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Heart of Darkness: dust obscuration of the central stellar component in globular clusters younger than ~100Myr in multiple stellar population modelsJan 06 2015To explain the observed anomalies in stellar populations within globular clusters, many globular cluster formation theories require two independent episodes of star formation. A fundamental prediction of these models is that the clusters must accumulate ... More

Maser Source Finding Methods in HOPSNov 24 2011The {\bf H}$_2${\bf O} Southern Galactic {\bf P}lane {\bf S}urvey (HOPS) has observed 100 square degrees of the Galactic plane, using the Mopra radio telescope to search for emission from multiple spectral lines in the 12\,mm band (19.5\,--\,27.5\,GHz). ... More

Molecular gas in the inner 500pc of the MilkyWay: violating star formation relations and on the verge of forming extreme stellar clustersNov 06 2012With the HOPS, MALT90 and HiGAL Galactic plane surveys we are mapping a significant fraction of the dense, star-forming, molecular gas in the Galaxy. I present results from two projects based on this combined dataset, namely, (i) looking for variations ... More

The Simultaneous Formation of Massive Stars and Stellar ClustersAug 26 2009We show that massive stars and stellar clusters are formed simultaneously, the global evolution of the forming cluster is what allows the central stars to become massive. We predict that massive star forming clumps, such as those observed in Motte et ... More

Star Formation Rates of Massive Molecular Clouds in the Central Molecular ZoneJan 23 2019Feb 21 2019We investigate star formation at very early evolutionary phases in five massive clouds in the inner 500 pc of the Galaxy, the Central Molecular Zone. Using interferometer observations of H$_2$O masers and ultra-compact H II regions, we find evidence of ... More

Accurate water maser positions from HOPSMay 16 2014We report on high spatial resolution water maser observations, using the Australia Telescope Compact Array, towards water maser sites previously identified in the H2O southern Galactic Plane Survey (HOPS). Of the 540 masers identified in the single-dish ... More

The implications of clustered star formation for (proto)planetary systems and habitabilityJan 14 2019Star formation is spatially clustered across a range of environments, from dense stellar clusters to unbound associations. As a result, radiative or dynamical interactions with neighbouring stars disrupt (proto)planetary systems and limit their radii, ... More

An uncertainty principle for star formation. I. Why galactic star formation relations break down below a certain spatial scaleJan 17 2014Galactic scaling relations between the (surface densities of) the gas mass and the star formation (SF) rate are known to develop substantial scatter or even change form when considered below a certain spatial scale. We quantify how this behaviour should ... More

Comparing molecular gas across cosmic time-scales: the Milky Way as both a typical spiral galaxy and a high-redshift galaxy analogueSep 02 2013Detailed observations of the nearest star-forming regions in the Milky Way (MW) provide the ultimate benchmark for studying star formation. The extent to which the results of these Galaxy-based studies can be extrapolated to extragalactic systems depends ... More

The dynamical evolution of molecular clouds near the Galactic Centre - I. Orbital structure and evolutionary timelineDec 01 2014We recently proposed that the star-forming potential of dense molecular clouds in the Central Molecular Zone (CMZ, i.e. the central few 100 pc) of the Milky Way is linked to their orbital dynamics, potentially giving rise to an absolute-time sequence ... More

The Molecular Gas Environment in the 20 km s$^{-1}$ Cloud in the Central Molecular ZoneMar 20 2017We recently reported a population of protostellar candidates in the 20 km s$^{-1}$ cloud in the Central Molecular Zone of the Milky Way, traced by H$_2$O masers in gravitationally bound dense cores. In this paper, we report high-angular-resolution ($\sim$3'') ... More

Understanding hydrogen recombination line observations with ALMA and EVLAJun 29 2012Hydrogen recombination lines are one of the major diagnostics of H II region physical properties and kinematics. In the near future, the Expanded Very Large Array (EVLA) and the Atacama Large Millimeter Array (ALMA) will allow observers to study recombination ... More

Is protostellar heating sufficient to halt fragmentation? A case study of the massive protocluster G8.68-0.37Nov 05 2010If star formation proceeds by thermal fragmentation and the subsequent gravitational collapse of the individual fragments, how is it possible to form fragments massive enough for O and B stars in a typical star-forming molecular cloud where the Jeans ... More

Star formation rates on global and cloud scales within the Galactic CentreSep 27 2016The environment within the inner few hundred parsecs of the Milky Way, known as the "Central Molecular Zone" (CMZ), harbours densities and pressures orders of magnitude higher than the Galactic Disc; akin to that at the peak of cosmic star formation (Kruijssen ... More

A search for High Mass Stars Forming in Isolation using CORNISH & ATLASGALNov 07 2015Theoretical models of high mass star formation lie between two extreme scenarios. At one extreme, all the mass comes from an initially gravitationally-bound core. At the other extreme, the majority of the mass comes from cluster scale gas, which lies ... More

How to Find Young Massive Cluster ProgenitorsAug 16 2012Aug 22 2012We propose that bound, young massive stellar clusters form from dense clouds that have escape speeds greater than the sound speed in photo-ionized gas. In these clumps, radiative feedback in the form of gas ionization is bottled up, enabling star formation ... More

Astro2020 Science White Paper: What is the lifecycle of gas and stars in galaxy centers?Mar 11 2019The closest galaxy center, our own Central Molecular Zone (CMZ; the central 500 pc of the Milky Way), is a powerful laboratory for studying the secular processes that shape galaxies across cosmic time, from large-scale gas flows and star formation to ... More

EVLA Observations of the Barnard 5 Star-Forming Core: Embedded Filaments RevealedJun 27 2011We present a ~6.5'x8' Expanded Very Large Array (EVLA) mosaic observations of the NH3 (1,1) emission in the Barnard 5 region in Perseus, with an angular resolution of 6". This map covers the coherent region, where the dense gas presents subsonic non-thermal ... More

What controls star formation in the central 500 pc of the Galaxy?Mar 25 2013Mar 12 2014The star formation rate (SFR) in the Central Molecular Zone (CMZ, i.e. the central 500 pc) of the Milky Way is lower by a factor of >10 than expected for the substantial amount of dense gas it contains, which challenges current star formation theories. ... More

Ionised gas kinematics in bipolar H II regionsMay 01 2018Stellar feedback plays a fundamental role in shaping the evolution of galaxies. Here we explore the use of ionised gas kinematics in young, bipolar H II regions as a probe of early feedback in these star-forming environments. We have undertaken a multiwavelength ... More

Pilot Observations for MALT-45: A Galactic Plane Survey at 7mmNov 05 2012We introduce the MALT-45 (Millimetre Astronomer's Legacy Team - 45 GHz) Galactic plane survey and describe pilot survey results with the Australia Telescope Compact Array (ATCA). The pilot survey was conducted to test the instrumentation and observational ... More

An uncertainty principle for star formation - II. A new method for characterising the cloud-scale physics of star formation and feedback across cosmic historyApr 30 2018Sep 04 2018The cloud-scale physics of star formation and feedback represent the main uncertainty in galaxy formation studies. Progress is hampered by the limited empirical constraints outside the restricted environment of the Local Group. In particular, the poorly-quantified ... More

Deeply Embedded Protostellar Population in the Central Molecular Zone Suggested by H$_2$O Masers and Dense CoresSep 27 2016The Central Molecular Zone (CMZ), usually referring to the inner 500 pc of the Galaxy, contains a dozen of massive ($\sim10^5$ $M_\odot$) molecular clouds. Are these clouds going to actively form stars like Sgr B2? How are they affected by the extreme ... More

Excitation Conditions in the Multi-component Submillimeter Galaxy SMM J00266+1708Nov 03 2014We present multiline CO observations of the complex submillimeter galaxy SMM J00266+1708. Using the Zpectrometer on the Green Bank Telescope, we provide the first precise spectroscopic measurement of its redshift (z=2.742). Based on followup CO(1-0), ... More

An uncertainty principle for star formation - IV. On the nature and filtering of diffuse emissionOct 26 2018Diffuse emission is observed in galaxies in many tracers across the electromagnetic spectrum, including tracers of star formation, such as H$\alpha$ and ultraviolet (UV), and tracers of gas mass, such as carbon monoxide (CO) transition lines and the 21-cm ... More

Deeply Embedded Protostellar Population in the 20 km s-1 Cloud of the Central Molecular ZoneOct 16 2015We report the discovery of a population of deeply embedded protostellar candidates in the 20 km s$^{-1}$ cloud, one of the massive molecular clouds in the Central Molecular Zone (CMZ) of the Milky Way, using interferometric submillimeter continuum and ... More

Star Formation Rates of Massive Molecular Clouds in the Central Molecular ZoneJan 23 2019We investigate star formation at very early evolutionary phases in five massive clouds in the inner 500 pc of the Galaxy, the Central Molecular Zone. Using interferometer observations of H$_2$O masers and ultra-compact H II regions, we find evidence of ... More

Using young massive star clusters to understand star formation and feedback in high-redshift-like environmentsJan 11 2016The formation environment of stars in massive stellar clusters is similar to the environment of stars forming in galaxies at a redshift of 1 - 3, at the peak star formation rate density of the Universe. As massive clusters are still forming at the present ... More

G337.342-0.119 (the "Pebble"): A Cold, Dense, High-Mass Molecular Cloud with Unusually Large Linewidths and a Candidate High-Mass Star Cluster ProgenitorNov 14 2018Nov 16 2018Exactly how high-mass star clusters form, especially the young massive clusters (YMCs: age $<100$ Myr; mass $>10^4$ solar masses), remains an open problem, largely because they are so rare that examples of their cold, dense, molecuar progenitors remain ... More

The Formation and Early Evolution of Young Massive ClustersJan 16 2014We review the formation and early evolution of the most massive and dense young stellar clusters, focusing on the role they can play in our understanding of star and planet formation as a whole. Young massive cluster (YMC) progenitor clouds in the Galactic ... More

An uncertainty principle for star formation - III. The characteristic emission time-scales of star formation rate tracersOct 25 2018We recently presented a new statistical method to constrain the physics of star formation and feedback on the cloud scale. Fundamentally, this new method is only able to recover the relative durations of different evolutionary phases. It therefore requires ... More

Reproducible $k$-means clustering in galaxy feature data from the GAMA surveyOct 01 2018A fundamental bimodality of galaxies in the local Universe is apparent in many of the features used to describe them. Multiple sub-populations exist within this framework, each representing galaxies following distinct evolutionary pathways. Accurately ... More

A Pilot Survey for the H$_2$O Southern Galactic Plane Survey (HOPS)Apr 25 2008We describe observations with the Mopra radiotelescope designed to assess the feasibility of the H$_2$O maser southern Galactic plane survey (HOPS). We mapped two one-square-degree regions along the Galactic plane using the new 12 mm receiver and the ... More

Flavour Democracy in Strong UnificationApr 29 1998We show that the fermion mass spectrum may naturally be understood in terms of flavour democratic fixed points in supersymmetric theories which have a large domain of attraction in the presence of "strong unification". Our approach provides an alternative ... More

Reliability of swarming algorithms for mobile sensor network applicationsSep 24 2012There are many well-studied swarming algorithms which are often suited to very specific purposes. As mobile sensor networks become increasingly complex, and are comprised of more and more agents, it makes sense to consider swarming algorithms for movement ... More

Supermatrix Representations of Semigroup BandsSep 19 1996Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups ... More

Six-dimensional Methods for Four-dimensional Conformal Field Theories II: Irreducible FieldsSep 20 2012Sep 29 2012This note supplements an earlier paper on conformal field theories. There it was shown how to construct tensor, spinor, and spinor-tensor primary fields in four dimensions from their counterparts in six dimensions, where conformal transformations act ... More

Effective Field Theories in the Large $N$ LimitJun 06 1997Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number $N$ of fields of some type becomes large. These include extended versions of the U(N) Gross-Neveu model, the non-linear O(N) $\sigma$-model, ... More

Theories of the Cosmological ConstantOct 07 1996This is a talk given at the conference ``Critical Dialogues in Cosmology'' at Princeton University, June 24-- 27, 1996. It gives a brief summary of our present theoretical understanding regarding the value of the cosmological constant, and describes how ... More

Effective Action and Renormalization Group Flow of Anisotropic SuperconductorsJun 27 1993We calculate the effective action of a superconductor, without assuming that either the electron-electron potential or the Fermi surface obey rotational invariance. This approach leads to the same gap equation and equilibrium free energy as more conventional ... More

Pions in Large-$N$ Quantum ChromodynamicsSep 08 2010Dec 14 2010An effective field theory of quarks, gluons, and pions, with the number $N$ of colors treated as large, is proposed as a basis for calculations of hadronic phenomena at moderate energies. The qualitative consequences of the large $N$ limit are similar ... More

Living with InfinitiesMar 03 2009Apr 21 2009This is the written version of a talk given in memory of Gunnar K\"{a}ll\'{e}n, at the Departments of Theoretical Physics, Physics, and Astronomy of Lund University on February 13, 2009. It will be published in a collection of the papers of Gunnar K\"{a}ll\'{e}n, ... More

Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?May 24 2006Jun 22 2006This is a sequel to a previous detailed study of quantum corrections to cosmological correlations. It was found there that except in special cases these corrections depend on the whole history of inflation, not just on the behavior of fields at horizon ... More

Cosmological Fluctuations of Short WavelengthJul 18 2002This paper presents a completely analytic treatment of cosmological fluctuations whose wavelength is small enough to come within the horizon well before the energy densities of matter and radiation become equal. This analysis yields a simple formula for ... More

Making High T$_c$ Higher: A Theoretical ProposalSep 09 2001There is considerable evidence that the highest $T_c$ obtainable in a copper-oxide plane is limitted by the competition between two effects: On the one hand, as the concentration of doped-holes, $ x$, is increased, the pairing scale, which is related ... More

Using the D1D5 CFT to Understand Black HolesDec 01 2010In this dissertation, we review work presented in arXiv:0906.2015, arXiv:0907.1663, arXiv:1002.3132, arXiv:1003.2746, and arXiv:1007.2202 on the D1D5 system. We begin with some motivational material for black holes in string theory. In Chapter 2, we review ... More

Elementary development of the gravitational self-forceAug 31 2009The gravitational field of a particle of small mass $\mu$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(\mu)$. One part is an ... More

ProofPeer - A Cloud-based Interactive Theorem Proving SystemJan 02 2012ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented as a solution ... More

Idempotents and Nilpotents Modulo nMay 01 2006We study asymptotic properties of periods and transient phases associated with modular power sequences. The latter are simple; the former are vaguely related to the reciprocal sum of square-free integer kernels.

Lectures in (2+1)-Dimensional GravityMar 14 1995Mar 18 1995These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of the classical ... More

PhonologyApr 11 2002Phonology is the systematic study of the sounds used in language, their internal structure, and their composition into syllables, words and phrases. Computational phonology is the application of formal and computational techniques to the representation ... More

The 21 Centimeter ForestApr 10 2006We examine the prospects for studying the pre-reionization intergalactic medium (IGM) through the so-called 21 cm forest in spectra of bright high-redshift radio sources. We first compute the evolution of the mean optical depth for models that include ... More

A Mass Partition Problem Related to Equivariant Sections of Stiefel BundlesNov 08 2010Jun 19 2012We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of m mass distributions on R^n, the existence of k linearly independent regular q-fans, each of which equipartitions ... More

Gauge theory of gravity and matterAug 08 2014It is shown how to write the first order action for gravity in a gauge theoretic formalism where the spin connection and frame field degrees of freedom are assimilated together into a gauge connection. It is then shown how to couple the theory to spin-0, ... More

Philosophical Solution to P=?NP: P is Equal to NPMar 19 2016The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a scientific rather ... More

Measure Partitions via Fourier Analysis II: Center Transversality in the $L^2$-norm for Complex HyperplanesJun 22 2015Sep 13 2015Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms. Considering the ... More

A Ham Sandwich Analogue for Quaternionic Measures and Finite Subgroups of S^3Sep 29 2010Sep 03 2011A "ham sandwich" theorem is established for n quaternionic Borel measures on quaternionic space H^n. For each finite subgroup G of S^3, it is shown that there is a quaternionic hyperplane H and a corresponding tiling of H^n into |G| fundamental regions ... More

From the Ham Sandwich to the Pizza Pie: A Simultaneous Z_m Equipartition of Complex MeasuresJun 23 2010Sep 03 2011A "ham sandwich" theorem is derived for n complex Borel measures on C^n. For each integer m>=2, it shown that there exists a regular m-fan centered about a complex hyperplane, satisfying the condition that for each complex measure, the "Z_m rotational ... More

A review of Dan's reduction method for multiple polylogarithmsMar 11 2017In this paper we will give an account of Dan's reduction method for reducing the weight $ n $ multiple logarithm $ I_{1,1,\ldots,1}(x_1, x_2, \ldots, x_n) $ to an explicit sum of lower depth multiple polylogarithms in $ \leq n - 2 $ variables. We provide ... More

On Arthur's Φ-FunctionMar 24 2005Write $\Theta^E$ for the stable character associated to a finite dimensional representation $E$ of a connected real reductive group $G$. Let $M$ be the centralizer of a maximal torus $T$, and denote by $\Phi_M(\gm,\Theta^E)$ Arthur's extension of $ |D_M^G(\gm)|^{\half} ... More

Stably Newton non-degenerate singularitiesJun 02 2014Jan 28 2015We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. The answer is negative. The easiest example can be given in characteristic $p$: the function $x^p$ is not stably equivalent ... More

Lower Bounds for Cubical PseudomanifoldsSep 30 2009Apr 02 2011It is verified that the number of vertices in a $d$-dimensional cubical pseudomanifold is at least $2^{d+1}$. Using Adin's cubical $h$-vector, the generalized lower bound conjecture is established for all cubical 4-spheres, as well as for some special ... More

Degenerations of elliptic curves and cusp singularitiesDec 21 1995We give more or less explicit equations for all two-dimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein's equations for universal curves with level n structure. The main technical result is a description ... More

No Quantum Brooks' TheoremNov 27 2014First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be described as ... More

Non-uniform covering array with symmetric forbidden edge constraintsJan 08 2019It has been conjectured that whenever an optimal covering array exists there is also a uniform covering array with the same parameters and this is true for all known optimal covering arrays. When used as a test suite, the application context may have ... More

Non-embeddable 1-convex manifoldsSep 27 2012Nov 11 2013We show that every small resolution of a three-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve ... More

Quartic and Octic Characters Modulo nJul 28 2009Mar 25 2016The average number of primitive quadratic Dirichlet characters of modulus n tends to a constant as n->infty. The same is true for primitive cubic characters. It is therefore surprising that, as n->infty, the average number of primitive quartic characters ... More

Idempotents and Nilpotents Modulo nMay 01 2006Nov 18 2017We study asymptotic properties of periods and transient phases associated with modular power sequences. The latter are simple; the former are vaguely related to the reciprocal sum of square-free integer kernels.

Topological complexity of n points on a treeJul 27 2016Jan 24 2018The topological complexity of a path-connected space $X,$ denoted $TC(X),$ can be thought of as the minimum number of continuous rules needed to describe how to move from one point in $X$ to another. The space $X$ is often interpreted as a configuration ... More

On the Descending Central Series of Higher Commutators for Simple AlgebrasDec 12 2018This paper characterizes the potential behaviors of higher commutators in a simple algebra.

Polyadic integer numbers and finite (m,n)-fieldsJul 03 2017Jul 13 2017The polyadic integer numbers, which form a polyadic ring, are representatives of a fixed congruence class. The basics of polyadic arithmetic are presented: prime polyadic numbers, the polyadic Euler function, polyadic division with a remainder, etc. are ... More

Polyadic Hopf algebras and quantum groupsNov 07 2018Apr 04 2019This article continues the study of concrete algebra-like structures in our polyadic approach, where the arities of all operations are initially taken as arbitrary, but the relations between them, the arity shapes, are to be found from some natural conditions ... More

Donaldson invariants of symplectic manifoldsJan 03 2013Jan 07 2013We prove that symplectic 4-manifolds with $b_1 = 0$ and $b^+ > 1$ have nonvanishing Donaldson invariants, and that the canonical class is always a basic class. We also characterize in many situations the basic classes of a Lefschetz fibration over the ... More

The contact homology of Legendrian knots with maximal Thurston-Bennequin invariantDec 22 2010We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classical invariants but nonvanishing contact homology.

Random Cyclic QuadrilateralsOct 03 2016The circumcircle of a planar convex polygon P is a circle C that passes through all vertices of P. If such a C exists, then P is said to be cyclic. Fix C to have unit radius. While any two angles of a uniform cyclic triangle are negatively correlated, ... More

Random Gaussian TetrahedraMay 06 2010Dec 17 2015Given independent normally distributed points A,B,C,D in Euclidean 3-space, let Q denote the plane determined by A,B,C and D^ denote the orthogonal projection of D onto Q. The probability that the tetrahedron ABCD is acute remains intractible. We make ... More

Initial Blow-up of Solutions of Semilinear Parabolic InequalitiesNov 19 2009We obtain an upper bound on the initial blow-up of nonnegative solutions of second order semilinear parabolic inequalities when a superlinear exponent in the inequalities is not too large.

Six-dimensional Methods for Four-dimensional Conformal Field TheoriesJun 17 2010Aug 02 2010The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as projections of fields ... More

A No-Truncation Approach to Cosmic Microwave Background AnisotropiesJul 05 2006Sep 12 2006We offer a method of calculating the source term in the line-of-sight integral for cosmic microwave background anisotropies without using a truncated partial-wave expansion in the Boltzmann hierarchy.

Damping of Tensor Modes in CosmologyJun 16 2003Oct 05 2003An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves. The solution ... More

The Cosmological Constant Problems (Talk given at Dark Matter 2000, February, 2000)May 12 2000The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help ... More

Must Cosmological Perturbations Remain Non-Adiabatic After Multi-Field Inflation?May 20 2004Jul 20 2004Even if non-adiabatic perturbations are generated in multi-field inflation, the perturbations will become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities, and will remain adiabatic ... More

The Making of the Standard ModelJan 03 2004This is the edited text of a talk given at CERN on Septembr 16, 2003, as part of a celebration of the 30th anniversary of the discovery of neutral currents and the 20th anniversary of the discovery of the W and Z particles.

Adiabatic Modes in CosmologyFeb 17 2003We show that the field equations for cosmological perturbations in Newtonian gauge always have an adiabatic solution, for which a quantity ${\cal R}$ is non-zero and constant in all eras in the limit of large wavelength, so that it can be used to connect ... More

Black Hole Thermodynamics and Statistical MechanicsJul 28 2008We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical ... More

Notes on the (2+1)-Dimensional Wheeler-DeWitt EquationSep 02 1993In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of information ... More

The Sum over Topologies in Three-Dimensional Euclidean Quantum GravityJun 26 1992In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit of small cosmological ... More

Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave FunctionMay 11 1992In most attempts to compute the Hartle-Hawking ``wave function of the universe'' in Euclidean quantum gravity, two important approximations are made: the path integral is evaluated in a saddle point approximation, and only the leading (least action) extremum ... More

(2+1)-Dimensional Chern-Simons Gravity as a Dirac Square RootSep 04 1991Sep 16 1991For (2+1)-dimensional spacetimes with the spatial topology of a torus, the transformation between the Chern-Simons and ADM versions of quantum gravity is constructed explicitly, and the wave functions are compared. It is shown that Chern-Simons wave functions ... More

A lexical database tool for quantitative phonological researchJul 22 1997A lexical database tool tailored for phonological research is described. Database fields include transcriptions, glosses and hyperlinks to speech files. Database queries are expressed using HTML forms, and these permit regular expression search on any ... More

Topological quantum field theory and quantum gravityAug 07 2014This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same result as the ... More

Polyadic systems, representations and quantum groupsAug 19 2013Jun 08 2014Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic systems having ... More

Nonlocal invariants in index theoryJul 21 1997This article surveys the relations among local and nonlocal invariants in Atiyah-Singer index theory. We discuss the local invariants that arise from the heat equation approach to the index theorem for geometric operators, as well as the nonlocal invariants ... More

Deforming nonnormal isolated surface singularities and constructing 3-folds with $\mathbb{P}^1$ as exceptional setDec 11 2015Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as isolated, non ... More

Quasilinear reformulation of Lovelock gravityApr 30 2015Jun 04 2015Here we give an extended review of the quasilinear reformulation of the Lovelock gravitational field equations in harmonic gauge presented in 1409.6656 [gr-qc]. This is important in order to establish rigorously well-posedness of the theory perturbed ... More

Low Correlation Noise Stability of Symmetric SetsNov 02 2015Sep 02 2016We study the Gaussian noise stability of subsets A of Euclidean space satisfying A=-A. It is shown that an interval centered at the origin, or its complement, maximizes noise stability for small correlation, among symmetric subsets of the real line of ... More

Lindblad Decoherence in Atomic ClocksOct 08 2016It is shown how possible corrections to ordinary quantum mechanics described by the Lindblad equation might be detected by exploiting the great precision of atomic clocks.

Topological complexity of n points on a treeJul 27 2016The topological complexity of a path-connected space $X,$ denoted $TC(X),$ can be thought of as the minimum number of continuous rules needed to describe how to move from one point in $X$ to another. The space $X$ is often interpreted as a configuration ... More

A Characterisation of Manhart's Relative Normal Vector FieldsDec 20 2009In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces in the affine ... More

Average-Value Tverberg Partitions via Finite Fourier AnalysisJan 19 2015Jul 25 2016The long-standing topological Tverberg conjecture claimed, for any continuous map from the boundary of an $N(q,d):=(q-1)(d+1)$-simplex to $d$-dimensional Euclidian space, the existence of $q$ pairwise disjoint subfaces whose images have non-empty $q$-fold ... More