Paolo Aluffi's publications


Published papers:

These versions are hopefully up-to-date, correcting typos and inaccuracies in the printed versions.


Stringy Chern classes, 5 pages, abstract for 2005 Arbeitstagung lecture, MPIM2005-60o.

We survey some notions of characteristic classes for singular varieties, with particular attention devoted to the recently introduced notion of `stringy' Chern classes.

Quantum Cohomology at the Mittag-Leffler Institute
Appunti della Scuola Normale Superiore di Pisa (1998) 163 pages, ISBN: 978-88-7642-257-7.

These are transcripts of notes taken at (some of the) lectures given by the mentioned speakers at the Mittag-Leffler institute during the first semester of the 1996/97 year on Enumerative geometry and its interaction with theoretical physics.
The first part of this collection consists of notes from talks on the basics of quantum cohomology, as developed in [F-P]. These talks formed the main body of the Tuesday seminar series at the Institute. The second part treats more advanced topics in quantum cohomology, which were primarily addressed in the Thursday seminar series. The third part consists of background material and related topics and contains material from both of these two series. An appendix, kindly provided by A. Kresch, gives a description of his C-program farsta for quantum cohomology computations.

Fare Matematica. Astratto e concreto nella matematica elementare.
Aracne editrice, A01, vol. 129 (2009) 144 pages, ISBN: 978-88-548-2479-9. In Italian.

This book is aimed at the general public. It consists of a brief introduction to a few elementary themes in mathematics, emphasizing the interplay between the abstractness of the material and the concreteness of the mathematical approach to it.

Algebra: Chapter 0.
American Mathematical Society, Graduate Studies in Mathematics Volume 104 (2009) 713 pages. (Reprinted with corrections, 2016.) ISBN-10: 0-8218-4781-3 ISBN-13: 978-0-8218-4781-7

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Proceedings of the AMS Special Session on Singularities and Physics, Knoxville, 2014
Journal of Singularities, volume 15 (2016) 149 pages, ISSN: 1949-2006

A Special Session on Singularities and Physics was organized for the AMS Sectional Meeting held in Knoxville, TN on March 21-23, 2014. The session focused on the theory of singularities and its interactions with different branches of theoretical physics: singularities of elliptic fibrations in string theory, renormalization issues in quantum field theory, Landau-Ginzburg models, wall-crossing phenomena, and other recent points of contact. The aim was to bring together the mathematics and physics communities, to foster further interactions.

This volume collects articles written by some of the speakers on the occasion of this meeting, expanding on the content of their talks or reporting on research originated in discussions begun at the conference.

Algebra: Notes from the Underground.
Cambridge University Press, Cambridge, 2021. 472 pp. ISBN: 978-1-108-95823-3

From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics -- such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory -- are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the problems quoted from the main text, and an appendix with general background on basic logic and naive set theory.

Facets of Algebraic Geometry - A Collection in Honor of William Fulton's 80th Birthday, Vol.1 and Vol.2
Coedited with David Anderson, Milena Hering, Mircea Mustata, and Sam Payne.
Cambridge University Press, Cambridge, 2022, xiv+402 pp. & xiv+379 pp., ISBN: 978-1-108-87006-1

Written to honor the 80th birthday of William Fulton, the articles collected in these volumes present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.

BibTeX references for most of the publications listed above (thanks to MathSciNet).