#### by Wee Teck Gan

I first met Dick Gross in the spring semester of 1994. At that time, I was a third-year undergraduate student at Cambridge University, applying for PhD programs in US schools, with the plan to specialize in number theory. Fortunate enough to be admitted to Princeton and Harvard, I took up the invitation to visit both schools at the end of March. This was less than two years after Andrew Wiles had announced his proof of Fermat’s Last Theorem, so for an aspiring number theorist, the temptation to simply accept Princeton’s offer and study with Wiles was very strong indeed. At least, that was my initial thinking when I began my US trip. It was during my visit to Harvard that I met Dick for the first time. I recalled sitting in his office and explaining the hard choice I had to make. Dick did not try to convince me to pick Harvard. Rather, he advised me to simply pick the place that felt right or resonated with me, saying (paraphrase): “For number theory, you cannot go wrong with either place; plus, you can always come here for a postdoc after your PhD in Princeton, or vice versa.” (Naively, I had believed that would be the natural course of events.) I was surprised by Dick’s frank and open advice and the ease of communication with him, and left his office feeling energized. That conversation sealed my decision, and would serve as a mold for the many conversations I have had with Dick since: I always come away with renewed energy and a fresh perspective, feeling inspired and empowered.

After his important work
[2]
with
Zagier
appeared, Dick’s
research spectrum began to broaden to incorporate the representation
theory of reductive Lie groups, so as to provide a representation
theoretic formulation of the Gross–Zagier theorem which is more
amenable to generalization to
higher ranks. Before 1990, his work was
largely focused on the arithmetic of elliptic curves and modular
forms. The period of transition to include the representation theory
of higher-rank groups was essentially complete by the time I entered
Harvard in 1994, with the exceptional groups being of particular interest to
him. Two highlights from this period were his *Crelle* paper
[3]
with
Nolan Wallach
on quaternionic representations of quaternionic
groups and his *Compositio* paper
[4]
with
Gordan Savin
on
exceptional theta correspondences and the proposed construction of a
__\( G_2 \)__-motive. My current NUS colleague,
Hung Yean Loke,
was Dick’s
student at that time and two years ahead of me. I learned from Hung
Yean that he was working on branching problems for the minimal
representation of quaternionic exceptional groups. At that time, I did
not know anything about Lie groups or Lie algebras, and wondered why a
number theorist would need to learn such things at all, instead of the
more usual elliptic curves, class field theory, algebraic geometry and
modular forms. To compensate for my ignorance, I attended in my second
semester an undergraduate course on Lie algebras given by
Shlomo Sternberg
and also spent a weekend reading Serre’s delightful little
book
[e1].
Somewhat fortuitously, in the middle of the semester,
Dick initiated a learning seminar on the Langlands program, in which
he gave the first few talks, discussing the Satake isomorphism, the
Langlands dual group and the functoriality principle. Dick has this
magical ability to make the mathematics and ideas come alive and
appear inevitable. I was completely mesmerized by the beauty of the
mathematics and his incredibly clear exposition. After this seminar
series, I requested Dick to be my advisor, deciding that the
representation theoretic aspects of number theory was what resonated
most with me. So it is not an exaggeration to say that Dick’s seminar
series had a life-changing impact on
me.

Dick had many PhD students in the 1990s, especially in the year ahead of me, and he worked very closely with some of them (for example, David Pollack, Josh Lansky and Seth Padowitz). For me, however, his supervision was more hands-off. My thesis problem came about after I told Dick that I had been learning about the representation theory of finite reductive groups (à la Deligne–Lusztig) from Carter’s book [1] over the winter break. He mentioned casually that I could consider the finite field analog of his work with Savin, and this became the beginning of my thesis project. During the course of my thesis work, I did not receive much direct supervision from him (for example, we did not have regular meetings). What I received was better: the opportunity to work with Dick as a collaborator. Indeed, by the end of my PhD studies, I had written two papers with him [5], [6], and completed two more [7], [8] over the next couple of years.

This early collaboration with Dick taught me a few things. Firstly, the papers we wrote together then were mostly about the arithmetic of exceptional groups and their automorphic forms. In the grand scheme of things, these are far from being Dick’s most important papers, but he approached them with the same enthusiasm, joy and degree of care, because at that moment, that was the mathematics that captured his interest and imagination. I learned from this experience that I am free to pursue my own mathematical taste and interest without worrying about how it may be perceived by others. Secondly, it gave me the chance to learn firsthand from him how to write papers, clearly a valuable skill for our profession, and I would be hard-pressed to find a better instructor for this. Finally, as a consequence of our collaboration, I have over the years received several handwritten letters from Dick (even though he could have used email). These letters were perfectly written with beautiful handwriting and almost no revisions, and of course the clarity of the line of thinking in them is crystal. It always amazes me to receive such a letter from Dick.

Almost 24 years after my PhD, I am still collaborating with
Dick! Our second bout of collaboration began when
Dipendra Prasad
visited me at UC San Diego during the academic year 2007–08, and we
started thinking about the extension of the Gross–Prasad conjecture to
the setting of all classical groups. As we were formulating the
so-called GGP conjectures, I asked Dipendra for the motivation of the
recipe for the characters of component groups intervening in the
original GP conjecture. Dipendra told me that the recipe was entirely
due to Dick and I should check with him. When I finally got the chance
to do that, Dick’s response was (paraphrase): “I used
Waldspurger’s
and Dipendra’s results in low rank as a guide and came up with the
simplest recipe I could think of for a character which is trivial on
the identity component of the centralizer of the __\( L \)__-parameter.” Anyone
who has looked at those characters will know that it is not at all
obvious to guess what they should be from such scant evidence, and
Dick’s answer basically confirmed what I suspected: it was a stroke of
genius.

Our papers
[9],
[10]
took about 2 years to complete and
appeared in 2012 as part of an Astérisque volume with Waldspurger (who
had given a brilliant proof of the
__\( p \)__-adic case of the GP conjecture).
Two years ago, Dick, Dipendra and I followed up with a paper
[11]
extending the conjectures to the setting of
__\( A \)__-packets, and
currently we are preparing another paper
[12]
on a twisted
version of GGP.

I feel very fortunate that I have been able to work with and learn from Dick over the past 27–28 years. In preparing for this article, I took a look at Dick’s Mathscinet page and noted the large number of collaborators he has had over many areas, a testament to his broad mathematical interest and strong collaborative skills. This will not surprise those who know him. I was however (pleasantly) surprised that (at this time of writing), I happen to be his most frequent collaborator. Suffice it to say that if this is the only thing I will be recognized for professionally, I shall be very content.

*Wee Teck Gan was a PhD student of Dick Gross from 1994–98. He works on the theory of automorphic
forms and the Langlands program.
After a postdoc at Princeton (1998–2003), he became a faculty member at the University of California,
San Diego (2003–2011), before moving
back to Singapore (where he grew up) in 2011. He is currently the Tan Chin Tuan Centennial Professor at
the National University of Singapore.*