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Discovery of $ω$-free high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019Aug 01 2019The rapid degradation of the functional properties of many Ti-based alloys is due to the precipitation of the $\omega$ phase. In the conventional high-temperature shape memory alloy Ti-Ta the formation of this phase compromises completely the shape memory ... More

Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019Jul 24 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More

Discovery of new stable and high-temperature Ti-Ta-X shape memory alloys from first principles calculationsMay 14 2019In conventional Ti-Ta shape memory alloys (SMAs), high (>100{\deg}C) transformation temperatures cannot be achieved without compromising the stability of the shape memory effect. A solution to this problem is the addition of other elements to form Ti-Ta-X ... More

Doing More for Less -- Cache-Aware Parallel Contraction Hierarchies PreprocessingAug 13 2012Contraction Hierarchies is a successful speedup-technique to Dijkstra's seminal shortest path algorithm that has a convenient trade-off between preprocessing and query times. We investigate a shared-memory parallel implementation that uses $O(n+m)$ space ... More

The Gibbs Paradox RevisitedFeb 28 2010The Gibbs paradox has frequently been interpreted as a sign that particles of the same kind are fundamentally indistinguishable; and that quantum mechanics, with its identical fermions and bosons, is indispensable for making sense of this. In this article ... More

Probability in modal interpretations of quantum mechanicsMar 02 2007Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but yields probabilities. ... More

The Adventure and the PrizeSep 12 2011This article presnts a condensed summary of separate, overlapping, presentations to the Workshop on Polarized Drell-Yan Physics (Santa Fe, NM, Oct. 31-Nov.1, 2010),the GHP 2011 Worshop (Anaheim, CA, Apr.21-27, 2011) and the Transversity 2011 Workshop ... More

Chiral Dynamics and Single-Spin AsymmetriesNov 20 2007Parity-conserving single-spin asymmetries provide a specific measure of coherent spin-orbit dynamics in quantum chromodynamics. The origin of these effects can be traced to the interplay of chiral dynamics and confinement in the theory. The most elegant ... More

Chiral Mechanisms Leading to Orbital Quantum Structures in the NucleonApr 13 2007Color confinement and chiral symmetry specify some important territory for the study of hadronic physics. Any hadron can be defined as a color-singlet composite system of qurks and gluons, the fundamental fields of qcd, while the landscape of the hadronic ... More

Extending Immersions into the SphereDec 22 2010We study the problem to extend an immersed circle f in the 2-dimensional sphere to an immersion of the disc. We analyze existence and uniqueness for this problems in terms of the combinatorial structure of a word assigned to f. Our techniques are based ... More

Non-Gaussian signatures of Tachyacoustic CosmologyJun 02 2012Sep 22 2012I investigate non-Gaussian signatures in the context of tachyacoustic cosmology, that is, a noninflationary model with superluminal speed of sound. I calculate the full non-Gaussian amplitude $\mathcal{A}$, its size $f_{\rm NL}$, and corresponding shapes ... More

On the Evolution Equation for Magnetic GeodesicsNov 05 2007Apr 29 2009In this paper we prove the existence of long time solutions for the parabolic equation for closed magnetic geodesics.

The local and global versions of the Whittaker categoryNov 06 2018Nov 12 2018Given a category C acted on by the loop group G((t)), we define its Whittaker model Whit(C) as C^{N((t)),\chi}, where \chi is a non-degenerate character. We study the properties of this construction. When C is the category of sheaves on the quotient of ... More

SU(2) Charges with Spherical Symmetry and Confining Boundary ConditionsMay 04 2019Applying the static Yang-Mills Maxwell equations to a simple system of SU(2) charges with spherical symmetry and confining boundary conditions provides for a demonstration of the likelihood that the confinement mechanism in non-Abelian gauge theories ... More

On the slope of the moduli space of genus 15 and 16 curvesMay 01 2019We revisit the work of Chang and Ran on bounding the slopes of $\overline{\mathscr{M}_{15}}$ and $\overline{\mathscr{M}_{16}}$, correct one of the formulas used at the conclusion of the argument, and recompute the lower bounds on the slopes, yielding ... More

The semi-infinite intersection cohomology sheafMar 12 2017Aug 11 2017We introduce the semi-infinite category of sheaves on the affine Grassmannian, and construct a particular object in it, which we call the the semi-infinite intersection cohomology sheaf. We relate it to several other entities naturally appearing in the ... More

Clues to the nature of ultra diffuse galaxies from estimated galaxy velocity dispersionsSep 26 2016Oct 17 2016We describe how to estimate the velocity dispersions of ultra diffuse galaxies, UDGs, using a previously defined galaxy scaling relationship. The method is accurate for the two UDGs with spectroscopically measured dispersions, as well as for ultra compact ... More

Summary Statistics in Approximate Bayesian ComputationDec 17 2015This document is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) edited by S. Sisson, Y. Fan, and M. Beaumont. Since the earliest work on ABC, it has been recognised that using summary statistics is essential ... More

Adaptive Sensing Resource Allocation Over Multiple Hypothesis TestsOct 03 2014Nov 03 2014This paper considers multiple binary hypothesis tests with adaptive allocation of sensing resources from a shared budget over a small number of stages. A Bayesian formulation is provided for the multistage allocation problem of minimizing the sum of Bayes ... More

A Discontinuity Adjustment for Subdistribution Function Confidence Bands Applied to Right-Censored Competing Risks DataFeb 03 2017The wild bootstrap is the resampling method of choice in survival analytic applications. Theoretic justifications rely on the assumption of existing intensity functions which is equivalent to an exclusion of ties among the event times. However, such ties ... More

$\mathbb{Z}^2$-algebras as noncommutative blow-upsJan 02 2017Jul 31 2017The goal of this note is to first prove that for a well behaved $\mathbb{Z}^2$-algebra $R$, the category $QGr(R) := Gr(R)/Tors(R)$ is equivalent to $QGr(R_\Delta)$ where $R_\Delta$ is a diagonal-like sub-$\mathbb{Z}$-algebra of $R$. Afterwards we use ... More

Divisors on the moduli space of curves from divisorial conditions on hypersurfacesJan 31 2019In this note, we extend work of Farkas and Rim\'anyi on applying quadric rank loci to finding divisors of small slope on the moduli space of curves by instead considering all divisorial conditions on the hypersurfaces of a fixed degree containing a projective ... More

Unions of arcs from Fourier partial sumsFeb 03 2010Mar 03 2010Elementary complex analysis and Hilbert space methods show that a union of at most n arcs on the circle is uniquely determined by the nth Fourier partial sum of its characteristic function. The endpoints of the arcs can be recovered from the coefficients ... More

Lewis Carroll and the Red Hot PotatoMar 30 2018The Lewis Carroll identity expresses the determinant of a matrix in terms of subdeterminants obtained by deleting one row and column or a pair of rows and columns. Using the matrix tree theorem, we can convert this into an equivalent identity involving ... More

A note on $r$ hypersurfaces intersecting in $\mathbb{P}^r$Aug 05 2019We consider the locus of $r$-tuples of homogeneous forms of some fixed degree whose common vanishing locus in $\mathbb{P}^r$ is positive dimensional. We show that any component of maximal dimension of that locus either consists of homogeneous forms all ... More

On degenerate sections of vector bundlesMar 30 2017We consider the locus of sections of a vector bundle on a projective scheme that vanish in higher dimension than expected. We show that after applying a high enough twist, any maximal component of this locus consists entirely of sections vanishing along ... More

Contact Geometry of Hyperbolic Equations of Generic TypeApr 09 2008Aug 19 2008We study the contact geometry of scalar second order hyperbolic equations in the plane of generic type. Following a derivation of parametrized contact-invariants to distinguish Monge-Ampere (class 6-6), Goursat (class 6-7) and generic (class 7-7) hyperbolic ... More

Bootstrapping the Kaplan-Meier Estimator on the Whole LineMay 18 2016This article is concerned with proving the consistency of Efron's (1981) bootstrap for the Kaplan-Meier estimator on the whole support of a survival function. While other works address the asymptotic Gaussianity of the estimator itself without restricting ... More

A note on rational curves on general Fano hypersurfacesSep 27 2017Jan 31 2019We show the Kontsevich space of rational curves of degree at most roughly $\frac{2-\sqrt{2}}{2}n$ on a general hypersurface $X\subset \mathbb{P}^n$ of degree $n-1$ is equidimensional of expected dimension and has two components: one consisting generically ... More

Clues to the nature of ultra diffuse galaxies from estimated galaxy velocity dispersionsSep 26 2016We describe how to estimate the velocity dispersions of ultra diffuse galaxies, UDGs, using a previously defined galaxy scaling relationship. The method is accurate for the two UDGs with spectroscopically measured dispersions, as well as for ultra compact ... More

The excess formula in functorial formMay 01 2012This article is motivated by the need for better understanding of refined Riemann-Roch theorems and the behavior of the determinant of the cohomology. This poses a certain problem of functoriality and can be understood as that of giving refined constructions ... More

The club of simplicial setsJan 13 2010Dec 15 2010A club structure is defined on the category of simplicial sets. This club generalizes the operad of associative rings by adding "amalgamated" products.

Degenerating Riemann surfaces and the Quillen metricJun 15 2011The degeneration of the Quillen metric for a one-parameter family of Riemann surfaces has been studied by Bismut-Bost and Yoshikawa. In this article we propose a more geometric point of view using Deligne's Riemann-Roch theorem. We obtain an interpretation ... More

The Michelson-Morley experiment in an accelerated reference frameDec 15 2010We analyze the Michelson-Morley experiment in a reference frame moving with constant proper acceleration. Interestingly, we find an expected fringe shift which depends not only on the interferometer's rate of acceleration, but also on its speed relative ... More

Non-Markovian Beables vs. Massive ParallelismMar 16 2010A simple dynamical model over a discrete classical state space is presented. In a certain limit, it reduces to one in a class of models subsuming Bell's field-theoretic version of Bohmian mechanics. But it exhibits the massive parallelism native to quantum ... More

Construction of central elements in the affine Hecke algebra via nearby cyclesDec 09 1999Oct 27 2000Let $G$ be a reductive group, let $Gr=G((t))/G[[t]]$ be the corresponding affine Grassmannian and let $Fl=G((t))/I$ be the affine flag variety. We construct, following an idea of Belinson, a 1-parametric deformation of the product $Gr\times G/B$ to $Fl$. ... More

Notes on 2D Conformal Field Theory and String TheoryNov 09 1998May 27 1999We explain the basics of conformal theory using the language of chiral algebras of Beilinson and Drinfeld.

Contractibility of the space of rational mapsAug 08 2011Feb 23 2012We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space Bun(G) of G-bundles on X is uniformized ... More

Chiral Dynamics of the Polarizing Fracture Functions for Baryon ProductionNov 14 2008The concept of spin-directed momentum provides a useful and restrictive framework for describing dynamical mechanisms that can lead to single-spin observables. The value of this framework can be demonstrated by consideration of the polarizing fracture ... More

Algebra, Topology and Algebraic Topology of 3D Ideal FluidsOct 13 2010There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for incompressible ... More

Open and Closed String field theory interpreted in classical Algebraic TopologyFeb 26 2003There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined. ... More

A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian ExcursionsJul 22 2016Nov 21 2016This paper studies the excursion set of a real stationary isotropic Gaussian random field above a fixed level. We show that the standardized Lipschitz-Killing curvatures of the intersection of the excursion set with a window converges in distribution ... More

Lattice HydrodynamicsOct 31 2018Using the combinatorics of two interpenetrating face centered cubic lattices together with the part of calculus naturally encoded in combinatorial topology, we construct from first principles a lattice model of 3D incompressible hydrodynamics on triply ... More

Automatic structure estimation of predictive models for symptom developmentSep 12 2018Online mental health treatment has the premise to meet the increasing demand for mental health treatment at a lower cost than traditional treatment. However, online treatment suffers from high drop-out rates, which might negate their cost effectiveness. ... More

Parameterization of factorizable line bundles by K-theory and motivic cohomologyApr 07 2018Nov 12 2018This note corrects a certain construction in (the old version of) the paper [GL]. The construction in question starts from a Brylinski-Deligne datum, which is an extension of a group G by K_2, and produces a factorization line bundle on the affine Grassmannian ... More

A Constant-Factor Bi-Criteria Approximation Guarantee for $k$-means++May 16 2016This paper studies the $k$-means++ algorithm for clustering as well as the class of $D^\ell$ sampling algorithms to which $k$-means++ belongs. It is shown that for any constant factor $\beta > 1$, selecting $\beta k$ cluster centers by $D^\ell$ sampling ... More

Spin-Directed Momentum Transfers in SIDIS Baryon ProductionDec 08 2015The measurement of transverse single-spin asymmetries for baryon production in the target fragmentation region of semi-inclusive deep-inelastic scattering (SIDIS), can produce important insight into those nonperturbative aspects of QCD directly associated ... More

Direct Bootstrapping and Permuting of Observations fail for Aalen-Johansen EstimatorsAug 11 2014Dec 15 2014This article provides rigorous proofs that neither Efron's bootstrap nor permutation techniques can be applied directly to the observations to construct consistent resampling tests for transition probability matrices of finite-state Markov processes. ... More

gk: An R Package for the g-and-k and generalised g-and-h DistributionsJun 21 2017The g-and-k and (generalised) g-and-h distributions are flexible univariate distributions which can model highly skewed or heavy tailed data through only four parameters: location and scale, and two shape parameters influencing the skewness and kurtosis. ... More

The local and global versions of the Whittaker categoryNov 06 2018Jun 24 2019Given a category C acted on by the loop group G((t)), we define its Whittaker model Whit(C) as C^{N((t)),\chi}, where \chi is a non-degenerate character. We study the properties of this construction. When C is the category of sheaves on the quotient of ... More

A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian ExcursionsJul 22 2016Feb 20 2017This paper studies the excursion set of a real stationary isotropic Gaussian random field above a fixed level. We show that the standardized Lipschitz-Killing curvatures of the intersection of the excursion set with a window converges in distribution ... More

Arithmetically nef line bundlesJun 21 2018Let $L$ be a line bundle on a scheme $X$, proper over a field. The property of $L$ being nef can sometimes be "thickened", allowing reductions to positive characteristic. We call such line bundles arithmetically nef. It is known that a line bundle $L$ ... More

What is the higher dimensional infinitesimal groupoid of a manifold?Oct 29 2009The construction (by Kapranov) of the space of infinitesimal paths on a manifold is extended to include higher dimensional infinitesimal objects, encoding contractions of infinitesimal loops. This full infinitesimal groupoid is shown to have the algebra ... More

Space, Time and Coordinates in a Rotating WorldJan 31 2010The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than in the special ... More

Higher dimensional operadsSep 14 2009Dec 15 2010The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked subvarieties of arbitrary ... More

Functors given by kernels, adjunctions and dualityMar 12 2013Nov 24 2015Let X_1 and X_2 be schemes of finite type over a field of characteristic 0. Let Q be an object in the category D-mod(X_1\times X_2) and consider the functor F:D-mod(X_1)->Dmod(X_2) defined by Q. Assume that F admits a right adjoint also defined by an ... More

The notion of category over an algebraic stackJul 09 2005The goal of this note is to spell out the (apparently well-known and intuitively clear) notion of abelian category over an algebraic stack. In the future we will discuss the (much less evident) notion, when instead of an abelian category one considers ... More

Hilbert space compression for free products and HNN-extensionsFeb 22 2010Jul 06 2010Given the Hilbert space compression of two groups, we find bounds on the Hilbert space compression of their free product. We also investigate the Hilbert space compression of an HNN-extension of a group relative to a finite normal subgroup or a finite ... More

A Central Limit Theorem for Lipschitz-Killing Curvatures of Gaussian ExcursionsJul 22 2016This paper studies the excursion set of a real stationary isotropic Gaussian random field above a fixed level. We show that the standardized Lipschitz-Killing curvatures of the intersection of the excursion set with a window converges in distribution ... More

Quantum Number Density Asymmetries Within QCD Jets Correlated With Lambda PolarizationJun 20 2011Jul 27 2011The observation of jets in a variety of hard-scattering processes has allowed the quantitative study of perturbative quantum chromodynamics (PQCD) by comparing detailed theoretical predictions with a wide range of experimental data. This paper examines ... More

Coherent Spin Manipulations of a Polarized Beam With a Localized RF Magnetic FieldOct 12 2007The coherent manipulation of spin observables in storage rings provides opportunities to test the application of some fundamental dynamical principles. In this context, it is possible to confirm, using gauge invariance and Lorentz invariance, a conjecture ... More

Perturbed and Permuted: Signal Integration in Network-Structured Dynamic SystemsJun 23 2011Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding of the system ... More

Kane-Pumplin-Repko Factorization: its application to precision measurements of transverse spin asymmetries and to the study of TMD evolutionJul 22 2013This article presents a summary of overlapping presentations by the author to the QCD Evolution 2013 Workshop and to the Opportunities for Polarized Physics at Fermilab Workshop. It contains an introduction to the concept of Kane-Pumplin-Repko (KPR) factorization ... More

On hypercomplexifying real forms of arbitrary rankSep 28 2002For certain problems involving vector fields, it is possible to find an associated imaginary field that, in conjunction with the first, forms a complex field for which the equation can be solved. This result is generalized to arbitrary Clifford algebras, ... More

Control aspects of holonomic quantum computationFeb 10 2002Mar 27 2018A unifying framework for the control of quantum systems with non-Abelian holonomy is presented. It is shown that, from a control theoretic point of view, holonomic quantum computation can be treated as a control system evolving on a principal fiber bundle. ... More

Chow's theorem and universal holonomic quantum computationNov 14 2001Feb 11 2002A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra are presented ... More

Detection of Exoplanets Using the Transit MethodMar 15 2018Apr 20 2018I conducted differential photometry on a star GSC 3281-0800, a known host to exoplanet HAT-P-32b, using analysis software AstroImageJ. I plotted the measurements from a series of images taken during the transit, via ADU count given from an earth-based ... More

Some Comments on the Stochastic Eulerian Tour ProblemMar 13 2015The Stochastic Eulerian Tour Problem was introduced in 2008 as a stochastic variant of the well-known Eulerian Tour Problem. In a follow-up paper the same authors investigated some heuristics for solving the Stochastic Eulerian Tour Problem. After a thorough ... More

Recent progress in geometric Langlands theoryJun 30 2016Sep 10 2016The is the English version of the text of the talk at S\'eminaire Bourbaki on February 16, 2016

Von Neumann's Impossibility Proof: Mathematics in the Service of RhetoricsJan 28 2018According to what has become a standard history of quantum mechanics, in 1932 von Neumann persuaded the physics community that hidden variables are impossible as a matter of principle, after which leading proponents of the Copenhagen interpretation put ... More

Time Coordinates and Clocks: Einstein's StruggleJan 28 2018In his Autobiographical Notes, Einstein mentioned that on his road to the final theory of general relativity it was a major difficulty to accustom himself to the idea that coordinates need not possess an immediate physical meaning in terms of lengths ... More

Adapting the ABC distance functionJul 03 2015Dec 15 2015Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are close enough to ... More

Ideas in transverse spin physicsSep 08 2014Three simple ideas about transverse spin observables are presented for the purpose of stimulating discussion. The manuscript is based on a presentation at the "Transversity 2014" workshop in Torre Chia, Sardinia, Italy on June 9-13, 2014 where approximately ... More

Quantum Reality, Perspectivalism and CovarianceMay 13 2019Paul Busch has emphasized on various occasions the importance for physics of going beyond a merely instrumentalist view of quantum mechanics. Even if we cannot be sure that any particular realist interpretation describes the world as it actually is, the ... More

Variational Bayesian hierarchical regression for data analysisNov 08 2018Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived results and prediction ... More

Exceptionally simple PDEMar 27 2016Sep 29 2016We give local descriptions of parabolic contact structures and show how their flat models yield explicit PDE having symmetry algebras isomorphic to all complex simple Lie algebras except $\mathfrak{sl}_2$. This yields a remarkably uniform generalization ... More

Invariant Yang-Mills connections over Non-Reductive Pseudo-Riemannian Homogeneous SpacesOct 09 2007Apr 17 2008We study invariant gauge fields over the 4-dimensional non-reductive pseudo-Riemannian homogeneous spaces G/K recently classified by Fels & Renner (2006). Given H compact semi-simple, classification results are obtained for principal H-bundles over G/K ... More

On two relaxations of quadratically-constrained cardinality minimizationOct 18 2012This paper considers a quadratically-constrained cardinality minimization problem with applications to digital filter design, subset selection for linear regression, and portfolio selection. Two relaxations are investigated: the continuous relaxation ... More

Regularity for a Local-Nonlocal Transmission ProblemApr 04 2014Jan 31 2015We formulate and study an elliptic transmission-like problem combining local and nonlocal elements. Let $\mathbb{R}^{n}$ be separated into two components by a smooth hypersurface $\Gamma$. On one side of $\Gamma$, a function satisfies a local second-order ... More

Ind-coherent sheavesMay 24 2011Sep 22 2012We develop the theory of ind-coherent sheaves on schemes and stacks. The category of ind-coherent sheaves is closely related, but inequivalent, to the category of quasi-coherent sheaves, and the difference becomes crucial for the formulation of the categorical ... More

The Fractured Boer-Mulders Effect in the Production of Polarized BaryonsOct 28 2009The fractured Boer-Mulders functions describe an inriguing class of polarization effects for the production of baryons in the target fragmentation region of deep-inelastic processes. These functions characterize transverse momentum asymmetries related ... More

Single-Spin Observables and Orbital Structures in Hadronic DistributionsSep 07 2006Within the light-quark sector of the standard model, P-odd observables are generated from point-like electroweak processes while A_t- odd observables (neglecting quark mass parameters) come from dynamic spin-orbit correlations within hadrons or within ... More

Discriminants and Artin conductorsJun 15 2011We study questions of multiplicities of discriminants for degenerations coming from projective duality over discrete valuation rings. The main result is a type of discriminant-different formula in the sense of classical algebraic number theory, and we ... More

Implications and Applications of Kinematic Galaxy Scaling RelationsSep 19 2012Galaxy scaling relations, which describe a connection between ostensibly unrelated physical characteristics of galaxies, testify to an underlying order in galaxy formation that requires understanding. I review the development of a scaling relation that ... More

Twisted Whittaker model and factorizable sheavesMay 31 2007Mar 27 2008Let G be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group ^LG in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian Gr_G=G((t))/G[[t]] of the original group ... More

Grothendieck topologies and deformation theory IIAug 08 1995This paper is a continuation of ``Operads, Grothendieck topologies and deformation theory'' (alg-geom/9502010). We show how to develop a cohomology theory that would control deformations of a sheaf of associative algebras over a scheme by means of introducing ... More

A finite time blowup result for quadratic ODE'sNov 01 2010This short paper is dedicated to Mauricio Peixoto who abstracted the practical theory of ODE's and to David Rand who applied the subsequent powerful abstract theory to practical problems.

A Free Boundary Problem Related to Thermal Insulation: Flat Implies SmoothNov 18 2015We show that for a new free boundary problem studied by Caffarelli and the author, the interface is locally the union of the graphs of two $C^{1,\alpha}$ functions at most points. Specifically, this happens at all points where the interface is trapped ... More

$C^{1,α}$ Interior Regularity for Nonlinear Nonlocal Elliptic Equations With Rough KernelsApr 28 2013We prove a $C^{1,\alpha}$ interior regularity theorem for fully nonlinear uniformly elliptic integro-differential equations without assuming any regularity of the kernel. We then give some applications to linear theory and higher regularity of a special ... More

The Atiyah-Bott formula for the cohomology of the moduli space of bundles on a curveMay 10 2015This paper is a companion of the paper "Weil's conjecture for function fields" by J. Lurie and the author. We present a different exposition of essentially the same algebro-geometric proof of the Atiyah-Bott for the cohomology of Bun(G), which subsequently ... More

Shape/Phase Transitions and Critical Point Symmetries in Atomic NucleiJul 28 2008Shape/phase transitions in atomic nuclei have first been discovered in the framework of the Interacting Boson Approximation (IBA) model. Critical point symmetries appropriate for nuclei at the transition points have been introduced as special solutions ... More

Derived manifolds and Kuranishi modelsDec 05 2012Jan 12 2014A model structure is defined on the category of derived differentiable schemes, and it is used to analyse the truncation 2-functor from derived manifolds to d-manifolds. It is proved that the induced 1-functor between the homotopy categories is full and ... More

The Logic of Identity: Distinguishability and Indistinguishability in Classical and Quantum PhysicsMay 13 2014The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical statistical mechanics. ... More

The Atiyah-Bott formula for the cohomology of the moduli space of bundles on a curveMay 10 2015Jun 24 2019This paper is a companion of the paper "Weil's conjecture for function fields" by J. Lurie and the author. We present a different exposition of essentially the same algebro-geometric proof of the Atiyah-Bott for the cohomology of Bun(G), which subsequently ... More

Lazier ABCJan 21 2015ABC algorithms involve a large number of simulations from the model of interest, which can be very computationally costly. This paper summarises the lazy ABC algorithm of Prangle (2015), which reduces the computational demand by abandoning many unpromising ... More

Eisenstein series and quantum groupsMay 10 2015May 23 2016We sketch a proof of a conjecture of [FFKM] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum group.

Pure Spinor String and Generalized GeometryJun 13 2019We consider the pure spinor sigma model in an arbitrary curved background. The use of Hamiltonian formalism allows for a uniform description of the worldsheet fields where matter and ghosts enter the action on the same footing. This approach naturally ... More

Field-Strength Descriptions for a System of Classical SU(2) Charges with Spherical Symmetry and Confining Boundary ConditionsFeb 01 2019The existence of a mechanism within the non-Abelian dynamics of QCD that confines quarks and gluons to the interior of hadrons has long been accepted empirically. To explore what this mechanism might look like, this paper examines field-strength descriptions ... More

Prolate over oblate dominance in deformed nuclei as a consequence of the SU(3) symmetry and the Pauli principleJul 12 2017We show that the dominance of prolate over oblate shapes in even-even deformed nuclei can be derived from the SU(3) symmetry and the Pauli principle.

On the Chow Ring of the Stack of truncated Barsotti-Tate GroupsNov 27 2016We determine the Chow ring of the stack of truncated displays and more generally the Chow ring of the stack of G-zips. We also investigate the pull-back morphism of the truncated display functor. From this we can determine the Chow ring of the stack of ... More