Robert C. Gunning
Professor of Mathematics
Mailing address: Fine Hall, Washington Road, Princeton, NJ 08544
List of graduate students
Current project: Topics in the Function Theory of
Compact Riemann Surfaces (June 10, 2007; revised and extended from
time to time since then)
This is a leisurely survey of compact Riemann surfaces from the point of view of
function theory. It combines material from graduate lectures I have given on this
topic over a number of years; some earlier lectures had been published
in other forms but have been reworked and considerably extended for inclusion here,
while the rest of the material is from more recent lectures.
The book is a work in progress. Included here are those chapters that
are in fairly final form; the table of contents lists other chapters
that are still being revised or written, to be added eventually.
I would greatly appreciate any corrections or suggestions that readers
would care to send on to me.
Undergraduate teaching My current undergraduate course is an
introduction to analysis, an intensive honors course for freshmen that
was just introduced in the academic year 2012/2013; it covers in one
academic year the topics in the traditional honors program in
mathematics (calculus in one and several variables and linear algerbra,
in a three semester sequence) rather more rapidly and extensively;
students have the option of either the traditional sequence or
the accelerated sequence. The text for the course is the
set of course notes available to the students to download, either
in a ps version ps version or a pdf version
(which does not seem to print the diagrams) pdf version.
During the predceding few years I taught one of the terms
of the regular honors sequence, that covering just calculus in several
variables, using the
math218 notes (revised version, January 2012)
as text for the course. The material in these notes has been incorporated
in the notes for the year-long intensive honors course.
There are a number of misprints and errors of one sort and another in
the volumes of Introduction to Holomorphic Functions of Several
Variables. Kenneth Koenig kindly sent along to me a list of some of
the errors he found while reading the book as a Princeton
undergraduate, and I have attached his list here:
Laura Wesson, who began her studies in algebra but
whose interest in functions of several complex variables
was inspired by Roger Penrose's book Road to Reality,
has also been reading Volume I and has compiled a
Peter Landweber kindly sent along the following further
I would welcome any other contributions to the list of corrections.
The American Mathematical Society has reprinted the book Analytic Functions
of Several Complex Variables that Hugo Rossi and I wrote a number of
years ago; we would like to express our thanks to the Society for its
interest in doing so, and in particular to Edward Dunne who pursued this
project until its completion. There were a number of errors in the book,
which we had hoped to correct in a second printing; but we had not had
the chance to rework the book, and in the end it seemed easier just to
reprint the book in its initial form and to add references to
at least some of the corrections here, among
other places. We also wish to thank those readers who sent suggestions
and corrections along to us, particularly Heisuke Hironaka.
A number of years ago I wrote a preliminary version of
Part II of the
paper Some Identies for Abelian Integrals, American Journal of
Math., vol. 108 (1986), pp 39 - 71. I circulated it at the time, but
other duties intervened and prevented me from doing the planned
revision and extension; and subsequently my interests have
turned in other directions, so I have done nothing about finishing that
paper. Since there have been some references to the preliminary version,
though, I decided to make it available here, in case there remains any
interest in it.
Several years ago I gave a series of graduate courses on
surfaces and second-order theta functions. Preliminary and rather
informal (and uncorrected) notes of the courses were prepared, but other
distractions have so far prevented me from reworking this material.
However it is available here, in case
there is any interest in it.
70th birthday conference: former students pictured (left to right standing)
Richard S. Hamilton, Yum-Tong Siu, Mrs. Xavier Gomez-Mont, Xavier Gomez-Mont,
Bun Wong, Henry B. Laufer, Michael G. Eastwood, G. Cristan Poor,
L. Andrew Campbell, Sheldon H. Katz
60th birthday conference
Robert and Wanda Gunning, Princeton, 2004; photograph by David Dobkin
Robert and Wanda Gunning, 70th birthday conference