# Inventiones Mathematicae Submit Online Essays

S. Mohammad Mozaffari

The paper presents a critical review of the iterative process used by Shams al-Dīn Muh{combining dot below)ammad al-Wābkanawī (Iran, Maragha, ca. 1270-1320) in order to compute the annular solar eclipse of 30 January 1283 from the solar and lunar parameter values obtained by Muh{combining dot below)yī al-Dīn al-Maghribī (Maragha, 1260-1274). The position of this prediction in medieval astronomy will also be discussed. Wābkanawī uses an observation as evidence for the correctness of his prediction, and his results agree to a remarkable extent with modern astronomical computations of the same eclipse. © 2013 Elsevier Inc.

Jemma Lorenat

© 2014 Elsevier Inc. In the early nineteenth century debate over geometric methodology, Jean-Victor Poncelet characterized pure geometry as reasoning in which the figure is never lost from view. Whether illustrated, described or constructed, Poncelet presented the figure as the primary form of geometrical evidence, a means of justification based in sensory perception. In Poncelet's pure geometry, the objects of geometry were emphatically representational and tangible. By contrast, though classified as analytic geometry, Julius Plücker's contemporary research treated coordinate equations as visual geometric objects-evidence-by focusing on their form and endeavouring to avoid calculations. Working from Poncelet's division between pure and analytic geometries we focus on five versions by three different geometers, of a single conic section construction written between 1817 and 1826. Despite the similarity of their results, Poncelet, Plücker, and Joseph Diaz Gergonne each addressed the problem from contrasting methodological perspectives. We examine how the figure-based distinction materialized in contemporary geometric practices, and what constituted geometric evidence when the figure was lost from view.

Lukas Verburgt

The goal of this paper is to provide an extensive account of Robert Leslie Ellis's largely forgotten work on philosophy of science and probability theory. On the one hand, it is suggested that both his 'idealist' renovation of the Baconian theory of induction and a 'realism' vis-à-vis natural kinds were the result of a complex dialogue with the work of William Whewell. On the other hand, it is shown to what extent the combining of these two positions contributed to Ellis's reformulation of the metaphysical foundations of traditional probability theory. This parallel is assessed with reference to the disagreement between Ellis and Whewell on the nature of (pure) mathematics and its relation to scientific knowledge. © 2013 Elsevier Inc.

Satyanad Kichenassamy

© 2015 Elsevier Inc. We analyze Tartaglia's account, in 1546, of the circumstances leading to his breakthrough regarding the solution of cubic equations. He claims that he solved x 3 +rx 2 =q in 1530, well before he could handle, in 1535, equations with a linear term px (and no quadratic term). This claim is at variance with Cardano's narrative as well as with later treatments of the problem, in which the solution of equations of the latter type provides the basis for the solution of all the other types of cubic equations. We show that Tartaglia's claim is supported in his text by the use of the theory of continued proportions, that occurs as a Leitmotiv. We show that relations on continued proportions stressed by Pacioli as basic "keys" provide a simple derivation of the results given by Tartaglia, that is consistent with their chronological order. Thus, his narrative contains not only priority claims, but also proposes an account of the mathematical steps that led him to his results.

Sabine Rommevaux

The famous French physician Jean Fernel published in 1528 in Paris the De proportionibus libri duo. This treatise belongs to the tradition of texts on proportion that follow Bradwardine's Tractatus de proportionibus seu de proportionibus velocitatum in motibus (1328). In the first book, Fernel presented a theory of ratios that is traditional but contains some distinctive features, on denominating ratios, on fractions, on irrational ratios. The second book is devoted to a theory of ratio of ratios of which I give an account in this paper. © 2013 Elsevier Inc.

Jean Christianidis | Jeffrey Oaks

Medieval algebra is distinguished from other arithmetical problem-solving techniques by its structure and technical vocabulary. In an algebraic solution one or several unknowns are named, and via operations on the unknowns the problem is transferred to the artificial setting of an equation expressed in terms of the named powers, which is then simplified and solved. In this article we examine Diophantus' Arithmetica from this perspective. We find that indeed Diophantus' method matches medieval algebra in both vocabulary and structure. Just as we see in medieval Arabic and Italian algebra, Diophantus worked out the operations expressed in the enunciation of a problem prior to setting up a polynomial equation. Further, his polynomials were regarded as aggregations with no operations present. © 2012 Elsevier Inc.

Valérie Debuiche

During his whole life, Leibniz attempted to elaborate a new kind of geometry devoted to relations and not to magnitudes, based on space and situation, independent of shapes and quantities, and endowed with a symbolic calculus. Such a "geometric characteristic" shares some elements with the perspective geometry: they both are geometries of situational relations, founded in a transformation preserving some invariants, using infinity, and constituting a general method of knowledge. Hence, the aim of this paper is to determine the nature of the relation between Leibniz's new geometry and the works on perspective, namely Desargues' ones. © 2013 Elsevier Inc.

Mitsuko Wate-Mizuno

© 2014 Elsevier Inc. Dénes König (1884-1944) is a Hungarian mathematician well known for his treatise on graph theory (König, 1936). When he was a student, he published two books on mathematical recreations (König, 1902, 1905a). Does his work on mathematical recreations have any relation to his work on graph theory? If yes, how are they connected? To answer these questions, we will examine his books of 1902, 1905 and 1936, and compare them with each other. We will see that the books of 1905 and 1936 include many common topics, and that the treatment of these topics is different between 1905 and 1936. Dénes König (1884-1944) est un mathématicien hongrois très connu pour son traité sur la théorie des graphes (1936). En 1902 et 1905, il a publié deux livres sur les récréations mathématiques. Ses æuvres sur les récréations mathématiques sont-elles liées à son traité sur la théorie des graphes ? Si oui, de quelle façon ? Pour répondre à ces questions, nous examinerons ses livres de 1902, 1905 et 1936, et les comparerons les uns aux autres. Nous verrons qu'à la différence de l'ouvrage de 1902, les livres de 1905 et 1936 comportent beaucoup de sujets communs, mais que les manières de traiter ces sujets diffèrent entre 1905 et 1936.

Christian Marinus Taisbak

Did Heron (or his teachers) use sequences of differences to find an approximate value of the cube root of an integer? I venture a conjecture of his heuristics and a couple of possible mathematical proofs of his method. © 2013 Elsevier Inc.

Alex D.D. Craik

The little-known Scottish mathematician William Spence was an able analyst, one of the first in Britain to be conversant with recent continental advances, and having original views. His major work on "logarithmic transcendents" gives the first detailed account of polylogarithms and related functions. A theory of algebraic equations was published just after his early death; and further essays, edited by John Herschel, were published posthumously. The most substantial of these concern an extension of his work on "logarithmic transcendents", and the general solution of linear differential and difference equations. But awareness of Spence's works was long delayed by their supposed unavailability. Spence's life, the story of his "lost" publications, and a summary of all his essays are here described. © 2013 Elsevier Inc.

Jacqueline Feke

Bringing the meta-mathematics of Hero of Alexandria and Claudius Ptolemy into conversation for the first time, I argue that they employ identical rhetorical strategies in the introductions to Hero's Belopoeica, Pneumatica, Metrica and Ptolemy's Almagest. They each adopt a paradigmatic argument, in which they criticize the discourses of philosophers and declare epistemological supremacy for mathematics by asserting that geometrical demonstration is indisputable. The rarity of this claim-in conjunction with the paradigmatic argument-indicates that Hero and Ptolemy participated in a single meta-mathematical tradition, which made available to them rhetoric designed to introduce, justify, and bolster the value of mathematics. Mettendo in relazione per la prima volta la meta-matematica di Erone di Alessandria con quella di Claudio Tolomeo, sostengo che questi due autori hanno impiegato strategie retoriche identiche nelle introduzioni alla Belopoeica, Pneumatica, Metrica e nell'Almagesto. Entrambi adottano un argomento paradigmatico, nel quale essi criticano i discorsi dei filosofi e dichiarano la supremazia epistemologica della matematica, asserendo che la dimostrazione geometrica è indisputabile. La rarità di questa affermazione - unita alla natura paradigmatica dell'argomento in questione - indicano che Erone e Tolomeo partecipavano ad un'unica tradizione meta-matematica che metteva a loro disposizione risorse retoriche volte a introdurre, giustificare, e promuovere il valore delle matematiche. © 2014 Elsevier Inc.

Henrik Kragh Sørensen

The present paper analyses the confluence of agendas held by Danish mathematicians and German refugees from Nazi oppression as they unfolded and shaped the mathematical milieu in Copenhagen during the 1930s. It does so by outlining the initiatives to aid emigrant intellectuals in Denmark and contextualises the few mathematicians who would be aided. For most of those, Denmark would be only a transit on the route to more permanent immigration, mainly in the US. Thus, their time in Copenhagen would exert only temporary influence over Danish mathematics; but as it will be argued, the impacts of their transit would be more durable both for the emigrants and for the Danish mathematical milieu. It is thus argued that the influx of emigrant mathematicians helped develop the institutional conditions of mathematics in Copenhagen in important ways that simultaneously bolstered the international outlook of Danish mathematicians. These confluences of agendas became particularly important for Danish mathematics after the war, when the networks developed during the 1930s could be drawn upon. © 2013 Elsevier Inc.

Viktor Blåsjö

© 2017 Elsevier Inc. A number of scholars have recently maintained that a theorem in an unpublished treatise by Leibniz written in 1675 establishes a rigorous foundation for the infinitesimal calculus. I argue that this is a misinterpretation.

Anne Marie Décaillot

© 2014 Elsevier Inc. The article is devoted to Edouard Lucas's contribution to the development of mathematical recreations in the France of the post 1870 war period. Lucas's name is associated to four volumes of Récréations mathématiques published between 1882 and 1894 (the last two having been published posthumously) and to a posthumous volume L'Arithmétique amusante, which appeared in 1895. The author analyzes the context of reform of science education in relation to which mathematical recreations appeared as a means of attracting a wider public to scientific activities and inspiring young people to study science. The article brings to light how the milieu of new associations which took shape to promote science (Association Française pour l'Avancement des Sciences, Société Mathématique de France) allowed the constitution of social groups internationally connected and quite active in the promotion and development of mathematical recreations. Lastly, the article suggests that this type of mathematical activity allowed the cultivation of fields that at the time the French academic milieu perceived as marginal such as number theory and analysis situs as well as their applications.

Christopher Hollings

© 2014 Elsevier Inc. During the several decades of the USSR's existence, Soviet mathematicians produced, at intervals, a number of volumes of survey articles which provide us with a series of 'snapshots' of Soviet mathematics down the years. In this paper, I introduce these volumes as a resource for historians of Soviet mathematics, and consider the picture they paint of the development of abstract algebra in the USSR, paying particular attention to the aspects in which these surveys differ from later, retrospective accounts of Soviet algebra.

Albrecht Heeffer

© 2014 Elsevier Inc. This paper deals with a sub-class of recreational problems which are solved by a simple memorized rule resulting from an elementary arithmetical or algebraic solution, called proto-algebraic rules. Their recreational aspect is derived from a surprise or trick solution which is not immediately obvious to the subjects involved. Around 1560 many such problems wane from arithmetic and algebra textbooks to reappear in the eighteenth century. Several hypotheses are investigated why popular Renaissance recreational problems lost their appeal. We arrive at the conclusion that the emergence of algebra as a general problem solving method changed the scope of what is considered recreational in mathematics. Questo saggio tratta di una sottoclasse di problemi ricreativi risolti tramite memorizzazione di una semplice regola risultante da una soluzione algebraica o aritmetica, chiamata regola proto-algebraica. L'aspetto ricreativo di questi problemi deriva da una soluzione a sorpresa o da un trucco non immediatamente ovvi ai soggetti coinvolti. Intorno al 1560 svariati problemi di questo tipo sparirono dai manuali di algebra e aritmetica, per riapparire nel diciottesimo secolo. Diverse ipotesi sono vagliate sul perché problemi ricreativi popolari nel Rinascimento persero attrattività, per giungere alla conclusione che l'emergere dell'algebra come metodo generale di risoluzione di problemi cambiò la portata di ciò che era considerato ricreativo in matematica.

François Lê

© 2014 Elsevier Inc. Felix Klein's Erlanger Programm (1872) has been extensively studied by historians. If the early geometrical works in Klein's career are now well-known, his links to the theory of algebraic equations before 1872 remain only evoked in the historiography. The aim of this paper is precisely to study this algebraic background, centered around particular equations arising from geometry, and participating on the elaboration of the Erlanger Programm. Another result of the investigation is to complete the historiography of algebraic equations, in which those "geometrical equations" do not appear.

Dirk Schlimm

The extant correspondence, consisting of ten letters from the period from 1882 to 1902, from Moritz Pasch to Felix Klein is presented together with an English translation and a short introduction. These letters provide insights into the views of Pasch and Klein regarding the role of intuition and axioms in mathematics, and also into the hiring practices of mathematics professors in the 1880s. © 2013 Elsevier Inc.

Maarten Van Dyck | Koen Vermeir

© 2014 Elsevier Inc. Akin to the mathematical recreations, John Wilkins' Mathematicall Magick (1648) elaborates the pleasant, useful and wondrous part of practical mathematics, dealing in particular with its material culture of machines and instruments. We contextualize the Mathematicall Magick by studying its institutional setting and its place within changing conceptions of art, nature, religion and mathematics. We devote special attention to the way Wilkins inscribes mechanical innovations within a discourse of wonder. Instead of treating 'wonder' as a monolithic category, we present a typology, showing that wonders were not only recreative, but were meant to inspire Wilkins' readers to new mathematical inve ntions. Conformément aux récréations mathématiques, le Mathematicall Magick (1648) de John Wilkins développe les parties plaisantes, utiles et merveilleuses des mathématiques pratiques, traitant en particulier la culture matérielle des machines et des instruments. Nous étudions le Mathematicall Magick en contexte, en explorant son cadre institutionnel et sa place dans un ensemble de conceptions en pleine transformation à l'époque - conceptions de l'art, de la nature, de la religion et des mathématiques. Nous portons une attention particulière à la manière dont les innovations mécaniques s'inscrivent dans un discours sur le merveilleux. Au lieu de traiter « le merveilleux » comme une catégorie monolithique, nous offrons une typologie, montrant que les merveilles ne sont pas seulement récréatives, mais qu'elles cherchent à inspirer à des lecteurs l'envie de créer de nouvelles inventions mathématiques.

## Publications

### Books

D. Joyce, * 'Compact manifolds with special holonomy'*, 436 pages, Oxford Mathematical Monographs series, OUP, July 2000. Reprinted 2003. Reprinted 2006 (twice).

-- Buy it on on the Web from OUP or Amazon.

M. Gross, D. Huybrechts and D. Joyce, * 'Calabi-Yau Manifolds and Related Geometries'*, 239 pages, Universitext series, Springer, Berlin, 2003.

-- Buy it on on the Web from Springer or Amazon.

D. Joyce, * 'Riemannian holonomy groups and calibrated geometry'*, 303 pages, Oxford Graduate Texts in Mathematics 12, OUP, March 2007.

-- Buy it on on the Web from OUP in paperback or hardback, or from Amazon in paperback or hardback.

D. Joyce and Y. Song, *'A theory of generalized Donaldson-Thomas invariants'*, 216 pages, Memoirs of the AMS 217 (2012), pages 1-216. Published online here.

-- Also available on the Web as arXiv:0810.5645.

### Journal articles

J. Gillis and D. Joyce, * 'Some results on combinatorial interpretations for the integral of the product of several classical orthogonal polynomials'*, Oxford Quarterly Journal of Mathematics 42 (1991), 57-75.

D. Joyce, * 'The hypercomplex quotient and the quaternionic quotient'*, Mathematische Annalen 290, (1991), 323-340. pdf file

D. Joyce, * 'Compact hypercomplex and quaternionic manifolds'*, Journal of Differential Geometry 35 (1992), 743-761.

D. Joyce, * 'A twistor transform for complex manifolds with connection'*, Twistor Newsletter 35 (1992), 11-14. postscript file

D. Joyce, * 'Manifolds with many complex structures'*, Oxford Quarterly Journal of Mathematics 46 (1995), 169-184. postscript file

D. Joyce, * 'Explicit construction of self-dual *4*-manifolds'*, Duke Mathematical Journal 77 (1995), 519-552. postscript file

D. Joyce, * 'Compact *8*-manifolds with holonomy *Spin(7)*'*, Inventiones mathematicae 123 (1996), 507-552. postscript file

D. Joyce, * 'Compact Riemannian *7*-manifolds with holonomy *G_{2}*. I'*, Journal of Differential Geometry 43 (1996), 291-328. postscript file

D. Joyce, * 'Compact Riemannian *7*-manifolds with holonomy *G_{2}*. II'*, Journal of Differential Geometry 43 (1996), 329-375. postscript file

D. Joyce, * 'Hypercomplex Algebraic Geometry'*, Oxford Quarterly Journal of Mathematics 49 (1998), 129-162. postscript file

D. Joyce, * 'Deforming Calabi-Yau orbifolds'*, Asian Journal of Mathematics 3 (1999), 853-868. postscript file

D. Joyce, * 'A new construction of compact *8*-manifolds with holonomy *Spin(7)*'*, Journal of Differential Geometry 53 (1999), 89-130.

-- Also available on the web as math.DG/9910002.

D. Joyce, * 'Asymptotically Locally Euclidean metrics with holonomy *SU(*m*)*'*, Annals of Global Analysis and Geometry 19 (2001), 55-73.

-- Also available on the Web as math.AG/9905041.

D. Joyce, * 'Quasi-ALE metrics with holonomy *SU(*m*)* and *Sp(*m*)*'*, Annals of Global Analysis and Geometry 19 (2001), 103-132.

-- Also available on the Web as math.AG/9905043.

D. Joyce, * 'Constructing special Lagrangian m-folds in C^{m} by evolving quadrics'*, Mathematische Annalen 320 (2001), 757-797.

-- Also available on the Web as math.DG/0008155.

D. Joyce, * 'Evolution equations for special Lagrangian *3*-folds in C*

^{3}

*'*, Annals of Global Analysis and Geometry 20 (2001), 345-403.

-- Also available on the Web as math.DG/0010036.

D. Joyce, * 'Ruled special Lagrangian *3*-folds'*, Proceedings of the London Mathematical Society 85 (2002), 233-256.

-- Also available on the Web as math.DG/0012060.

D. Joyce, * 'Special Lagrangian m-folds in C^{m} with symmetries'*, Duke Mathematical Journal 115 (2002), 1-51.

-- Also available on the Web as math.DG/0008021.

D. Joyce, * 'Constant Scalar Curvature Metrics on Connected Sums'*, International Journal of Mathematics and Mathematical Sciences 2003:7 (2003), 405-450.

-- Also available on the Web as math.DG/0108022.

D. Joyce, * '*U(1)*-invariant special Lagrangian *3*-folds in C*

^{3}and special Lagrangian fibrations', Turkish Journal of Mathematics 27 (2003), 99-114.

-- Also available on the Web as math.DG/0206016.

D. Joyce, * 'Special Lagrangian submanifolds with isolated conical singularities. V. Survey and applications'*, Journal of Differential Geometry 63 (2003), 279-347.

-- Also available on the Web as math.DG/0303272.

D. Joyce, * 'Singularities of special Lagrangian fibrations and the SYZ Conjecture'*, Communications in Analysis and Geometry 11 (2003), 859-907.

-- Also available on the Web as math.DG/0011179.

D. Joyce, * 'Special Lagrangian submanifolds with isolated conical singularities. I. Regularity'*, Annals of Global Analysis and Geometry 25 (2004), 201-251.

-- Also available on the Web as math.DG/0211294.

D. Joyce, * 'Special Lagrangian submanifolds with isolated conical singularities. II. Moduli spaces'*, Annals of Global Analysis and Geometry 25 (2004), 301-352.

-- Also available on the Web as math.DG/0211295.

D. Joyce, * 'Special Lagrangian submanifolds with isolated conical singularities. III. Desingularization, the unobstructed case'*, Annals of Global Analysis and Geometry 26 (2004), 1-58.

-- Also available on the Web as math.DG/0302355.

D. Joyce, * 'Special Lagrangian submanifolds with isolated conical singularities. IV. Desingularization, obstructions and families'*, Annals of Global Analysis and Geometry 26 (2004), 117-174.

-- Also available on the Web as math.DG/0302356.

D. Joyce, * '*U(1)*-invariant special Lagrangian *3*-folds I. Nonsingular solutions'*, Advances in Mathematics 192 (2005), 35-71.

-- Also available on the Web as math.DG/0111324.

D. Joyce, * '*U(1)*-invariant special Lagrangian *3*-folds II. Existence of singular solutions'*, Advances in Mathematics 192 (2005), 72-134.

-- Also available on the Web as math.DG/0111326.

D. Joyce, * '*U(1)*-invariant special Lagrangian *3*-folds III. Properties of singular solutions'*, Advances in Mathematics 192 (2005), 135-182.

-- Also available on the Web as math.DG/0204343.

D. Joyce and S. Salur, * 'Deformations of Asymptotically Cylindrical coassociative submanifolds with cylindrical ends'*, Geometry and Topology 9 (2005), 1115-1146.

-- Also available on the Web as math.DG/0408137.

D. Joyce, * 'Configurations in abelian categories. I. Basic properties and moduli stacks'*, Advances in Mathematics 203 (2006), 194-255. doi: 10.1016/j.aim.2005.04.008.

-- Also available on the Web as math.AG/0312190.

D. Joyce, * 'Constructible functions on Artin stacks'*, Journal of the London Mathematical Society 74 (2006), 583-606.

-- Also available on the Web as math.AG/0403305.

D. Joyce, * 'Configurations in abelian categories. II. Ringel-Hall algebras'*, Advances in Mathematics 210 (2007), 635-706. doi: 10.1016/j.aim.2006.07.006.

-- Also available on the Web as math.AG/0503029.

D. Joyce, * 'Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds'*, Geometry and Topology 11 (2007), 667-725.

-- Also available on the Web as hep-th/0607039.

D. Joyce, * 'Motivic invariants of Artin stacks and 'stack functions' '*, Quarterly Journal of Mathematics 58 (2007), 345-392. doi: 10.1093/qmath/ham019.

-- Also available on the Web as math.AG/0509722.

D. Joyce, * 'Configurations in abelian categories. III. Stability conditions and identities'*, Advances in Mathematics 215 (2007), 153-219. doi: 10.1016/j.aim.2007.04.002.

-- Also available on the Web as math.AG/0410267.

D. Joyce, * 'Configurations in abelian categories. IV. Invariants and changing stability conditions'*, Advances in Mathematics 217 (2008), 125-204. doi: 10.1016/j.aim.2007.06.011.

-- Also available on the Web as math.AG/0410268.

D. Joyce, Y.-I. Lee and M.-P. Tsui, *'Self-similar solutions and translating solitons for Lagrangian mean curvature flow'*, Journal of Differential Geometry 84 (2010), 127-161.

-- Also available on the Web as arXiv:0801.3721.

M. Akaho and D. Joyce, *'Immersed Lagrangian Floer theory'*, Journal of Differential Geometry 86 (2010), 381-500. PDF file.

-- Also available on the Web as arXiv:0803.0717.

D. Joyce, Y.-I. Lee and R. Schoen, *'On the existence of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds'*, American Journal of Mathematics 133 (2011), 1067-1092.

-- Also available on the Web as arXiv:0902.3338.

*'A "Darboux theorem" for shifted symplectic structures on derived Artin stacks, with applications'*, Geometry and Topology 19 (2015), 1287-1359.

-- Also available on the Web as arXiv:1312.0090.

D. Joyce,

*'Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow'*, EMS Surveys in Mathematical Sciences 2 (2015), 1-62.

-- Also available on the Web as arXiv:1401.4949.

C. Brav, V. Bussi, D. Dupont, D. Joyce, and B. Szendr�i,

*'Symmetries and stabilization for sheaves of vanishing cycles'*, Journal of Singularities 11 (2015), 85-151.

-- Also available on the Web as arXiv:1211.3259.

D. Joyce,

*'A classical model for derived critical loci'*, Journal of Differential Geometry 101 (2015), 289-367.

-- Also available on the Web as arXiv:1304.4508.

Y. Imagi, D. Joyce, and J. Oliveira dos Santos,

*'Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in*, Duke Mathematical Journal 165 (2016), 847-933.

**C**^{m}'-- Also available on the Web as arXiv:1404.0271.

D. Joyce,

*'A generalization of manifolds with corners'*, Advances in Mathematics 299 (2016), 760-862. open access pdf file

-- Also available on the Web as arXiv:1501.00401.

D. Borisov and D. Joyce,

*'Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds'*, Geometry and Topology 21 (2017), 3231–3311.

-- Also available on the Web as arXiv:1504.00690.

### Articles in books

D. Joyce, * 'Compact Riemannian manifolds with exceptional holonomy'*, pages 39-65 in * 'Essays on Einstein Manifolds'*, editors C. LeBrun and M. Wang, Surveys in Differential Geometry VI, International Press, Cambridge, MA, 1999. postscript file

D. Joyce, * 'Singularities of special Lagrangian submanifolds'*, pages 163-198 in * 'Different Faces of Geometry'*, editors S.K. Donaldson, Y. Eliashberg and M. Gromov, International Mathematical Series volume 3, Kluwer/Plenum, 2004. Also to appear in Russian translation.

-- Also available on the Web as math.DG/0310460.

D. Joyce, * 'Calibrated geometry and special Lagrangian submanifolds'*, volume 1, pages 398-402 in J.-P. Fran�oise, G. Naber and T.S. Tsou, editors, *Encyclopedia of Mathematical Physics*, Elsevier, 2006.

D. Joyce, * 'Riemannian holonomy groups and exceptional holonomy'*, volume 4, pages 441-446 in J.-P. Fran�oise, G. Naber and T.S. Tsou, editors, *Encyclopedia of Mathematical Physics*, Elsevier, 2006.

D. Joyce, *'Generalized Donaldson-Thomas invariants'*, pages 125-160 in *'Geometry of special holonomy and related topics'*, editors N.C. Leung and S.-T. Yau, Surveys in Differential Geometry XVI, International Press, Cambridge, MA,(2011).

-- Also available on the Web as arXiv:0910.0105.

### Conference proceedings

D. Joyce, * 'Compact manifolds with exceptional holonomy'*, pages 245-252 in * 'Geometry and Physics'*, editors J.E. Andersen, J. Dupont, H. Pedersen and A. Swann, Lecture notes in pure and applied math. vol. 184, Marcel Dekker, New York, 1997. postscript file

D. Joyce, * 'Compact manifolds with exceptional holonomy'*, pages 361-370 in * Proceedings of the International Congress of Mathematicians, Berlin, 1998*, vol II. Documenta Mathematica, University of Bielefeld, 1998. Published online.

D. Joyce, * 'A theory of quaternionic algebra, with applications to hypercomplex geometry'*, pages 143-194 in * Proceedings of the Second Meeting on Quaternionic Structures in Mathematics and Physics, Rome, 1999*, editors S. Marchiafava, P. Piccinni and M. Pontecorvo, World Scientific, Singapore, 2001.

-- Also available in the math archive as math.DG/0010079.

D. Joyce, * 'Constructing compact *8*-manifolds with holonomy *Spin(7)* from Calabi-Yau orbifolds'*, pages 21-30 in Volume II of * Proceedings of the 3rd European Congress of Mathematics, Barcelona, July 10-14, 2000*, editors C. Casuberta, R.M. Mir�-Roig, J. Verdera and S. Xamb�-Descamps, Progress in Mathematics 202, Birkh�user, Basel, 2001. postscript file

D. Joyce, * 'On counting special Lagrangian homology *3*-spheres'*, pages 125-151 in *'Topology and Geometry: Commemorating SISTAG'*, editors A.J. Berrick, M.C. Leung and X.W. Xu, Contemporary Mathematics volume 314, A.M.S., 2002.

-- Also available on the Web as hep-th/9907013.

D. Joyce, * 'Constructing compact manifolds with exceptional holonomy'*, pages 177-191 in M. Douglas, J. Gauntlett and M. Gross, editors, * 'Strings and Geometry'*, Clay Mathematics Proceedings 3, A.M.S., 2004.

-- Also available on the Web as math.DG/0203158.

D. Joyce, * 'Lectures on special Lagrangian geometry'*, pages 667-695 in D. Hoffman, editor, * 'Global Theory of Minimal Surfaces'*, Clay Mathematics Proceedings 2, A.M.S., 2005.

-- Also available on the Web as math.DG/0111111.

D. Joyce, * 'The exceptional holonomy groups and calibrated geometry'*, pages 110-139 in S. Akbulut, T. �nder and R.J. Stern, editors, *'Proceedings of the G�kova Geometry-Topology Conference 2005'*, International Press, Somerville, MA, 2006. Published online.

-- Also available on the Web as math.DG/0406011.

D. Joyce, * 'Special Lagrangian *3*-folds and integrable systems'*, pages 189-233 in M. Guest, R. Miyaoka and Y. Ohnita, editors, *'Surveys on Geometry and Integrable Systems'*, Advanced Studies in Pure Mathematics 51, Mathematical Society of Japan, 2008.

-- Also available on the Web as math.DG/0101249.

D. Joyce, *'An introduction to C*^{∞}*-schemes and C*^{∞}*-algebraic geometry'*, pages 299-325 in H.-D. Cao and S.-T. Yau, editors, Surveys in Differential Geometry 17 (2012), Lectures given at the JDG symposium, June 2010, in memory of C.C. Hsiung.

-- Also available on the Web as arXiv:1104.4951.

D. Joyce, *'On manifolds with corners'*, pages 225-258 in S. Janeczko, J. Li and D.H. Phong, editors, *'Advances in Geometric Analysis'*, Advanced Lectures in Mathematics 21, International Press, Boston, 2012.

-- Also available on the Web as arXiv:0910.3518.

*'An introduction to d-manifolds and derived differential geometry'*, pages 230-281 in L. Brambila-Paz, O. Garcia-Prada, P. Newstead and R.P. Thomas, editors, 'Moduli spaces', London Mathematical Society Lecture Note Series 411, Cambridge University Press, 2014.

-- Also available on the Web as arXiv:1206.4207.

### Accepted for publication

D. Joyce,*'Algebraic Geometry over C*

^{∞}

*-rings'*, to appear in Memoirs of the A.M.S.

-- Also available on the Web as arXiv:1001.0023.

D. Joyce and P. Safronov,

*'A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes'*, to appear in Annales de la Faculte des Sciences de Toulouse.

-- Also available on the Web as arXiv:1506.04024.

### Work in progress

D. Joyce,*'Ringel-Hall style vertex algebra and Lie algebra structures on the homology of moduli spaces*

*'*, incomplete preprint, March 2018. pdf file. Comments welcome.

### Papers on the Web (excluding those listed above)

#### Available at http://xxx.lanl.gov/archive/math and http://xxx.lanl.gov/archive/hep-th

D. Joyce, * 'On the topology of deformations of Calabi-Yau orbifolds'*, math.AG/9806146, 1998. 25 pages.

(A rather longer version of 'Deforming Calabi-Yau orbifolds', Asian J. Math. 3 (1999), 853-868.)

D. Joyce, * 'Lectures on Calabi-Yau and special Lagrangian geometry'*, math.DG/0108088, version 3, June 2002. 58 pages.

(An expanded version of this is published as Part I of our book, M. Gross, D. Huybrechts and D. Joyce, *'Calabi-Yau Manifolds and Related Geometries'*, Springer, 2003. See top of page.)

D. Joyce, * 'Kuranishi homology and Kuranishi cohomology'*, arXiv:0707.3572, version 5, October 2008. 290 pages.

D. Joyce, * 'Kuranishi homology and Kuranishi cohomology: a User's Guide'*, arXiv:0710.5634, version 2, October 2008. 29 pages.

D. Joyce, *'D-manifolds, d-orbifolds and derived differential geometry: a detailed summary'*, arXiv:1208.4948, version 2, December 2012. 173 pages.

C. Brav, V. Bussi, and D. Joyce, *'A Darboux theorem for derived schemes with shifted symplectic structure'*, arXiv:1305.6302, version 3, June 2015. 54 pages.

V. Bussi, D. Joyce, and S. Meinhardt, *'On motivic vanishing cycles of critical loci'*, arXiv:1305.6428, version 2, December 2013. 32 pages.

*'A new definition of Kuranishi space'*, arXiv:1409.6908, version 3, October 2015. 193 pages.

D. Joyce,

*'Some new homology and cohomology theories of manifolds and orbifolds'*, arXiv:1509.05672, September 2015. 232 pages.

D. Joyce,

*'Kuranishi spaces as a*2

*-category'*, arXiv:1510.07444, October 2015. 61 pages.

D. Joyce,

*'Manifolds with analytic corners*

*'*, arXiv:1605.05913, May 2016. 73 pages.

D. Joyce,

*'Conjectures on counting associative*3

*-folds in*G

_{2}

*-manifolds'*, arXiv:1610.09836, version 2, May 2017. 74 pages.

D. Joyce and S. Karigiannis,

*'A new construction of compact*G

_{2}

*-manifolds by gluing families of Eguchi-Hanson spaces'*, arXiv:1707.09325, July 2017. 82 pages.

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