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Backreaction of superhorizon perturbations in scalar field cosmologiesAug 07 2008Aug 08 2008It has been suggested that the acceleration of the Universe may be due to the backreaction of perturbations to the Friedmann-Robertson-Walker background. For a Universe dominated by cold dark matter, it is known that the backreaction of superhorizon perturbations ... More

On the spectral properties of Feigenbaum graphsMar 02 2019A Horizontal Visibility Graph (HVG) is a simple graph extracted from an ordered sequence of real values, and this mapping has been used to provide a combinatorial encryption of time series for the task of performing network based time series analysis. ... More

Performance Analysis of NOMA-based Cooperative Relaying in α - μ Fading ChannelsMar 05 2019Non-orthogonal multiple access (NOMA) is widely recognized as a potential multiple access technology for efficient radio spectrum utilization in the fifth-generation (5G) wireless communications standard. In this paper, we study the average achievable ... More

User-Antenna Selection for Physical-Layer Network Coding based on Euclidean DistanceFeb 12 2019In this paper, we present the error performance analysis of a multiple-input multiple-output (MIMO) physical-layer network coding (PNC) system with two different user-antenna selection (AS) schemes in asymmetric channel conditions. For the first antenna ... More

Luminosity distance in Swiss cheese cosmology with randomized voids and galaxy halosJul 16 2012We study the fluctuations in luminosity distance due to gravitational lensing produced both by galaxy halos and large scale voids. Voids are represented via a "Swiss cheese" model consisting of a \LambdaCDM Friedman-Robertson-Walker background in which ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Apr 11 2018Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work ... 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

Dark Energy or Modified Gravity? An Effective Field Theory ApproachNov 29 2012Sep 23 2013We take an Effective Field Theory (EFT) approach to unifying existing proposals for the origin of cosmic acceleration and its connection to cosmological observations. Building on earlier work where EFT methods were used with observations to constrain ... More

Identifying Mild Traumatic Brain Injury Patients From MR Images Using Bag of Visual WordsOct 18 2017Feb 14 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests are used to both assess the patient condition and to monitor the patient progress. This work aims ... More

MTBI Identification From Diffusion MR Images Using Bag of Adversarial Visual FeaturesJun 27 2018In this work, we propose bag of adversarial features (BAF) for identifying mild traumatic brain injury (MTBI) patients from their diffusion magnetic resonance images (MRI) (obtained within one month of injury) by incorporating unsupervised feature learning ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests have been used to both assess the patient condition and to monitor the patient progress. This ... More

Luminosity distance in Swiss cheese cosmology with randomized voids. II. Magnification probability distributionsSep 09 2011Nov 14 2011We study the fluctuations in luminosity distances due to gravitational lensing by large scale (> 35 Mpc) structures, specifically voids and sheets. We use a simplified "Swiss cheese" model consisting of a \Lambda -CDM Friedman-Robertson-Walker background ... 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

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

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

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.

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

Neutrino Mass Ordering Studies with PINGU and IceCube/DeepCoreApr 29 2016The Precision IceCube Next Generation Upgrade (PINGU) is a proposed extension to the IceCube detector. The design of PINGU would augment the existing 86 strings with an additional 40 with the main goal of determining the neutrino mass ordering (NMO). ... More

Necessary and Sufficient Condition on the Lindblad Equation to Prevent Entropy IncreaseNov 18 2015Nov 23 2015It is shown that in order for the solutions of the Lindblad equation never to give a decreasing von Neumann entropy, it is necessary and sufficient that the operators appearing in this equation should be unitary linear combinations of their adjoints. ... More

Explicit examples of equivalence relations and factors with prescribed fundamental group and outer automorphism groupOct 18 2010Mar 13 2012In this paper we give a number of explicit constructions for II$_1$ factors and II$_1$ equivalence relations that have prescribed fundamental group and outer automorphism group. We construct factors and relations that have uncountable fundamental group ... 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

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

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

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.

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.

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

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

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

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

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

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.

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

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

On Alternative Supermatrix ReductionJun 02 1995Jun 16 1995We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible ... 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

Universal abelian covers of superisolated singularitiesJan 27 2006Jan 30 2008We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo-Velasco, Melle-Hernandez and Nemethi, thereby providing counterexamples to the ... 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

Higher cotangent cohomology of rational surface singularitiesApr 03 2002The cotangent cohomology groups T^1 and T^2 play an important role in deformation theory, the first as space of infinitesimal deformations, while the obstructions land in the second. Much work has been done to compute their dimension for rational surface ... 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

Semistable K3-surfaces with icosahedral symmetryJun 15 2001In a Type III degeneration of K3-surfaces the dual graph of the central fibre is a triangulation of the 2-sphere. We realise the tetrahedral, octahedral and especially the icosahedral triangulation in families of K3-surfaces, preferably with the associated ... More

Arithmetic universes and classifying toposesJan 17 2017Reasoning in the 2-category Con of contexts, certain sketches for arithmetic universes (i.e. list arithmetic pretoposes; AUs), is shown to give rise to base-independent results of Grothendieck toposes, provided the base elementary topos has a natural ... More

A Convex Maximization Problem: Continuous CaseDec 05 1999We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.

A Convex Maximization Problem: Discrete CaseDec 05 1999We study a specific convex maximization problem in n-dimensional space. The conjectured solution is proved to be a vertex of the polyhedral feasible region, but only a partial proof of local maximality is known. Integer sequences with interesting patterns ... More

Dual Selection GamesSep 27 2018Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger selection game ... More

Quasigeodesic flows and sphere-filling curvesOct 26 2012Given a closed hyperbolic 3-manifold M with a quasigeodesic flow we construct a \pi_1-equivariant sphere-filling curve in the boundary of hyperbolic space. Specifically, we show that any complete transversal P to the lifted flow on H^3 has a natural compactification ... More

Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamicsAug 05 2013Sep 07 2014A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number ... More

Union of n Disks: Remote Centers, Common OriginNov 16 2015Explicit area expressions are known for a special case, due to Tao & Wu (1987), and lead to calculation of integrals in applied probability.

Second N=1 Superanalog of Complex StructureOct 19 1995We found another N=1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N=1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex function theory. ... More

Stochastic Attribute-Value GrammarsOct 23 1996Probabilistic analogues of regular and context-free grammars are well-known in computational linguistics, and currently the subject of intensive research. To date, however, no satisfactory probabilistic analogue of attribute-value grammars has been proposed: ... More

An Incidence Bound Over FieldsSep 20 2016We prove an upper bound on incidences between points and lines in the plane over a field $\mathbb{F}$. In particular, given $n$ points and $m$ lines in $\mathbb{F}^2$ (where $n\leq m$, and if $\text{char}(\mathbb{F})=p>0$, then $n\leq p^{4/3}$), we prove ... More

Tetraquark Mesons in Large $N$ Quantum ChromodynamicsMar 02 2013It is argued that exotic mesons consisting of two quarks and two antiquarks are not ruled out in quantum chromodynamics with a large number $N$ of colors, as generally thought. They can come in two varieties: short-lived tetraquarks with decay rates proportional ... More

Asymptotically Safe InflationNov 16 2009Mar 30 2010Inflation is studied in the context of asymptotically safe theories of gravitation. Conditions are explored under which it is possible to have a long period of nearly exponential expansion that eventually comes to an end.

Non-Gaussian Correlations Outside the Horizon II: The General CaseOct 16 2008The results of a recent paper [0808.2909] are generalized. A more detailed proof is presented that under essentially all conditions, the non-linear classical equations governing matter and gravitation in cosmology have ``adiabatic'' solutions in which, ... More

A Tree Theorem for InflationMay 24 2008Aug 13 2008It is shown that the generating function for tree graphs in the "in-in" formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton ... More

Living in the MultiverseNov 03 2005This is the written version of the opening talk at the symposium "Expectations of a Final Theory," at Trinity College, Cambridge, on September 2, 2005. It is to be published in Universe or Multiverse?, ed. B. Carr (Cambridge University Press).

What is Quantum Field Theory, and What Did We Think It Is?Feb 04 1997This is a talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.

Effective Field Theory, Past and FutureAug 13 2009Sep 26 2009This is a written version of the opening talk at the 6th International Workshop on Chiral Dynamics, at the University of Bern, Switzerland, July 6, 2009, to be published in the proceedings of the Workshop. In it, I reminisce about the early development ... More

Can Non-Adiabatic Perturbations Arise After Single-Field Inflation?Jan 15 2004May 18 2004It is shown that non-adiabatic cosmological perturbations cannot arise during the period of reheating following inflation with a single scalar inflaton field.

Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$Mar 19 2001Aug 16 2001General asymptotic formulas are given for the coefficient $C_\ell$ of the term of multipole number $\ell$ in the temperature correlation function of the cosmic microwave background, in terms of scalar and dipole form factors introduced in a companion ... More

Permutation Complexity Related to the Letter Doubling MapAug 18 2011Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural numbers associated ... More

Permutation Complexity of the Thue-Morse WordMar 31 2010Apr 05 2010Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural numbers associated ... More

Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?Sep 17 2009Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the Wheeler-DeWitt equation. ... More

The Statistical Mechanics of the Three-Dimensional Euclidean Black HoleJun 17 1996Oct 08 1996In its formulation as a Chern-Simons theory, three-dimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting ... More

Computational PhonologyApr 10 2002Phonology, as it is practiced, is deeply computational. Phonological analysis is data-intensive and the resulting models are nothing other than specialized data structures and algorithms. In the past, phonological computation - managing data and developing ... More

l --> l' gamma in the Lepton Number Violating MSSMOct 30 2006A minimal particle content supersymmetric model with a discrete Z_3 symmetry, allowing lepton number violating terms, is studied. Within this model, the neutrino masses and mixing can be generated by lepton number violating couplings. Choosing parameters ... More

On the classification of rational surface singularitiesApr 01 2012A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the fundamental cycle. We classify completely certain types ... More

The versal deformation of cyclic quotient singularitiesJun 08 2009We describe the versal deformation of two-dimensional cyclic quotient singularities in terms of equations, following Arndt, Brohme and Hamm. For the reduced components the equations are determined by certain systems of dots in a triangle. The equations ... More

Partial Hamiltonian formalism, multi-time dynamics and singular theoriesJul 22 2013We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the initially reduced ... More

A Dynamical Mechanism for Large Volumes with Consistent CouplingsSep 05 2016A mechanism for addressing the 'decompactification problem' is proposed, which consists of balancing the vacuum energy in Scherk-Schwarzed theories against contributions coming from non- perturbative physics. Universality of threshold corrections ensures ... More

The localic compact interval is an Escardó-Simpson interval objectJun 26 2015The locale corresponding to the real interval [-1,1] is an interval object, in the sense of Escard\'o and Simpson, in the category of locales. The map c from 2^\omega to [-1,1], mapping a stream s of signs +1 or -1 to \Sum_{i=1}^\infty s_i 2^{-i}, is ... More

Hamiltonian analysis of self-dual gauge gravityApr 15 2015The Hamiltonian analysis of the self-dual gauge gravity theory is carried out. The resulting canonical structure is equivalent to that of self-dual gravity.

A semiclassical reversibility paradox in simple chaotic systemsSep 27 2015Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly chaotic, there ... More

Algebroids and Twistor SpacesDec 14 2015We introduce a plethora of skew algebroids on twistor spaces and describe the corresponding foliations. In a forthcoming paper, we use these algebroids to derive results about bihermitian manifolds, also known as generalized Kahler manifolds.

Simple surface singularitiesMar 04 2013By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be obtained from ... More

Aspects of the topology and combinatorics of Higgs bundle moduli spacesSep 15 2018Dec 08 2018This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of the moduli space ... More

Kulikov singularitiesDec 11 2018In the study of normal surface singularities the relation between analytical and topological properties and invariants of the singularity is a very rich problem. This relation is particularly close for surface singularities constructed from families of ... More

Chern-Weil theory for certain infinite-dimensional Lie groupsJun 18 2013Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques to detect cohomology ... More

Permutation Complexity and the Letter Doubling MapFeb 27 2011Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of uniformly recurrent ... More

Cosets, Voltages, and Derived EmbeddingsNov 17 2014Nov 09 2016An ordinary voltage graph embedding of a graph in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph $G$ in a surface with voltage group $A$ and a connected subgraph ... More

Applications Of Ordinary Voltage Graph Theory To Graph Embeddability, Part 1Jan 06 2015We study embeddings of a graph $G$ in a surface $S$ by considering representatives of different classes of $H_1(S)$ and their intersections. We construct a matrix invariant that can be used to detect homological invariance of elements of the cycle space ... More

The supercuspidal representations of p-adic classical groupsJul 25 2006Nov 12 2007Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. ... More