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Multimodal Machine Learning-based Knee Osteoarthritis Progression Prediction from Plain Radiographs and Clinical DataApr 12 2019May 06 2019Knee osteoarthritis (OA) is the most common musculoskeletal disease without a cure, and current treatment options are limited to symptomatic relief. Prediction of OA progression is a very challenging and timely issue, and it could, if resolved, accelerate ... More

Many-particle limits and non-convergence of dislocation wall pile-upsApr 06 2017The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repelling force on each other, resulting in a nontrivial equilibrium configuration. ... More

Multimodal Machine Learning-based Knee Osteoarthritis Progression Prediction from Plain Radiographs and Clinical DataApr 12 2019Knee osteoarthritis (OA) is the most common musculoskeletal disease without a cure, and current treatment options are limited to symptomatic relief. Prediction of OA progression is a very challenging and timely issue, and it could, if resolved, accelerate ... More

Trends in Space Astronomy and Cosmic Vision 2015-2025Oct 28 2005As a short introduction to the astronomy session, the response of the community to the Call for Themes issued by ESA and the specific themes selected by the Astronomy Working Group are briefly presented in connection with the four grand themes finally ... More

Upscaling of the dynamics of dislocation wallsNov 04 2014We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of the upscaling ... More

Discrete-to-continuum limits of particles with an annihilation ruleJul 30 2018Dec 29 2018In the recent trend of extending discrete-to-continuum limit passages for gradient flows of single-species particle systems with singular and nonlocal interactions to particles of opposite sign, any annihilation effect of particles with opposite sign ... More

Thermal Brownian motorMay 31 2005Aug 03 2005Recently, a thermal Brownian motor was introduced [Van den Broeck, Kawai and Meurs, Phys. Rev. Lett. (2004)], for which an exact microscopic analysis is possible. The purpose of this paper is to review some further properties of this construction, and ... More

Asymptotic analysis of boundary layers in a repulsive particle systemSep 12 2016This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations, dislocation dipoles ... More

New phases of finite temperature gauge theory from an extended actionOct 02 2007We study the behavior of the order parameter, the phase diagram, and the thermodynamics of exotic phases of finite temperature gauge theory. Lattice simulations were performed in SU(3) and SU(4) with an adjoint Polyakov loop term added to the standard ... More

The QCD sign problem as a total derivativeJun 13 2013Sep 09 2013We consider the distribution of the complex phase of the fermion determinant in QCD at nonzero chemical potential and examine the physical conditions under which the distribution takes a Gaussian form. We then calculate the baryon number as a function ... More

L^2-Theory for non-symmetric Ornstein-Uhlenbeck semigroups on domainsJul 04 2012Oct 26 2012We present some new results on analytic Ornstein-Uhlenbeck semigroups and use them to extend recent work of Da Prato and Lunardi for Ornstein-Uhlenbeck semigroups on open domains O to the non-symmetric case. Denoting the generator of the semigroup by ... More

Unipotent Invariant MatricesOct 11 2010Feb 24 2013We describe the variety of fixed points of a unipotent operator acting on the space of matrices. We compute the determinant and the rank of a generic (symmetric, or anti-symmetric) matrix in the fixed variety, yielding information about the generic singular ... More

Is adding charcoal to soil a good method for CO2 sequestration? - Modeling a spatially homogeneous soilAug 27 2012Jul 09 2013Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture ... More

Dynamics of screw dislocations: a generalised minimising-movements scheme approachSep 03 2015Feb 29 2016The gradient flow structure of the model introduced in [CG99] for the dynamics of screw dislocations is investigated by means of a generalised minimising-movements scheme approach. The assumption of a finite number of available glide directions, together ... More

Rectification of thermal fluctuations in ideal gasesJul 07 2004We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced in [Van den Broeck, Kawai and Meurs, \emph{Microscopic analysis of a thermal Brownian motor}, to appear in Phys. Rev. Lett.], by an expansion of ... More

Convergence and non-convergence of many-particle evolutions with multiple signsOct 11 2018We address the question of convergence of evolving interacting particle systems as the number of particles tends to infinity. We consider two types of particles, called positive and negative. Same-sign particles repel each other, and opposite-sign particles ... More

Upscaling of dislocation walls in finite domainsAug 23 2013We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle system, in which ... More

Exact microscopic analysis of a thermal Brownian motorDec 30 2003Jan 01 2004We study a genuine Brownian motor by hard disk molecular dynamics and calculate analytically its properties, including its drift speed and thermal conductivity, from microscopic theory.

Particle dynamics subject to impenetrable boundaries: existence and uniqueness of mild solutionsDec 21 2018We consider the dynamics of particle systems where the particles are confined by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$. When particles hit the boundary, we consider an instant change in velocity, which turns the systems ... More

Boundary-layer analysis of a pile-up of walls of edge dislocations at a lockFeb 20 2015Jun 06 2016In this paper we analyse the behaviour of a pile-up of vertically periodic walls of edge dislocations at an obstacle, represented by a locked dislocation wall. Starting from a continuum non-local energy $E_\gamma$ modelling the interactions$-$at a typical ... More

QCD with chemical potential on S^1 x S^3Dec 01 2010In this proceedings we summarize our calculation of the phase diagram of QCD at non-zero temperature and chemical potential on S^1 x S^3 from one-loop perturbation theory [1], which is valid in the limit R << 1/Lambda, where R is the radius of S^3. We ... More

The Role of the Gouy Phase in the Coherent Phase Control of the Photoionization and Photodissociation of Vinyl ChlorideDec 13 2006We demonstrate theoretically and experimentally that the Gouy phase of a focused laser beam may be used to control the photo-induced reactions of a polyatomic molecule. Quantum mechanical interference between one- and three-photon excitation of vinyl ... More

Analysis and improvement of the VTT mold growth model: application to bamboo fiberboardApr 05 2018Apr 10 2018The reliability of a model is its accuracy in predicting the physical phenomena using the known input parameters. It also depends on the model's ability to estimate relevant parameters using observations of the physical phenomena. In this paper, the reliability ... More

Deep Saliency Models : The Quest For The Loss FunctionJul 04 2019Recent advances in deep learning have pushed the performances of visual saliency models way further than it has ever been. Numerous models in the literature present new ways to design neural networks, to arrange gaze pattern data, or to extract as much ... More

Point Spread Function Estimation in X-ray Imaging with Partially Collapsed Gibbs SamplingSep 26 2017The point spread function (PSF) of a translation invariant imaging system is its impulse response, which cannot always be measured directly. This is the case in high energy X-ray radiography, and it must be estimated from images of calibration objects ... More

VVV Survey Microlensing: Catalog of Best and Forsaken EventsJul 09 2019We searched for microlensing events in the zero-latitude area of the Galactic bulge using the VVV Survey near-IR data. We have discovered a total sample of N=630 events within an area covering 20.68 deg2 between the years 2010 and 2015. In this paper ... More

Fast Multiplier Methods to Optimize Non-exhaustive, Overlapping ClusteringFeb 05 2016Clustering is one of the most fundamental and important tasks in data mining. Traditional clustering algorithms, such as K-means, assign every data point to exactly one cluster. However, in real-world datasets, the clusters may overlap with each other. ... More

Smash Products of Calabi-Yau Algebras by Hopf AlgebrasDec 03 2015Given a Hopf algebra H and an H-module differential graded (dg) algebra A, this text investigates the smash product A#H from the viewpoint of Calabi-Yau duality. First it proves that all Hopf algebras with Van den Bergh duality have invertible antipode. ... More

Smash Products of Calabi-Yau Algebras by Hopf AlgebrasDec 03 2015Jan 08 2019Let H be a Hopf algebra and A be an H-module algebra. This article investigates when the smash product A#H is (skew) Calabi-Yau, has Van den Bergh duality or is Artin-Schelter regular or Gorenstein. In particular, if A and H are skew Calabi-Yau, then ... More

Well-posedness of the equations of a viscoelastic fluid with a free boundaryNov 14 2009In this article, we prove the local well-posedness, for arbitrary initial data with certain regularity assumptions, of the equations of a Viscoelastic Fluid of Johnson-Segalman type with a free surface. More general constitutive laws can be easily managed ... More

Smash Products of Calabi-Yau Algebras by Hopf AlgebrasDec 03 2015Oct 26 2016Given a Hopf algebra H and an H-module differential graded (dg) algebra A, this article investigates the smash product A#H in terms of Calabi-Yau duality. First it proves that all Hopf algebras with Van den Bergh duality have invertible antipode. Next ... More

Topological invariants of piecewise hereditary algebrasFeb 15 2007Feb 26 2009We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we prove that there ... More

Galois coverings of weakly shod algebrasSep 30 2008Mar 27 2009We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence, ... More

Algebraic Geometry over $C^\infty$-ringsDec 31 2009Nov 01 2016If $X$ is a smooth manifold then the $\mathbb R$-algebra $C^\infty(X)$ of smooth functions $c:X\to\mathbb R$ is a $C^\infty$-$ring$. That is, for each smooth function $f:{\mathbb R}^n\to\mathbb R$ there is an $n$-fold operation $\Phi_f:C^\infty(X)^n\to ... More

Configurations in abelian categories. IV. Invariants and changing stability conditionsOct 11 2004Mar 12 2007This is the fourth in a series of papers math.AG/0312190, math.AG/0503029, math.AG/0410267 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration is a finite collection of objects and morphisms in ... More

Singularities of special Lagrangian submanifoldsOct 29 2003We survey what is known about singularities of special Lagrangian submanifolds (SL m-folds) in (almost) Calabi-Yau manifolds. The bulk of the paper summarizes the author's five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356, ... More

U(1)-invariant special Lagrangian 3-folds I. Nonsingular solutionsNov 30 2001Feb 20 2004This is the first of three papers math.DG/0111326, math.DG/0204343 studying special Lagrangian 3-submanifolds (SL 3-folds) N in C^3 invariant under the U(1)-action (z_1,z_2,z_3) --> (gz_1,g^{-1}z_2,z_3) for unit complex numbers g, using analytic methods. ... More

Lectures on Calabi-Yau and special Lagrangian geometryAug 13 2001Jun 25 2002This paper gives a leisurely introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by a survey of recent results on singularities of special Lagrangian submanifolds, and their ... More

A theory of quaternionic algebra, with applications to hypercomplex geometryOct 09 2000In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic geometry" of noncompact ... More

Manifolds with analytic cornersMay 19 2016Manifolds with boundary and with corners form categories ${\bf Man}\subset{\bf Man^b}\subset{\bf Man^c}$. A manifold with corners $X$ has two notions of tangent bundle: the tangent bundle $TX$, and the b-tangent bundle ${}^bTX$. The usual definition of ... More

Generalized Donaldson-Thomas invariantsOct 01 2009May 19 2010This is a survey of the book arXiv:0810.5645 with Yinan Song. Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers DT^a(t) which count stable sheaves with Chern character a on X, with respect to a Gieseker stability condition ... More

Special Lagrangian submanifolds with isolated conical singularities. II. Moduli spacesNov 19 2002Mar 21 2003This is the second in a series of five papers math.DG/0211294, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on ... More

On counting special Lagrangian homology 3-spheresJul 02 1999Nov 06 2001We attempt to define a new invariant I of (almost) Calabi-Yau 3-folds M, by counting special Lagrangian rational homology 3-spheres N in M in each 3-homology class, with a certain weight w(N) depending on the topology of N. This is motivated by the Gromov-Witten ... More

Conjectures on counting associative 3-folds in $G_2$-manifoldsOct 31 2016There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\varphi,*\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\omega)$. We can also generalize $(X,\varphi,*\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\varphi,\psi)$, where we compare ... More

On manifolds with cornersOct 19 2009Oct 13 2010Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic definitions in the ... More

Kuranishi homology and Kuranishi cohomology: a User's GuideOct 30 2007Oct 22 2008A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. This paper is a brief introduction to the author's book ... More

Kuranishi homology and Kuranishi cohomologyJul 24 2007Oct 22 2008A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. Let Y be an orbifold and R a commutative ring or Q-algebra. ... More

Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-foldsJul 06 2006Let X be a Calabi-Yau 3-fold, T=D^b(coh(X)) the derived category of coherent sheaves on X, and Stab(T) the complex manifold of Bridgeland stability conditions Z on T. It is conjectured that one can define rational numbers J^a(Z) for Z in Stab(T) and a ... More

Motivic invariants of Artin stacks and 'stack functions'Sep 30 2005Mar 12 2007An invariant I of quasiprojective K-varieties X with values in a commutative ring R is "motivic" if I(X)= I(Y)+I(X\Y) for Y closed in X, and I(X x Y)=I(X)I(Y). Examples include Euler characteristics chi and virtual Poincare and Hodge polynomials. We first ... More

Configurations in abelian categories. II. Ringel-Hall algebrasMar 02 2005Mar 15 2006This is the second in a series math.AG/0312190, math.AG/0410267, math.AG/0410268 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration (\sigma,\iota,\pi) is a finite collection of objects \sigma(J) ... More

Constructing compact manifolds with exceptional holonomyMar 15 2002The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat. This is a survey paper on constructions for compact 7- and 8-manifolds with holonomy G2 and Spin(7). The ... More

A classical model for derived critical lociApr 16 2013Dec 03 2013Let $f:U\to{\mathbb A}^1$ be a regular function on a smooth scheme $U$ over a field $\mathbb K$. Pantev, Toen, Vaquie and Vezzosi (arXiv:1111.3209, arXiv:1109.5213) define the "derived critical locus" Crit$(f)$, an example of a new class of spaces in ... More

On the topology of desingularizations of Calabi-Yau orbifoldsJun 26 1998Let X/G be a 3-dimensional Calabi-Yau orbifold with codimension 2 singularities. The topology of crepant resolutions of X/G is described by the McKay correspondence (Reid, Ito). We study Calabi-Yau 3-folds Y that arise by deforming the complex structure ... More

Simple connectedness of quasitilted algebrasMay 03 2007Let A be a basic connected finite dimensional algebra over an algebraically closed field. Assuming that A is quasitilted, we prove that A is simply connected if and only if its first Hochschild cohomology group HH^1(A) vanishes. This generalises a result ... More

On maximal diagonalizable Lie subalgebras of the first Hochschild cohomologyJan 10 2007Mar 27 2009Let A be a basic connected finite dimensional algebra over an algebraically closed field k and with ordinary quiver Q without oriented cycle. To any presentation of A by quiver and admissible relations, Martinez-Villa and de La Pena have associated the ... More

The universal cover of an algebra without double bypassJul 25 2005Nov 17 2006Let A be a basic finite dimensional and connected algebra over an algebraically closed field k with zero characteristic. If the ordinary quiver of A has no double bypasses, we show that A admits a Galois covering which satisfies a universal property with ... More

Crossed-products of Calabi-Yau algebras by finite groupsJun 06 2010May 02 2018Let a finite group G act on a differential graded algebra A. This article presents necessary conditions and sufficient conditions for the skew group algebra A*G to be Calabi-Yau. In particular, when A is the Ginzburg dg algebra of a quiver with an invariant ... More

Infinite self-gravitating systems and cosmological structure formationMay 09 2008The usual thermodynamic limit for systems of classical self-gravitating point particles becomes well defined, as a {\it dynamical} problem, using a simple physical prescription for the calculation of the force, equivalent to the so-called ``Jeans' swindle''. ... More

The exceptional holonomy groups and calibrated geometryJun 01 2004The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. Riemannian manifolds with these holonomy groups are Ricci-flat. This is a survey paper on exceptional holonomy, in two parts. Part I introduces the exceptional holonomy ... More

Constructible functions on Artin stacksMar 18 2004Jan 04 2006Let K be an algebraically closed field, X a K-scheme, and X(K) the set of closed points in X. A constructible set C in X(K) is a finite union of subsets Y(K) for finite type subschemes Y in X. A constructible function f : X(K) --> Q has f(X(K)) finite ... More

Special Lagrangian submanifolds with isolated conical singularities. I. RegularityNov 19 2002Mar 21 2003This is the first in a series of five papers math.DG/0211295, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on ... More

U(1)-invariant special Lagrangian 3-folds. III. Properties of singular solutionsApr 29 2002Feb 20 2004This is the third in a series of three papers math.DG/0111324, math.DG/0111326 studying special Lagrangian 3-submanifolds (SL 3-folds) N in C^3 invariant under the U(1)-action (z_1,z_2,z_3) --> (gz_1,g^{-1}z_2,z_3) for unit complex numbers g, using analytic ... More

U(1)-invariant special Lagrangian 3-folds II. Existence of singular solutionsNov 30 2001Feb 20 2004This is the second of three papers math.DG/0111324, math.DG/0204343 studying special Lagrangian 3-submanifolds (SL 3-folds) N in C^3 invariant under the U(1)-action (z_1,z_2,z_3) --> (gz_1,g^{-1}z_2,z_3) for unit complex numbers g, using analytic methods. ... More

Lectures on special Lagrangian geometryNov 09 2001Sep 29 2003We introduce special Lagrangian submanifolds in C^m and in (almost) Calabi-Yau manifolds, and survey recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture. The paper is aimed at graduate students ... More

Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flowJan 20 2014Sep 03 2014Let $M$ be a Calabi-Yau $m$-fold, and consider compact, graded Lagrangians $L$ in $M$. Thomas and Yau math.DG/0104196, math.DG/0104197 conjectured that there should be a notion of "stability" for such $L$, and that if $L$ is stable then Lagrangian mean ... More

Some new homology and cohomology theories of manifolds and orbifoldsSep 18 2015For each manifold or effective orbifold $Y$ and commutative ring $R$, we define a new homology theory $MH_*(Y;R)$, $M$-$homology$, and a new cohomology theory $MH^*(Y;R)$, $M$-$cohomology$. For $MH_*(Y;R)$ the chain complex $(MC_*(Y;R),\partial)$ is generated ... More

Special Lagrangian submanifolds with isolated conical singularities. III. Desingularization, the unobstructed caseFeb 28 2003Mar 21 2003This is the third in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302356, math.DG/0303272 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled ... More

A new construction of compact 8-manifolds with holonomy Spin(7)Oct 01 1999The exceptional holonomy groups are G2 in 7 dimensions, and Spin(7) in 8 dimensions. In a previous paper (Invent. math. 123 (1996), 507-552) the author constructed the first examples of compact 8-manifolds with holonomy Spin(7), by resolving orbifolds ... More

Conjectures on counting associative 3-folds in $G_2$-manifoldsOct 31 2016May 30 2017There is a strong analogy between compact, torsion-free $G_2$-manifolds $(X,\varphi,*\varphi)$ and Calabi-Yau 3-folds $(Y,J,g,\omega)$. We can also generalize $(X,\varphi,*\varphi)$ to 'tamed almost $G_2$-manifolds' $(X,\varphi,\psi)$, where we compare ... More

The universal cover of a monomial triangular algebra without multiple arrowsJan 10 2007Mar 06 2008Let A be a basic connected finite dimensional algebra over an algebraically closed field k. Assuming that A is monomial and that the ordinary quiver Q of A has no oriented cycle and no multiple arrows, we prove that A admits a universal cover with group ... More

On Galois coverings and tilting modulesSep 22 2006Jan 12 2007Let A be a basic connected finite dimensional algebra over an algebraically closed field, let G be a group, let T be a basic tilting A-module and let B the endomorphism algebra of T. Under a hypothesis on T, we establish a correspondence between the Galois ... More

The fundamental group of a triangular algebra without double bypassesMar 15 2005Apr 11 2005Let A be a basic connected finite dimensional algebra over a field k and let Q be the ordinary quiver of A. To any presentation of A with Q and admissible relations, R. Martinez-Villa and J. A. de La Pena have associated a group called the fundamental ... More

On the Morita Reduced Versions of Skew Group Algebras of Path AlgebrasOct 30 2018Let R be the skew group algebra of a finite group acting on the path algebra of a quiver. This article develops both theoretical and practical methods to do computations in the Morita reduced algebra associated to R. Reiten and Riedtmann proved that there ... More

Electroweak Baryogenesis without the Phase TransitionSep 11 1997Radiation domination at the electroweak epoch is a simplifying assumption, but one for which there is no observational basis. Treating the expansion rate as a variable, I re-examine electroweak baryogenesis in various scenarios. At a first order phase ... More

Cosmological simulations of structure formation and the Vlasov equationMay 11 2008In cosmology numerical simulations of structure formation are now of central importance, as they are the sole instrument for providing detailed predictions of current cosmological models for a whole class of important constraining observations. These ... More

Kuranishi spaces as a 2-categoryOct 26 2015This is a survey of the author's in-progress book arXiv:1409.6908. 'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic geometry (see e.g. arXiv:1503.07631), as the geometric structure on moduli spaces of $J$-holomorphic ... More

A generalization of manifolds with cornersJan 02 2015Jun 07 2016In conventional Differential Geometry one studies manifolds, locally modelled on ${\mathbb R}^n$, manifolds with boundary, locally modelled on $[0,\infty)\times{\mathbb R}^{n-1}$, and manifolds with corners, locally modelled on $[0,\infty)^k\times{\mathbb ... More

A new definition of Kuranishi spaceSep 24 2014Oct 27 2015'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic geometry (see e.g. arXiv:1106.4882), as the geometric structure on moduli spaces of $J$-holomorphic curves. An alternative to Kuranishi spaces is the 'polyfolds' ... More

Kuranishi spaces as a 2-categoryOct 26 2015Aug 28 2018This is a survey of the author's paper arXiv:1409.6908 and in-progress book. 'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic geometry (see e.g. arXiv:1503.07631), as the geometric structure on moduli spaces of ... More

Configurations in abelian categories. II. Moduli stacksDec 09 2003Apr 14 2005This paper has been withdrawn, because I have merged it with paper I of the series, math.AG/0312190. The main results of this paper now appear in sections 7-9 of the revised version of math.AG/0312190, with shortened and improved proofs.

Configurations in abelian categories. I. Basic properties and moduli stacksDec 09 2003Mar 15 2006This is the first in a series of papers math.AG/0503029, math.AG/0410267, math.AG/0410268 on "configurations" in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration (\sigma,\iota,\pi) is a finite collection of objects ... More

Constant Scalar Curvature Metrics on Connected SumsAug 03 2001Mar 12 2002Let (M,g) be a compact Riemannian manifold with dimension n > 2. The Yamabe problem is to find a metric with constant scalar curvature in the conformal class of g, by minimizing the total scalar curvature. The proof was completed in 1984. Suppose (M',g') ... More

Ruled special Lagrangian 3-folds in C^3Dec 08 2000This is the fourth in a series of papers math.DG/0008021, math.DG/0008155, math.DG/0010036 constructing explicit examples of special Lagrangian submanifolds (SL m-folds) in C^m. A submanifold of C^m is ruled if it is fibred by a family of real straight ... More

Singularities of special Lagrangian fibrations and the SYZ ConjectureNov 22 2000Jun 17 2003The SYZ Conjecture explains Mirror Symmetry between mirror Calabi-Yau 3-folds M,M' in terms of special Lagrangian fibrations f : M --> B and f' : M' --> B over the same base B, whose fibres are dual 3-tori, except for singular fibres. One of the main ... More

An introduction to d-manifolds and derived differential geometryJun 19 2012Dec 07 2012This is a survey of the author's book "D-manifolds and d-orbifolds: a theory of derived differential geometry", available at http://people.maths.ox.ac.uk/~joyce/dmanifolds.html We introduce a 2-category dMan of "d-manifolds", new geometric objects which ... More

Special Lagrangian submanifolds with isolated conical singularities. IV. Desingularization, obstructions and familiesFeb 28 2003Mar 21 2003This is the fourth in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0303272 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled ... More

U(1)-invariant special Lagrangian 3-folds in C^3 and special Lagrangian fibrationsJun 03 2002This is a survey of the author's series of three papers math.DG/0111324, math.DG/0111326, math.DG/0204343 using analysis to investigate special Lagrangian 3-folds (SL 3-folds) in C^3 invariant under the U(1)-action (z_1,z_2,z_3) --> (gz_1,g^{-1}z_2,z_3) ... More

Evolution equations for special Lagrangian 3-folds in C^3Oct 03 2000Aug 01 2001This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The previous paper in the series, math.DG/0008155, defined the idea of evolution data, which includes an (m-1)-submanifold P in R^n, and ... More

Special Lagrangian m-folds in C^m with symmetriesAug 02 2000Jul 31 2001This is the first in a series of papers on special Lagrangian submanifolds in C^m. We study special Lagrangian submanifolds in C^m with large symmetry groups, and give a number of explicit constructions. Our main results concern special Lagrangian cones ... More

Electroweak Baryogenesis and the Expansion Rate of the UniverseJun 04 1996Nov 25 1996The standard requirement for the production of baryons at the electroweak phase transition, that the phase transition be first order and the sphaleron bound be satisfied, is predicated on the assumption of a radiation dominated universe at that epoch. ... More

A Note on Spontaneous BaryogenesisJun 21 1994The original calculation of `spontaneous' baryogenesis overlooked the role played by transport of particles onto the bubbles wall. For typical `adiabatic' wall thicknesses and velocities one can model the problem in a fluid approximation and the mechanism ... More

D-manifolds, d-orbifolds and derived differential geometry: a detailed summaryAug 24 2012Dec 07 2012This is a long summary of the author's book "D-manifolds and d-orbifolds: a theory of derived differential geometry", available at http://people.maths.ox.ac.uk/~joyce/dmanifolds.html . A shorter survey paper on the book, focussing on d-manifolds without ... More

Configurations in abelian categories. III. Stability conditions and identitiesOct 11 2004Mar 12 2007This is the third in a series math.AG/0312190, math.AG/0503029, math.AG/0410268 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration (\sigma,\iota,\pi) is a finite collection of objects \sigma(J) ... More

Special Lagrangian submanifolds with isolated conical singularities. V. Survey and applicationsMar 21 2003This is the last in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled ... More

Quasi-ALE metrics with holonomy SU(m) and Sp(m)May 07 1999This is the sequel to "Asymptotically Locally Euclidean metrics with holonomy SU(m)", math.AG/9905041. Let G be a subgroup of U(m), and X a resolution of C^m/G. We define a special class of Kahler metrics g on X called Quasi Asymptotically Locally Euclidean ... More

An introduction to C-infinity schemes and C-infinity algebraic geometryApr 26 2011Nov 16 2012This is a survey of the author's paper arXiv:1001.0023 on "Algebraic Geometry over C-infinity rings". If X is a smooth manifold then the R-algebra C^\infty(X) of smooth functions c : X --> R is a "C-infinity ring". That is, for each smooth function f ... More

Special Lagrangian 3-folds and integrable systemsJan 30 2001Jul 31 2001This is the sixth in a series of papers constructing examples of special Lagrangian m-folds in C^m. We present a construction of special Lagrangian cones in C^3 involving two commuting o.d.e.s, motivated by the first two papers of the series. Then we ... More

Constructing special Lagrangian m-folds in C^m by evolving quadricsAug 21 2000Jan 31 2001This is the second in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The first paper was math.DG/0008021, which studied special Lagrangian m-folds with large symmetry groups. The third is math.DG/0010036, ... More

Asymptotically Locally Euclidean metrics with holonomy SU(m)May 07 1999Let G be a nontrivial finite subgroup of U(m) acting freely on C^m - 0. Then C^m/G has an isolated quotient singularity at 0. Let X be a resolution of C^m/G, and g a Kahler metric on X. We say that g is Asymptotically Locally Euclidean (ALE) if it is ... More

Duality for Differential Operators of Lie-Rinehart AlgebrasSep 12 2017Dec 21 2018Let (S,L) be a Lie-Rinehart algebra over a commutative ring R. This article proves that, if S is flat as an R-module and has Van den Bergh duality in dimension n, and if L is finitely generated and projective with constant rank d as an S-module, then ... More