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 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.
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: errata
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 list of corrections.
Peter Landweber kindly sent along the following further corrections.
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 Riemann 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