Research Interests

Books I have written, and am writing

My first book, Compact manifolds with special holonomy, 436 pages, was published in the Oxford Mathematical Monographs series by Oxford University Press in July 2000. You can buy it over the Web from OUP or Amazon.

It is a combination of a graduate textbook on Riemannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin(7). It is the first book on compact manifolds with exceptional holonomy, and contains much new research material and many new examples.

It is aimed at research mathematicians or graduate students interested in Differential Geometry or Algebraic Geometry, and at mathematical physicists working in String Theory.

Review of 'Compact manifolds with special holonomy' in Mathematical Reviews

Other reviews of Compact manifolds with special holonomy:
Ideal Christmas present for the mathematician in your life! Every home should have one! -- Woman's Own
This book changed my life! -- Jayne Joyce
What does 'compact' mean? -- Daily Mail
I couldn't pick it up! -- Farmer's Weekly
We look forward to the appearance of his last work. -- Belfast Times
This book has far-reaching implications for the scoring strategy in underwater badminton. -- Dr. Ruth Graham

401,998th on the Amazon best-sellers list! Over 13 copies sold!

My second book, 'Calabi-Yau Manifolds and Related Geometries', 239 pages, joint with Mark Gross and Daniel Huybrechts, was published in the Universitext series by Springer in 2003. You can buy it on on the Web from Springer or Amazon.

My contribution to the book is the first 70 pages, which is an introduction to Riemannian holonomy groups and calibrated geometry.

Review of 'Calabi-Yau Manifolds and Related Geometries' in Mathematical Reviews

My third book, 'Riemannian holonomy groups and calibrated geometry', 303 pages, was published in the Oxford Graduate Texts in Mathematics series by Oxford University Press in March 2007. You can buy it on on the Web from OUP in paperback or hardback, or from Amazon in paperback or hardback.

I should confess that a little more than half this book is an updated version of parts of my first book 'Compact manifolds with special holonomy'. That is, I am cheerfully guilty of rampant self-plagiarism. Nonetheless, you should buy several copies of both books, for you and all your friends (or enemies?).

Review of 'Riemannian holonomy groups and calibrated geometry' in Mathematical Reviews

My fourth book, 'A theory of generalized Donaldson-Thomas invariants', 199 pages, joint with Yinan Song, was published in Memoirs of the A.M.S. in May 2012. You can buy it online here, and it is available for free as arXiv:0810.5645.

Review of 'A theory of generalized Donaldson-Thomas invariants' in Mathematical Reviews

My fifth book, 'Algebraic Geometry over C-rings', 143 pages, is due to appear in Memoirs of the A.M.S. in 2017, and it is available for free as arXiv:1001.0023.

My sixth book is, 'Some new homology and cohomology theories of manifolds and orbifolds', arXiv:1509.05672 (preliminary version, 232 pages). I will revise it while I am writing the 'Kuranishi spaces and Symplectic Geometry' project below, and then look for a publisher.

I am currently working on books on 'D-manifolds and d-orbifolds: a theory of derived differential geometry', which you can read about on this page on my website, and on a series of books on 'Kuranishi spaces and Symplectic Geometry', which you can read about on this page on my website. I do realize that some people might consider all this excessive, but I can't seem to stop doing it.