Papers and preprints


Carlos Simpson 

-The twistor geometry of parabolic structures in rank two,
Proceedings - Mathematical Sciences, Indian Academy of Sciences, 132(2), 2022, article 54,
volume in honor of C.S. Seshadri.

-Stacks,
Chapter of New Spaces in Mathematics, I.3.2, M. Anel and G. Catren, eds., Cambridge University Press,
2021, joint with Nicole Mestrano.

-Degeneration of nonabelian Hodge structures, In Representation Theory,
Automorphic Forms & Complex Geometry, A Tribute to Wilfried Schmid,
S. Miller, S.-T. Yu, eds., International Press, Boston (2019), 5-10.

-Reflections on c_1^2 = 3c_2 and other things, In Notices of the International Congress
of Chinese Mathematicians Volume 7 (2019), 94-96.

-An explicit view of the Hitchin fibration on the Betti side for P^1 minus 5 points,
In Geometry and Physics: Volume 2---A Festschrift in honour of Nigel Hitchin, A. Dancer,
J.-E. Andersen, O. Garcia-Prada, eds., Oxford University Press (2018), 697-716.

-Reduction for SL(3) pre-buildings, String-Math 2016, AMS Proceedings of Symposia in
Pure Math. 98 (2018), 207-227, joint with Ludmil Katzarkov and Pranav Pandit.

-Rank 3 rigid representations of projective fundamental groups,
Compositio Mathematica 154.7 (2018), 1534-1570, joint with Adrian Langer.

-Classification of categories with matrices of coefficient 2 and order n,
Communications in Algebra 46.7 (2018), 3079-3091, joint with Samer Allouch.

-Irreducibility of the moduli space of stable vector bundles of rank two and odd degree on a very general
quintic surface, Pacific Journal of Math. 293.1 (2017), 121-172, joint with Nicole Mestrano.

-Approximate categorical structures,
Theory and Applications of Categories 32.44 (2017), 1522-1562, joint with Abdelkrim Aliouche

-Constructing buildings and harmonic maps, In Algebra, Geometry and Physics in the 21st Century
(Kontsevich Festschrift), D. Auroux, L. Katzarkov, T.  Pantev, Y. Soibelman, Y. Tschinkel, eds.,
Progress in Math. 324, Birkhauser (2017), 203-260,  joint with Ludmil Katzarkov, Alex Noll and Pranav Pandit.

-Moduli of sheaves, In Development of Moduli Theory --- Kyoto 2013 (Mukai 60),
Advanced Studies in Pure Math. 69 (2016), 77-172, joint with Nicole Mestrano.

-The dual boundary complex of the SL_2 character variety of a punctured sphere,
Annales de la Faculté des Sciences de Toulouse 25 (2016), 317-361.

-Harmonic maps to buildings and singular perturbation theory,
Communications in Math.  Physics 336 (2015), 317-361,
joint with Ludmil Katzarkov, Alex Noll and Pranav Pandit.

-Descent, In Alexandre Grothendieck: A Mathematical Portrait, L. Schneps, ed.,
International Press, Boston (2014), 83-141.

-Classification des matrices associées aux catégories finies,
Cahiers Topol. Géom. Différ. Catég. 55 (2014), 205-240, joint with Samer Allouch.

-Common fixtures of several maps on 2-metric spaces,
Indian J. Math. 56 (2014), 229-262, Special Volume dedicated to Professor Billy E. Rhodes,
joint with Abdelkrim Aliouche.

-Seminatural bundles of rank two, degree one and c_2 = 10 on a quintic surface,
Kyoto Journal of Mathematics 53 (2013),155-195, Maruyama Volume,
joint with Nicole Mestrano.

-Fixed points and lines in 2-metric spaces, Advances in Mathematics, January 2012,
joint with Abdelkrim Aliouche.

-Foliations on the moduli space of rank two connections on the projective line minus four points,
Geometric and differential Galois theories, Séminaires et Congrès 27, 2012,
joint with Frank Loray and Masa-Hiko Saito.

-Homotopy Theory of Higher Categories,
Cambridge University Press, New Mathematical Monographs, October 2011.

-Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures,
JEMS, Volume 13, 2011, Arxiv version,
joint with Philippe Eyssidieux.

-Local systems on proper algebraic V-manifolds, PAMQ 7 (2011), 1675-1760, Eckart Viehweg's volume.

-Obstructed bundles of rank two on a quintic surface -- International Journal of Math. 22 (2011), 789-836,
joint with Nicole Mestrano.

-Iterated destabilizing modifications for vector bundles with connection. Arxiv version, December 2008.
Contemporary Math 522, 2010 (Proceedings of the Ramanan Conference, Madrid, 2008).

-A weight two phenomenon for the moduli of rank one local systems on open varieties arxiv abstract--pdf,
in Augsburg proceedings.

-Regulators of canonical extensions are torsion: the smooth divisor case arxiv abstract--pdf,
joint with Jaya Iyer.

-On the classification of rank two representations of quasiprojective fundamental groups arxiv abstract--pdf,
joint with Kevin Corlette, Compositio Math. 144 (2008), 1271-1331. 

-Algebraic cycles from a computational point of view
Proceedings of the Galligo conference, Theoretical Computer Science 392 (2008), 128-140.

-The Chern character of a parabolic bundle, and a parabolic Reznikov theorem in the case of finite order at infinity arxiv abstract--pdf,
joint with Jaya Iyer. In "Geometry and Dynamics of Groups and Spaces: in memory of Alexander Reznikov",
Progress in Mathematics 265, Birkhauser (2008).

-A relation between the parabolic Chern characters of the de Rham bundles arxiv abstract--pdf,
joint with Jaya Iyer, Math. Annalen 338 (2007), no. 2, 347-383. 

-Katz's middle convolution algorithm arxiv abstract--pdf,
see also some notes for my talk in Paris, Feb. 1st, 2007.

-Geometricity of the Hodge filtration on the infinity-stack of perfect complexes over X_DR  arxiv abstract-- ps, pdf,
see also the slides (in jpg images) for my talk at the Deligne conference in Princeton, Oct. 18th, 2005.
Updated version, 2008.

- Explaining Gabriel-Zisman localization to the computer ps, pdf
(see also Files for Gabriel-Zisman localization ps, pdf, gzfiles.tar.gz)

-Formalized proof, computation and the construction problem in algebraic geometry ps, pdf (version revised for publication)

- Information technology implications for mathematics: a view from the French riviera, joint with Marco Maggesi (a very preliminary version in html format or ps or pdf 5 jul 04)

- Computer theorem proving in math, A paper based on my talk at the PQR conference, Brussels, June 2003.

-Mathematical quotients and quotient types in Coq, joint with
Laurent Chicli and Loic Pottier, version (ps) of November 2002,
see also the proof scripts which go with this paper;

-Some properties of the theory of n-categories (arxiv ps file), October 2001;

-Density of monodromy actions on non-abelian cohomology, joint with
Ludmil Katzarkov and Tony Pantev (arxiv ps file), January 2001;

-Calculating maps between n-categories (arxiv ps file), September 2000;

-Nonabelian mixed Hodge structures, joint with
Ludmil Katzarkov and Tony Pantev (arxiv ps file), June 2000;

for these and earlier preprints consult the xxx e-print archives (result of arxiv search).

-Asymptotics for general connexions at infinity (notes for my talk in Toulouse)
Version 1 (24/09/03): ps, pdf, dvi, tex

-The construction problem in Kahler geometry, to appear in English and in Russian translation in the volume "Different Faces of Geometry", International Mathematical Series, third volume Plenum/Kluwer, Tamara Rozhkovskaya, publisher of the Russian translation; Eds.: Mikhail Gromov, Simon K.Donaldson, Yakov Eliashberg. If you download the paper (ps, pdf, dvi, tex), please ask your library to purchase the book!

The Coq proof files which went with the first version of "Computer theorem-proving in math" are now bundled with a short note which also replaces one of the chapters which was removed in revision:
Set-theoretical mathematics in Coq (tex, ps, pdf, dvi), math.LO/0402336.
See the index file for the proof files (these come in a tar archive in the Arxiv version).

Posted:

---to the electromagnetic bubble emanating from our planet:
Waiting for Godel: the quantum nature of typical ambiguity (tex; ps ).