) giving the Ramanujan
Commemmoration Lecture on his joint work with Kaisa Matomaki
with whom he shared the 2016 SASTRA Prize.

and Chowla’s conjecture, previously believed to
be well beyond reach. Their stunning work on
multiplicative functions in short intervals is best
illustrated in terms of the Liouville lambda function which takes value 1 when an integer has
an even number of prime factors (counted withmultiplicity), and value −1 when an integer has an
odd number of prime factors. The statement thatthe lambda function takes values 1 and −1 withasymptotically equal frequency is equivalent to
the Prime Number Theorem; more refined statements on the relative error in this equal frequency
are related to the Riemann Hypothesis. Such equal
distribution results were known also for shortintervals, namely intervals [x, x + h], where h isa fractional power (<1) of x. The Riemann Hypothesis implies that powers of h larger than 1/2
will work. Instead of every interval of length h,
if we require only “almost all” intervals of lengthh, it was known that h could be made as small
as the 1/6th power of x, and as small as log x
by assuming the Riemann Hypothesis. Matomaki
and Radziwill shocked the world, by showing unconditionally that equal frequency holds almost
always as long as h tends to infinity with x. Theirmethods are expected to transform the subject ina major way.
Sarvadaman Chowla conjectured that if any
k collection of values of 1 and −1 are given in
any order, then the lambda function will takethat sequence of values at k consecutive integers
with asymptotic frequency 1/2k . This conjecture is
yet unsolved. In 2016, Matomaki, Radziwill, andTerence Tao proved that when k = 3, each of theeight sign choices occur with positive proportion.
Kaisa Matomaki was born in Nakkila, Finland,on April 30, 1985. While in high school, she won

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December 2018, Volume 8 No 1

Kaisa Matomaki [Photo Courtesy: Pekka Matomaki.]the first prize in the national mathematical competition for Finnish students. She did her Masters
at the University of Turku and received the Ernst
Lindelöf Award for the best Masters thesis in
Finland in 2005. After completing her PhD at theRoyal Holloway College, London in 2009 under
the direction of Glynn Harman, she returned to
the University of Turku where she is presently.
Maksym Radziwill was born in Moscow, Russia on February 24, 1988. In 1991 his family first
moved to Poland, and then in 2006, to Canada.
After writing a superb undergraduate thesis at
McGill University in 2009 under the guidance ofAndrew Granville, he joined Stanford University
where he completed his PhD in 2013 under thesupervision of Kannan Soundararajan. He was at
the Institute for Advanced Study in 2013–14, andwas Hill Assistant Professor at Rutgers during
2014–17, before joining the permanent faculty at
McGill University, where he is presently.
The 2017 Prize: Maryna Viazovska of the
Swiss Federal Institute of Technology, Lausanne,
was awarded the 2017 SASTRA Prize for her
stunning solution in dimension 8 of the spherepacking problem, and for her equally impressive
joint work with Henry Cohn, Abhinav Kumar,
Stephen D Miller, and Danylo Radchenko, resolving the sphere packing problem in dimension
24, by building upon her fundamental ideas indimension 8.
The sphere packing problem has a long andillustrious history. Johannes Kepler wanted to findan optimal way to stack cannon balls (of uniform radius) and conjectured a configuration, but
could not prove it. This Kepler Conjecture wasAsia Pacific Mathematics Newsletter
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The 2018 Prize: The 2018 SASTRA Ramanujan
Prize was jointly awarded to Yifeng Liu (Yale
University, USA) and Jack Thorne (Cambridge
University, England).

(L to R) Henry Cohn (Microsoft Research) in discussion with 2017
SASTRA Prize Winner Maryna Viazovska (EPF Lausanne) and Ken
Ono (Emory).

resolved by Thomas Hales in 1998 by combining
ingenious geometric optimization arguments withmachine calcuations. The sphere packing problem
in higher dimensions remained open.
In dimension 8 there is E8 , an exceptional
Lie group with a root lattice of rank 8, and indimension 24 there is the Leech lattice. This gavesome hope that the sphere packing problem could
be solved in dimensions 8 and 24. Noam Elkies
and Henry Cohn made significant progress andconjectured the existence of certain magic auxiliary functions in dimensions 8 and 16, which if
determined, would resolve the conjecture in these
dimensions. But these magic functions remained
elusive. Viazovska produced these functions indimension 8 by the ingenious use of modular
forms. Within the span of a week, working at afurious pace, by extending the ideas in dimension
8, the sphere packing problem in dimension 24
was resolved by Cohn, Kumar, Miller, Radchenko
and Viazovska.
Viazovska’s modular form techniques are by
no means limited to the sphere packing problem.
She has discovered something profound that willplay a broader role in discrete geometry, analytic
number theory, and harmonic analysis.
Maryna Viazovska was born in Kiev, Ukraine,on November 4, 1984. She completed her highschool in Kiev in 2001 and her Bachelors in Mathematics in 2005. After completing her Masters
at the University of Kaiserslautern in 2007, shejoined the University of Bonn where she completed her PhD in 2013 under the direction of Don
Zagier. She received the Salem Prize in 2016 andthe Clay Research Award in 2017. She received the
New Horizons Prize in 2018 along with two other
SASTRA Prize winners, Wei Zhang and Zhiwei
Yun.

Yifeng Liu had made spectacular contributions to arithmetic geometry and number theory
spanning a wide spectrum of topics — arithmetic
theta lifts, derivatives of L-functions, the Gan–
Gross–Prasad Conjecture, the Beilinson–Bloch–
Kato Conjecture, the geometric Langlands program, the p-adic Waldspurger theorem, and thestudy of étale cohomology of Artin stacks.
His PhD thesis at Columbia University went
well beyond the work of Kudla, Rapoport andYang on L-series connected with the minimal level
for Shimura curves over the rationals. Then inthree papers pertaining to Bessl and Fourier–
Jacobi models, he made significant progress on
the Gan–Gross–Prasad Conjecture in the representation theory of classical groups. In collaboration with Shouwu Zhang and Wei Zhang, hestudied the p-adic logarithm of Heegner points
and proved p-adic versions of theorems of Waldspurger and of Gross–Zagier.
In the 80s, Gross–Zagier and Kolyvagin
proved some surprising theorems which implied
the celebrated Birch–Swinnerton–Dyer Conjecture
for elliptic curves when the analytic rank is either 0 or 1. Liu has successfully extended Kolyvagin type results to higher ranks in the moregeneral framework of the Beilinson–Bloch–Kato
Conjecture. Liu has also made inroads into nonArchimedean geometry; he established a nonArchimedean analogue of the famous Calabi Conjecture for abelian varieties over certain p-adic
fields.
Yifeng Liu was born in Shanghai, China, andreceived his BS Degree from Peking University in2007 after which he joined Columbia University,
New York, where he received his PhD in 2012
under the direction of Shouwu Zhang. Followingthat he held the C L E Moore Instructorshipat MIT (2012–15) and assistant professorship at
Northwestern University (2015–18) before being
appointed as an associate professor at Yale University in 2018. He was a recipient of a Sloan
Fellowship in 2017.
Jack Thorne had made far reaching contributions to number theory, representation theory, andalgebraic geometry. He works in two rather dif-

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ferent areas: modularity of Galois representations
and arithmetic invariant theory. His outstanding
2012 PhD thesis written at Harvard University
was jointly supervised by Professors Richard Taylor and Benedict Gross, two of the dominantfigures in contemporary number theory. One outcome of the thesis was his work on arithmetic
invariant theory which lead to new results about
the sizes of Selmer groups for abelian varieties ofsmall dimension, and bounds for the number ofrational and integral points on various types ofalgebraic curves of genus greater than 1.
Regarding modularity of Galois representations, Thorne has been a central force in eliminating restrictions on the Taylor–Wiles method.
Some of the most striking results of Thorne’s
have appeared in papers with Laurent Clozel.
The main input by Thorne is a new method for
eliminating the most stubborn restriction in the
Taylor–Wiles method, namely the assumption thatthe residual (mod ) Galois representation underconsideration is irreducible.
Thorne’s 2015 work with Khare on potential
automorphy and the Leopoldt Conjecture introduced a “trick” that plays a key role in an ongoing ten-author collaboration including Thorne,that will establish a potential version of the
Shimura–Taniyama Conjecture for elliptic curves
over imaginary quadratic fields. Thorne’s recent
paper establishing that all elliptic curves over Q∞
are modular is viewed as another major breakthrough.
Jack Thorne received his BA Mathematics degree from Cambridge University in 2007. He thenwent to Harvard University where he completed
his PhD in 2012. Following that he was appointed

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Reader at Cambridge University in 2013, but during the period 2012–17, he was also a Clay Research Fellow of the Clay Mathematics Institute.
In 2017 he was awarded the Whitehead Prizeof the London Mathematical Society and in 2018
was promoted to full professorship at Cambridge
University.
Shaping the development of mathematics:
The Fields Medals, with an age limit of 40 for
the winners, were instituted with two lofty goals
in mind: (i) to recognize pioneering works by brilliant young mathematicians, and (ii) to encouragethese young researchers to continue to influence
the growth of mathematics. The Fields Medallists
have lived up to these great expectations. The
SASTRA Ramanujan Prize has a more stringent
age limit of 32, and so has recognized brilliant
mathematicians even earlier in their careers. It is
no exaggeration to say, that the winners of the
SASTRA Ramanujan Prizes have also shaped thedevelopment of mainstream mathematics and willcontinue to do so in the years ahead; the fact that
the SASTRA laureates have subsequently won
major prizes with hallowed traditions, is a testimony to this. Indeed, two of the four 2018 Fields
Medalists are former SASTRA Ramanujan Prize
Winners — Akshay Venkatesh and Peter Scholze!
Similarly, three of the four 2018 New Horizons inMathematics Prize winners are former SASTRA
awardees — Wei Zhang, Zhiwei Yun and Maryna
Viazovska.
References[1] K. Alladi, Ramanujan’s Place in the World of Mathematics — Essays Providing a Comparative Study(Springer, New Delhi, 2012), 177 pp.
[2] K. Alladi, Srinivasa Ramanujan’s going strong at
125, Part 1, Notices AMS 59 (2012) 1522–1537; Part
2, Notices AMS 60 (2013) 10–22.
[3] K. Ono, Honoring a gift from Kumbakonam, Notices
AMS 53 (2006) 641–651.

First published in Notices of the American MathematicalSociety in Jan 2019, published by American Mathematical Society ©2019 American Mathematical Society.

Yifeng Liu and Jack Thorne in conversation prior to the award
ceremony.

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Asia Pacific Mathematics Newsletter

Krishnaswami Alladi
University of Florida, USA
alladik@ufl.edu
Krishnaswami Alladi is professor of mathematics at the University of Florida,
where he was department chairman during 1998–2008. He received his PhDfrom UCLA in 1978. His area of research is number theory. He is the Founder

14

and Editor-in-Chief of The Ramanujan Journal published by Springer. He helped

About the author: Krishnaswami
Alladi is a Professor of Mathematics at the University of Florida, Gainesville,
create the SASTRA Ramanujan Prize given to very young mathematicians andwhere he was Department Chairman during 1998–2008. He received his PhD from UCLA in 1978. His area ofhas chaired the prize committee since its inception in 2005.
research is number theory. He is the Founder and Editor-in-Chief of The Ramanujan Journal published by Springer.
He helped create the SASTRA Ramanujan Prize which is given to very young mathematicians, and has chaired
the prize committee since its inception in 2005.

Photo Credits:
All photos, unless otherwise stated, are courtesy of Krishnaswami Alladi.

December 2018, Volume 8 No 137