Results for "Scott Fallows"

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Modeling emission of acoustic energy during bubble expansion in PICO bubble chambersJun 11 2019The PICO experiment uses bubble chambers filled with superheated C$_3$F$_8$ for spin-dependent WIMP dark matter searches. One of the main sources of background in these detectors is alpha particles from decays of environmental $^{222}\mathrm{Rn}$, which ... More
Sensitivity of the PICO-500 Bubble Chamber to Supernova Neutrinos Through Coherent Nuclear Elastic ScatteringJun 04 2018Nov 05 2018Ton-scale direct dark matter search experiments should be sensitive to neutrino-induced recoil events from either $^8$B solar neutrinos or the brief but intense flux from a core collapse supernova in the Milky Way. These low-threshold detectors are sensitive ... More
Equatorwards Expansion of Unperturbed, High-Latitude Fast Solar WindJul 17 2012We use dual-site radio observations of interplanetary scintillation (IPS) with extremely long baselines (ELB) to examine meridional flow characteristics of the ambient fast solar wind at plane-of-sky heliocentric distances of 24-85 solar radii (R\odot). ... More
Encoding Data for HTM SystemsFeb 18 2016Hierarchical Temporal Memory (HTM) is a biologically inspired machine intelligence technology that mimics the architecture and processes of the neocortex. In this white paper we describe how to encode data as Sparse Distributed Representations (SDRs) ... More
Dynamics of a soccer ballApr 11 2014Exploiting the symmetry of the regular icosahedron, Peter Doyle and Curt McMullen constructed a solution to the quintic equation. Their algorithm relied on the dynamics of a certain icosahedral equivariant map for which the icosahedron's twenty face-centers--one ... More
Solving the quintic by iteration in three dimensionsMar 09 1999Oct 06 1999The requirement for solving a polynomial is a means of breaking its symmetry, which in the case of the quintic, is that of the symmetric group S_5. Induced by its five-dimensional linear permutation representation is a three-dimensional projective action. ... More
The statistical mechanics of planet orbitsApr 05 2015Jun 10 2015The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities until their orbits ... More
Noisy 1-Bit Compressed Sensing Embeddings Enjoy a Restricted Isometry PropertyApr 12 2016We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse hemispheres. This approach ... More
The Whitney Extension Theorem for $C^1$, horizontal curves in $\mathbb{H}^n$Jul 08 2015Jul 16 2015For a real valued function defined on a compact set $K \subset \mathbb{R}^m$, the classical Whitney Extension Theorem from 1934 gives necessary and sufficient conditions for the existence of a $C^k$ extension to $\mathbb{R}^m$. In this paper, we prove ... More
The Complexity of AgreementJun 30 2004A celebrated 1976 theorem of Aumann asserts that honest, rational Bayesian agents with common priors will never "agree to disagree": if their opinions about any topic are common knowledge, then those opinions must be equal. Economists have written numerous ... More
Quantum Lower Bound for the Collision ProblemNov 20 2001The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Theta(n^{1/5}) on the number of queries needed by a quantum computer to solve this problem ... More
The Equivalence of Sampling and SearchingSep 26 2010In a sampling problem, we are given an input x, and asked to sample approximately from a probability distribution D_x. In a search problem, we are given an input x, and asked to find a member of a nonempty set A_x with high probability. (An example is ... More
Quantum Computing and Hidden Variables II: The Complexity of Sampling HistoriesAug 19 2004This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory satisfying a reasonable ... More
Book Review: 'A New Kind of Science'Jun 13 2002Jul 30 2002This is a critical review of the book 'A New Kind of Science' by Stephen Wolfram. We do not attempt a chapter-by-chapter evaluation, but instead focus on two areas: computational complexity and fundamental physics. In complexity, we address some of the ... More
A Fundamental Scale for Acceleration from the Holographic PrincipleMay 25 2005Jun 26 2005From the Eddington-Weinberg relationship, which may be explained by the holographic principle and the cosmic coincidence in a flat Universe, it follows that the characteristic gravitational acceleration aN associated with the nucleon and its Compton wavelength ... More
The Large Number Coincidence, The Cosmic Coincidence and the Critical AccelerationFeb 09 2005May 19 2006The coincidence problem among the pure numbers of order near 10^{40} is resolved with the Raychaudhuri and Friedmann-Robertson-Lemaitre-Walker equations and a trivial relationship involving the fine structure constant. The fact that the large number coincidence ... More
An Inertial Reaction to Cosmological AccelerationsSep 01 2003May 17 2005Mach's "fixed stars" are actually not fixed at all. The distant clusters of galaxies are not only receding from each observer but they are also accelerating since the rate of cosmological expansion is not constant. If the distant cosmic masses in someway ... More
Stars and the holographic upper bound on gravitational actionApr 14 2007Dec 22 2008The holographic upper bound on entropy is applied to the gravitational action associated with the non-relativistic contraction of a nebula. A critical radius is identified, as a function of the initial radius and mass, for which the number of bits associated ... More
A Cosmological Modification to Energy from Mach-Hamilton ConsistencyMar 24 2004If Mach's Principle explains the Newtonian inertial reaction to acceleration then the role of the 'fixed stars' should also be manifest through Hamilton's formulation of mechanics. This consistency may be achieved if the expression for relativistic energy ... More
The Real Problem with MONDDec 06 2011Gravitational potentials in the cosmos are deeper than expected from observed visible objects, a phenomenon usually attributed to dark matter, presumably in the form of a new fundamental particle. Until such a particle is observed, the jury remains out ... More
Cross-Correlating Probes of Primordial Gravitational WavesJan 27 2010One of the most promising ways of detecting primordial gravitational waves generated during inflation is to observe B-modes of polarization, generated by Thomson scattering after reionization, in the cosmic microwave background (CMB). Large scale foregrounds ... More
A geometric invariant for the study of planar curves and its application to spiral tip meanderFeb 25 2016Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total curvature ... More
Moduli Stabilization with the String Higgs EffectApr 23 2004May 02 2004We review the notion of the Higgs effect in the context of string theory. We find that by including this effect in time dependent backgrounds, one is led to a natural mechanism for stabilizing moduli at points of enhanced gauge symmetry. We consider this ... More
An Exposition on Inflationary CosmologyApr 29 2000May 27 2000This paper is intended to offer a pedagogical treatment of cosmological modeling and inflationary cosmology. In recent years, inflation has become accepted as a standard scenario making predictions that are testable by observations of the cosmic background. ... More
General Charge Balance Functions, A Tool for Studying the Chemical Evolution of the Quark-Gluon PlasmaSep 16 2011Jan 13 2012In the canonical picture of the evolution of the quark-gluon plasma during a high-energy heavy-ion collision, quarks are produced in two waves. The first is during the first fm/c of the collision, when gluons thermalize into the QGP. After a roughly isentropic ... More
Universal Flow in the Early Stages at RHICMar 09 2009Pre-thermal flow plays an important role in the final state evolution of heavy ion collisions at RHIC. We show that flow has universal features for a wide range of models. This significantly reduces the uncertainty in initializing hydrodynamic models ... More
Refractive Distortions of Two-Particle CorrelationsNov 02 2005Using optical model calculations it has recently been shown that refractive phenomena from the collective mean field can significantly alter the sizes inferred from two-pion correlations. We demonstrate that such effects can be accounted for in classical ... More
Canonical and Microcanonical Distributions for Fermi SystemsMay 26 1999Oct 14 1999Recursion relations are presented that allow exact calculation of canonical and microcanonical partition functions of degenerate Fermi systems, assuming no explicit two-body interactions. Calculations of the level density, sorted by angular momentum, ... More
Searches for Particle Dark Matter: An IntroductionOct 12 2011The identity of dark matter is one of the key outstanding problems in both particle and astrophysics. In this thesis, I describe a number of complementary searches for particle dark matter. I discuss how the impact of dark matter on stars can constrain ... More
One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized UnitarityAug 01 2011Dec 06 2011We combine the six-dimensional helicity formalism of Cheung and O'Connell with D-dimensional generalized unitarity to obtain a new formalism for computing one-loop amplitudes in dimensionally regularized QCD. With this procedure, we simultaneously obtain ... More
On the effective cone of higher codimension cycles in $\overline{\mathcal{M}}_{g,n}$Oct 25 2017We exhibit infinitely many extremal effective codimension-$k$ cycles in $\overline{\mathcal{M}}_{g,n}$ in the cases $g\geq 3, n\geq g-1$ and $k=2$, $g\geq 2$, $k\leq n-g,g,$ and $g=1$, $k\leq n-2$. Hence in these cases the effective cone is not rational ... More
Relative Zeta Determinants and the Quillen MetricOct 27 1999We compute the relative zeta-function metric on the determinant line bundle for a family of elliptic boundary value problems of Dirac-type. To do this we prove a general formula relating the zeta-determinant to a Fredholm determinant over the boundary ... More
Supersymmetry in the Very Early UniverseJun 16 1995Jun 24 1995Supersymmetric flat directions can have a number of important consequences in the very early universe. Depending on the form of the SUSY breaking potential arising from the finite energy density at early times, coherent production of scalar condensates ... More
Baryons and Dark Matter from the Late Decay of a Supersymmetric CondensateJun 09 1995The possibility that both the baryon asymmetry and dark matter arise from the late decay of a population of supersymmetric particles is considered. If the decay takes place below the LSP freeze out temperature, a nonthermal distribution of LSPs results. ... More
Electromagnetic Contributions to the Schiff MomentFeb 07 1994The Schiff moment, $\smij$, is a parity and time reversal violating fermion-fermion coupling. The nucleus-electron Schiff moment generically gives the most important contribution to the electric dipole moments of atoms and molecules with zero net intrinsic ... More
Reciprocity and rationality for the greedy normal form of a Coxeter groupSep 12 2008We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of ... More
Supercharacter theories constructed by the method of little groupsMay 21 2014May 22 2014The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of semidirect ... More
Szemerédi's Regularity Lemma for matrices and sparse graphsOct 04 2010Nov 08 2010Szemer\'edi's Regularity Lemma is an important tool for analyzing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we ... More
Classifying Spinor StructuresJun 10 2001I begin by explaining how Riemannian geometry can be understood in terms of principal fibre bundles and connections thereon. I then introduce and motivate the definition of a spinor structure in terms of familiar geometrical ideas. The central result ... More
Recent results from T2KJun 03 2016Jan 03 2017The T2K long-baseline neutrino oscillation experiment has produced the first observation of $\nu_{e}$ appearance and the most precise measurement of the mixing angle $\theta_{23}$ from $6.57 \times 10^{20}$ protons-on-target (POT) of neutrino beam data. ... More
Pricing for Large Positions in Contingent ClaimsFeb 17 2012Dec 11 2013Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches ... More
On graph products of multipliers and the Haagerup property for $C^*$-dynamical systemsMar 05 2018We consider the notion of the graph product of actions of groups $\left\{G_v\right\}$ on a $C^*$-algebra $\mathcal{A}$ and show that under suitable commutativity conditions the graph product action $\bigstar_\Gamma \alpha_v: \bigstar_\Gamma G_v \curvearrowright ... More
Elementary treatment of $p^a \pm p^b + 1 = x^2$Aug 31 2006We give a shorter simpler proof of a result of Szalay on the equation $2^a + 2^b + 1 = x^2$. We give an elementary proof of a result of Luca on the equation of the title for prime $p > 2$. The elementary treatment is made possible by a lemma which is ... More
Generalized Moonshine IV: Monstrous Lie algebrasAug 30 2012Aug 20 2016For each element of the Fischer-Griess Monster sporadic simple group, we construct an infinite dimensional Lie algebra equipped with a projective action of the centralizer of that element. Our construction is given by a string-theoretic "add a spacetime ... More
Augmented Homotopical Algebraic GeometryNov 07 2017We develop the framework for augmented homotopical algebraic geometry. This is an extension of homotopical algebraic geometry, which itself is a homotopification of classical algebraic geometry. To do so, we define the notion of augmentation categories, ... More
The evolution of galaxy formationDec 01 2011Our history of understanding galaxy formation could be traced through the development of individual ideas. A cynic might be tempted to suggest that new catchphrases are developed at a faster rate than genuine progress is made.
CMB ANISOTROPIES: AN OVERVIEWFeb 02 1995A brief outline of the current status of CMB anisotropies and what they might mean, heavily biased towards the perspective of Berkeley theorists. Based on a talk presented at the 17th Texas Symposium on Relativistic Astrophysics held in Munich, December ... More
Sobolev extensions of Lipschitz mappings into metric spacesAug 02 2016Aug 02 2017Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ ... More
51 constructions of the Moonshine moduleJul 10 2017Jul 18 2017We show using Borcherds products that for any fixed-point free automorphism of the Leech lattice satisfying a "no massless states" condition, the corresponding cyclic orbifold of the Leech lattice vertex operator algebra is isomorphic to the Monster vertex ... More
Optical Kerr effect in vacuumAug 02 2019From an effective field theory of electromagnetism in vacuum including all lowest-order nonlinear terms consistent with Lorentz invariance and locality of photon/photon interactions, we derive an effective medium description of strong background fields ... More
Torus Invariant CurvesApr 13 2013Jul 30 2013Using the language of T-varieties, we study torus invariant curves on a complete normal variety $X$ with an effective codimension-one torus action. In the same way that the $T$-invariant Weil divisors on $X$ are sums of "vertical" divisors and "horizontal" ... More
Vogan Duality for ~Spin(p,q)Aug 13 2009The main purpose of this paper is to describe a symmetry in the set genuine parameters for even rank nonlinear Spin groups in type B at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the corresponding generalized ... More
Supercharacters of unipotent groups defined by involutionsNov 07 2013Dec 15 2014We construct supercharacter theories of finite unipotent groups in the orthogonal, symplectic and unitary types. Our method utilizes group actions in a manner analogous to that of Diaconis and Isaacs in their construction of supercharacters of algebra ... More
The odd couple: quasars and black holesJul 23 2014Quasars emit more energy than any other objects in the universe, yet are not much bigger than the solar system. We are almost certain that quasars are powered by giant black holes of up to $10^{10}$ times the mass of the Sun, and that black holes of between ... More
On the origin of irregular structure in Saturn's ringsNov 07 2002We suggest that the irregular structure in Saturn's B ring arises from the formation of shear-free ring-particle assemblies of up to ~100 km in radial extent. The characteristic scale of the irregular structure is set by the competition between tidal ... More
A Counterexample to the Generalized Linial-Nisan ConjectureOct 27 2011In earlier work, we gave an oracle separating the relational versions of BQP and the polynomial hierarchy, and showed that an oracle separating the decision versions would follow from what we called the Generalized Linial-Nisan (GLN) Conjecture: that ... More
Why Philosophers Should Care About Computational ComplexityAug 08 2011Aug 14 2011One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue ... More
QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum ProtocolsOct 31 2005Apr 02 2006This paper introduces a new technique for removing existential quantifiers over quantum states. Using this technique, we show that there is no way to pack an exponential number of bits into a polynomial-size quantum state, in such a way that the value ... More
Are Quantum States Exponentially Long Vectors?Jul 26 2005I'm grateful to Oded Goldreich for inviting me to the 2005 Oberwolfach Meeting on Complexity Theory. In this extended abstract, which is based on a talk that I gave there, I demonstrate that gratitude by explaining why Goldreich's views about quantum ... More
Limits on Efficient Computation in the Physical WorldDec 20 2004Feb 15 2005More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the ... More
Limitations of Quantum Advice and One-Way CommunicationFeb 15 2004Oct 01 2004Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only limited advantages ... More
Is Quantum Mechanics An Island In Theoryspace?Jan 12 2004Mar 17 2004This recreational paper investigates what happens if we change quantum mechanics in several ways. The main results are as follows. First, if we replace the 2-norm by some other p-norm, then there are no nontrivial norm-preserving linear maps. Second, ... More
The Ghost in the Quantum Turing MachineJun 02 2013Jun 07 2013In honor of Alan Turing's hundredth birthday, I unwisely set out some thoughts about one of Turing's obsessions throughout his life, the question of physics and free will. I focus relatively narrowly on a notion that I call "Knightian freedom": a certain ... More
Lower Bounds for Local Search by Quantum ArgumentsJul 21 2003Feb 05 2004The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0,1}^n, we show a lower bound of Omega(2^{n/4}/n) on the number of ... More
Quantum Computing and Dynamical Quantum ModelsMay 11 2002A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum state. We study ... More
Three Discrete Models of Planar Lie Group Equivariant PresheavesAug 25 2016We utilise the theory of crossed simplicial groups to introduce a collection of Quillen model structures on the category of simplicial presheaves with a compact planar Lie group action on a small Grothendieck site.
Action in a fractal universe and the holographic upper boundFeb 28 2008Aug 13 2008The basic scaling laws for structures in a fractal universe require that the characteristic quantity of action associated with astronomical bodies should be of order near the maximum possible action allowed by the holographic upper bound. That conclusion ... More
A fundamental scale of mass for black holes from the cosmological constantJan 24 2007Dec 22 2008The existence of a positive cosmological constant leads naturally to two fundamental scales of length, being the De Sitter horizon and the radius of the cell associated with a holographic degree of freedom. Associated with each of those scales of length ... More
Scaling Law for the Cosmological Constant from Quantum Cosmology with Seven Extra DimensionsOct 09 2006Mar 16 2008According to a model of quantum cosmology the maximum number of degrees of freedom allowed in our three dimensions was determined by the size of seven extra dimensions in an initial excited state before inflation. The size of the extra dimensions can ... More
The fundamental scales of structures from first principlesApr 15 2008May 29 2008Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe, clusters, galaxies, ... More
Coherent Phase Argument for InflationSep 05 2003Cosmologists have developed a phenomenally successful picture of structure in the universe based on the idea that the universe expanded exponentially in its earliest moments. There are three pieces of evidence for this exponential expansion -- {\it inflation} ... More
Anisotropies in the Cosmic Microwave Background: TheoryFeb 14 1997Anisotropies in the Cosmic Microwave Background (CMB) contain a wealth of information about the past history of the universe and the present values of cosmological parameters. I ouline some of the theoretical advances of the last few years. In particular, ... More
Diversification Return, Portfolio Rebalancing, and the Commodity Return PuzzleSep 06 2011Diversification return is an incremental return earned by a rebalanced portfolio of assets. The diversification return of a rebalanced portfolio is often incorrectly ascribed to a reduction in variance. We argue that the underlying source of the diversification ... More
Symmetries of the Standard ModelOct 27 2004Feb 24 2005I present an overview of the standard model, concentrating on its global continuous symmetries, both exact and approximate. There are four lectures, dedicated to spacetime symmetry, flavor symmetry, custodial symmetry, and scale symmetry. Topics include ... More
Hadron Colliders, the Standard Model, and BeyondDec 02 2002I argue that the Fermilab Tevatron will contribute to our knowledge of the pieces of the standard model that we know the least about. I discuss five of the most important areas in which the Tevatron can confront the standard model: precision electroweak, ... More
A dynamical systems approach to actin-based motility in Listeria monocytogenesFeb 26 2010Nov 30 2010A simple kinematic model for the trajectories of Listeria monocytogenes is generalized to a dynamical system rich enough to exhibit the resonant Hopf bifurcation structure of excitable media and simple enough to be studied geometrically. It is shown how ... More
A New Dimensionally Reduced Effective Action for QCD at High TemperatureJul 18 1994New terms are derived for the three-dimensional effective action of the static modes of pure gauge SU(N) at high temperature. In previous works, effective vertices have been obtained by evaluating diagrams involving 2, 3 or 4 external static gluons with ... More
Mass Generation from Higgs-like GhostsNov 03 2008Covariant quantization of gauge theories generally requires the inclusion of Fadeev Popov ghosts in the gauge-fixed Lagrangian. Normally these ghosts have fermionic statistics, but in supersymmetric theories that include fermionic gauge fields, there ... More
Dark stars: structure, evolution and impacts upon the high-redshift UniverseJan 05 2011Feb 13 2011The most compelling and popular models for dark matter predict that it should congregate and annihilate in stellar cores. Stars where annihilation contributes substantially to the total energy budget look very different to those with which we are familiar. ... More
Viewing the Chemical Evolution of the Quark-Gluon Plasma with Charge Balance FunctionsApr 09 2013Correlations from charge conservation are affected by when charge/anticharge pairs are created during the course of a relativistic heavy ion collision. For charges created early, balancing charges are typically separated by the order of one unit of spatial ... More
Identifying the Charge Carriers of the Quark-Gluon PlasmaMar 20 2012Charge correlations in lattice gauge calculations suggest that up, down and strange charges move independently in the QGP (quark-gluon plasma), and that the density of such charges is similar to what is expected from simple thermal arguments. Here, we ... More
The Long Slow Death of the HBT Puzzle, Proceedings for QM 2009Jul 06 2009Oct 07 2009At the onset of the RHIC era femtoscopic source sizes inferred from two-particle correlations at RHIC defied description with hydrodynamic models. This failure, which became known as the HBT puzzle, now appears to be solved. The source of the discrepancy ... More
Extending the Reach of HydrodynamicsOct 30 2007Nov 13 2007Recent and ongoing improvements to hydrodynamic treatments at RHIC are extending the physics reach of hydrodynamics, and improving the phenomenology. Here, the links between technological improvements and the extension of physics are emphasized.
Solving the sextic by iteration: A study in complex geometry and dynamicsMar 18 1999Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map posseses "reliable" ... More
An obstruction to subfactor principal graphs from the graph planar algebra embedding theoremFeb 20 2013Oct 15 2013We find a new obstruction to the principal graphs of subfactors. It shows that in a certain family of 3-supertransitive principal graphs, there must be a cycle by depth 6, with one exception, the principal graph of the Haagerup subfactor.
On the concentration of the chromatic number of random graphsJun 02 2008Let 0<p<1 be fixed. Shamir and Spencer proved in the 1980s that the chromatic number of a random graph in G(n,p) is concentrated in an interval of length about n^{1/2}. We give an improvement on this, showing that the chromatic number is concentrated ... More
Banach Algebras of Integral Operators, Off-Diagonal Decay, and Applications in Wireless CommunicationsJun 09 2004In this dissertation I establish that a broad class of Banach *-algebras of infinite integral operators, defined by the property that the kernels of the elements of the algebras possess subexponential off-diagonal decay, is inverse closed in the Banach ... More
On the effective cone of $\overline{\mathcal{M}}_{g,n}$Jan 20 2017For every $g\geq 2$ and $n\geq g+1$ we exhibit infinitely many extremal effective divisors in $\overline{\mathcal{M}}_{g,n}$ coming from the strata of abelian differentials.
Moduli Inflation from Dynamical Supersymmetry BreakingMar 18 1995Jun 14 1995Moduli fields, which parameterize perturbative flat directions of the potential in supersymmetric theories, are natural candidates to act as inflatons. An inflationary potential on moduli space can result if the scale of dynamical SUSY breaking in some ... More
The theory of Hawking radiation in laboratory analoguesAug 11 2015Hawking radiation, despite being known to theoretical physics for nearly forty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from practical and conceptual difficulties. Of particular note ... More
Integral method for the calculation of Hawking radiation in dispersive media II. Asymmetric asymptoticsMar 27 2014Analogue gravity experiments make feasible the realisation of black hole spacetimes in a laboratory setting and the observational verification of Hawking radiation. Since such analogue systems are typically dominated by dispersion, efficient techniques ... More
Some results on tracial stability and graph productsAug 14 2018Mar 06 2019We establish the tracial stability of a certain class of graph products of C*-algebras. This result involves the development of the "pincushion class" of finite graphs. We then apply this result in two ways. The first application yields a selective version ... More
Fricke Lie algebras and the genus zero property in MoonshineJan 26 2017Jul 10 2017We give a new, simpler proof that the canonical actions of finite groups on Fricke-type Monstrous Lie algebras yield genus zero functions in Generalized Monstrous Moonshine, using a Borcherds-Kac-Moody Lie algebra decomposition due to Jurisich. We describe ... More
A Scalable Framework for NBA Player and Team Comparisons Using Player Tracking DataNov 13 2015Jan 10 2016The release of NBA player tracking data greatly enhances the granularity and dimensionality of basketball statistics used to evaluate and compare player performance. However, the high dimensionality of this new data source can be troublesome as it demands ... More
Explicit Examples in $NK_{1}$Jun 24 2015For certain rings $\mathcal{R}$, we construct explicit matrices representing nonzero classes in the algebraic $K$ theory group $NK_{1}(\mathcal{R})$.
Generalized Moonshine I: Genus zero functionsDec 18 2008Oct 14 2010We introduce a notion of Hecke-monicity for functions on certain moduli spaces associated to torsors of finite groups over elliptic curves, and show that it implies strong invariance properties under linear fractional transformations. Specifically, if ... More
Random Perturbations of Viscous Compressible Fluids: Global Existence of Weak SolutionsApr 03 2015This article is devoted to the well-posedness of the stochastic compressible Navier Stokes equations. We establish the global existence of an appropriate class of weak solutions emanating from large inital data, set within a bounded domain. The stochastic ... More
A Self-Dual Integral Form of the Moonshine ModuleOct 02 2017Apr 19 2019We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the proof of the ... More
Block-Toeplitz determinants, chess tableaux, and the type $\hat{A_1}$ Geiss-Leclerc-Schroer $φ$-mapJul 20 2007We evaluate the Geiss-Leclerc-Schroer $\phi$-map for shape modules over the preprojective algebra $\Lambda$ of type $\hat{A_1}$ in terms of matrix minors arising from the block-Toeplitz representation of the loop group $\SL_2(\mathcal{L})$. Conjecturally ... More
The Standard Model of Cosmology: A Skeptic's GuideApr 04 2018The status of the standard cosmological model, also known as "LCDM" is described. With some simple assumptions, this model fits a wide range of data, with just six (or seven) free parameters. One should be skeptical about this claim, since it implies ... More