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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

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.

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

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

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

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

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

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

Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programsMar 05 2008We interpret mathematically the pair (master equation, solution of master equation) up to equivalence, as the pair (a presentation of a free triangular dga T over a combination operad O, dga map of T into C, a dga over O) up to homotopy equivalence of ... 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

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

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

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

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

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

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

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

Dust and Stellar Populations in the Large Magellanic CloudAug 31 1999We present an analysis of line-of-sight extinction measurements obtained using data from the Magellanic Clouds Photometric Survey, which provides 4-filter photometry for millions of stars in the Large Magellanic Cloud. We find that visual extinctions ... More

The Mass and Extent of the Galactic HaloOct 05 1998We review the various techniques used to constrain the Galactic halo mass profile for radii > 20 kpc with particular emphasis on identifying a self-consistent halo model and resolving the apparent discrepancies present in the literature on this subject. ... More

Evidence For Recent Accretion in Nearby GalaxiesMay 11 1995I discuss observations of magnitude residuals from the B-band Tully-Fisher relationship, B-V color, chemical abundance gradients, and asymmetries in the H I and stellar disks of nearby spiral galaxies within the context of a model in which small satellites ... More

The Case of the Off-Center, Levitating Bar in the Large Magellanic CloudAug 28 2004I explore the hypothesis that many of the unusual aspects of the apparent stellar bar of the Large Magellanic Cloud are the result of viewing a triaxial stellar bulge that is embedded in a highly obscuring thin disk. Specifically, this hypothesis explains ... More

Topological characterization of various types of rings of smooth functionsAug 30 2011Oct 02 2011Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative algebra morphism ... More

Is There a Unique Physical Entropy? Micro versus MacroSep 05 2012Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical mechanics should ... More

On the dynamic nature of charge quantizationDec 29 2011It is commonly observed that objects in a gravitational field experience a rate of acceleration that is independent of their mass and that, as a result, all massive objects with the same initial conditions follow the same trajectory. It is not generally ... More

Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDESep 07 2010Of all real Lagrangian--Grassmannians $LG(n,2n)$, only $LG(2,4)$ admits a distinguished (Lorentzian) conformal structure and hence is identified with the indefinite M\"obius space $S^{1,2}$. Using Cartan's method of moving frames, we study hyperbolic ... More

Comment on "Harold Jeffreys's Theory of Probability Revisited"Jan 18 2010Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]

A Deligne-Riemann-Roch isomorphism I: Preliminaries on virtual categoriesApr 26 2009This is the first article in an upcoming series of papers. They have arisen through an attempt to answer open questions of Deligne proposed in "Le determinant de la cohomologie", Contemp. Mathematics 67 (1987). It amounts to functorial and metrized versions ... More

Outline of the proof of the geometric Langlands conjecture for GL(2)Feb 11 2013Nov 12 2014We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.

On de Jong's conjectureFeb 11 2004Apr 01 2006Let $X$ be a smooth projective curve over a finite field $F_q$. Let $\rho$ be a continuous representation $\pi(X)\to GL_n(F)$, where $F=F_l((t))$ with $F_l$ being another finite field of order prime to $q$. Assume that $\rho|_{\pi(\bar{X})}$ is irreducible. ... More

Hilbert space compression under direct limits and certain group extensionsSep 10 2010Sep 14 2010We find bounds on the Hilbert space compression of the limit of a directed metric system of groups. We also give estimates on the Hilbert space compression of group extensions of a group $H$ by a a word-hyperbolic group or a group of polynomial growth. ... More

Generalized Nonaveraging Integer SequencesJul 09 2011Let the sequence S_m of nonnegative integers be generated by the following conditions: Set the first term a_0 = 0, and for all k \geq 0, let a_k+1 be the least integer greater than a_k such that no element of {a_0,...,a_k+1} is the average of m - 1 distinct ... More

How Bandwidth Affects the $CONGEST$ ModelApr 20 2017The $CONGEST$ model for distributed network computing is well suited for analyzing the impact of limiting the throughput of a network on its capacity to solve tasks efficiently. For many "global" problems there exists a lower bound of $\Omega(D + \sqrt{n/B})$, ... More

On the Chow Ring of the Classifying Space of some Chevalley GroupsNov 23 2016Let $p$ be a prime and $q$ be a power of $p$. We compute the Chow ring of the classifying space of some Chevalley groups $G(\mathbb{F}_q)$, when considered as a finite algebraic group over a field of characteristic $p$ containing $\mathbb{F}_q$. Using ... More

Lazy ABCMay 30 2014Dec 04 2014Approximate Bayesian computation (ABC) performs statistical inference for otherwise intractable probability models by accepting parameter proposals when corresponding simulated datasets are sufficiently close to the observations. Producing the large quantity ... More

DBI analog of a decaying vacuum cosmologyJul 03 2013Jul 04 2013In this work I discuss the dynamical and thermodynamical equivalence between a general k-essence scalar field cosmology and an arbitrary cosmological model with a decaying vacuum, thus generalizing the approach proposed by Maia and Lima [Phys. Rev. D ... More

A conjectural extension of the Kazhdan-Lusztig equivalenceOct 22 2018Nov 12 2018A theorem of Kazhdan and Lusztig establishes an equivalence between the category of G(CO)-integrable representations of the Kac-Moody algebra \hat{g}_{-\kappa} at a negative level -\kappa and the category \Rep_q(G) of (algebraic) representations of the ... More

Quantum Mechanics and PerspectivalismJan 28 2018Jan 06 2019Experimental evidene of the last decades has made the status of "collapses of the wave function" even more shaky than it already was on conceptual grounds: interference effects turn out to be detectable even when collapses are typically expected to occur. ... More

Coresets for $(k,l)$-Clustering under the Fréchet DistanceJan 07 2019Feb 19 2019Clustering is the task of partitioning a given set of geometric objects. This is thoroughly studied when the objects are points in the euclidean space. There are also several approaches for points in general metric spaces. In this thesis we consider clustering ... More

Centrality and transverse momentum dependence of $J/ψ$ production in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV at mid-rapidity with ALICEOct 16 2017We present new results for the nuclear modification factor \RAA of \jpsi mesons as a function of centrality and transverse momentum at mid-rapidity. The measurement is carried out with the ALICE central barrel detectors in the acceptance range $|y|$ < ... More

General Relativity as a Hybrid theory: The Genesis of Einstein's work on the problem of motionMar 27 2018In this paper I describe the genesis of Einstein's early work on the problem of motion in general relativity (GR): the question of whether the motion of matter subject to gravity can be derived directly from the Einstein field equations. In addressing ... More

String Topology: Background and Present StateOct 22 2007The data of a "2D field theory with a closed string compactification" is an equivariant chain level action of a cell decomposition of the union of all moduli spaces of punctured Riemann surfaces with each component compactified as a pseudomanifold with ... More

Binomial Andrews-Gordon-Bressoud identitiesAug 03 2016Binomial versions of the Andrews-Gordon-Bressoud identities are given.

Collections of hypersurfaces containing a curveFeb 21 2017Jun 28 2018We consider the closed locus of $r$-tuples of hypersurfaces in $\mathbb{P}^r$ with positive dimensional intersection, and show in a large range of degrees that its largest component is the locus of $r$-tuples of hypersurfaces whose intersection contains ... More

A Free Boundary Problem Related to Thermal Insulation: Flat Implies SmoothNov 18 2015Sep 05 2017We study the regularity of the interface for a new free boundary problem introduced by Caffarelli and Kriventsov. We show that for minimizers of the functional \[ F_1(A,u) = \int_A |\nabla u|^2 d\mathcal{L}^n + \int_{\partial A} u^2 + \bar{C} \mathcal{L}^n(A) ... 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

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

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

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.

$C^{1,α}$ 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 semi-infinite intersection cohomology sheaf-II: the Ran space versionAug 23 2017Nov 12 2018This paper is a sequel to [Ga1]. We study the semi-infinite category on the Ran version of the affine Grassmannian, and study a particular object in it that we call the semi-infinite intersection cohomology sheaf. Unlike the situation of [Ga1], this version ... More

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

Quantum optimal control via gradient ascent in function space and the time-bandwidth quantum speed limitNov 01 2016Apr 03 2018A gradient ascent method for optimal quantum control synthesis is presented that employs a gradient derived with respect to the coefficients of a functional basis expansion of the control. Restricting the space of allowable controls to weighted sums of ... More

From geometric to function-theoretic Langlands (or how to invent shtukas)Jun 30 2016This is an informal note that explains that the classical Langlands theory over function fields can be obtained from the geometric one by taking the trace of Frobenius. The operation of taking the trace of Frobenius takes place at the categorical level, ... More

Quantum Langlands CorrespondenceJan 20 2016These are informal notes written in 2007 that outline the local and global quantum Langlands program. (I decided to make them public in view of the revived interest in the subject.)

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

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

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.

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

Symmetric noncommutative birational transformationsJul 28 2016In a previous paper (arXiv:1410.5207) certain birational transformations were constructed between the noncommutative schemes associated to quadratic and cubic three dimensional Sklyanin algebras. In the current paper we consider the inverse birational ... More

Measures on polyhedral cones: characterizations and kinematic formulasDec 04 2014Jul 29 2015This paper is about conic intrinsic volumes and their associated integral geometry. We pay special attention to the biconic localizations of the conic intrinsic volumes, the so-called support measures. An analysis of these quantities has so far been confined ... More

The AJ-conjecture and cabled knots over the figure eight knotMay 15 2014Apr 15 2015We show that most cabled knots over the figure eight knot in $S^3$ satisfy the AJ-conjecture, in particular, any $(r,s)$-cabled knot over the figure eight knot satisfies the $AJ$-conjecture if $r$ is not a number between $-4s$ and $4s$.

Complete families of immersed curvesNov 01 2017Jan 31 2019We extend results of Chang and Ran regarding large dimensional families of immersed curves of positive genus in projective space in two directions. In one direction, we prove a sharp bound for the dimension of a complete family of smooth rational curves ... 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

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