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A statistically significant lack of debris discs in medium separation binary systemsJul 10 2019Jul 11 2019We compile a sample of 341 binary and multiple star systems with the aim of searching for and characterising Kuiper belt-like debris discs. The sample is assembled by combining several smaller samples studied in previously published work with targets ... More

Empty gaps? Depleting annular regions in debris discs by secular resonance with a two-planet systemJun 22 2018We investigate the evolution on secular time-scales of a radially extended debris disc under the influence of a system of two coplanar planets interior to the disc, showing that the secular resonances of the system can produce a depleted region in the ... More

ALMA observations of the narrow HR 4796A debris ringJan 16 2018The young A0V star HR 4796A is host to a bright and narrow ring of dust, thought to originate in collisions between planetesimals within a belt analogous to the Solar System's Edgeworth-Kuiper belt. Here we present high spatial resolution 880$\mu$m continuum ... More

A statistically significant lack of debris discs in medium separation binary systemsJul 10 2019We compile a sample of 341 binary and multiple star systems with the aim of searching for and characterising Kuiper belt-like debris discs. The sample is assembled by combining several smaller samples studied in previously published work with targets ... More

A circumbinary protoplanetary disc in a polar configurationJan 15 2019Nearly all young stars are initially surrounded by `protoplanetary' discs of gas and dust, and in the case of single stars at least 30\% of these discs go on to form planets. The process of protoplanetary disc formation can result in initial misalignments, ... More

SL(2,R) covariant conditions for N=1 flux vacuaJul 15 2011Aug 25 2011Four-dimensional supersymmetric N = 1 vacua of type IIB supergravity are elegantly described by generalized complex geometry. However, this approach typically obscures the SL(2, R) covariance of the underlying theory. We show how to rewrite the pure spinor ... More

Anomaly Holography, the Wess-Zumino-Witten Term, and Electroweak Symmetry BreakingMar 04 2008I consider anomalies in effective field theories (EFTs) of gauge fields coupled to fermions on an interval in AdS_5, and their holographic duals. The anomalies give rise to constraints on the consistent EFT description, which are stronger than the usual ... More

Composite Leptoquarks at the LHCOct 09 2009Feb 02 2010If electroweak symmetry breaking arises via strongly-coupled physics, the observed suppression of flavour-changing processes suggests that fermion masses should arise via mixing of elementary fermions with composite fermions of the strong sector. The ... More

On the Chow motive of an abelian scheme with non-trivial endomorphismsOct 19 2011Oct 05 2012Let X be an abelian scheme over a base variety S with endomorphism algebra D. We prove that the relative Chow motive R(X/S) has a canonical decomposition as a direct sum of motives R^(\xi)$ where \xi runs over an explicitly determined finite set of irreducible ... More

The Surface Roughness of (433) Eros as Measured by Thermal-Infrared BeamingSep 22 2016In planetary science, surface roughness is regarded to be a measure of surface irregularity at small spatial scales, and causes the thermal-infrared beaming effect (i.e. re-radiation of absorbed sunlight back towards to the Sun). Typically, surface roughness ... More

Semidirect Products of Monoidal CategoriesOct 29 2015Jul 04 2016We introduce semidirect products of skew monoidal categories as a categorification of semidirect products of monoids (or, perhaps more familiarly, of groups). We also discuss how this construction interacts with monoidal, autonomous and closed monoidal ... More

Optimizing and Contrasting Recurrent Neural Network ArchitecturesOct 16 2015Recurrent Neural Networks (RNNs) have long been recognized for their potential to model complex time series. However, it remains to be determined what optimization techniques and recurrent architectures can be used to best realize this potential. The ... More

Incidences and pairs of dot productsSep 03 2015Sep 07 2015Let $\mathbb{F}$ be a field, let $P \subseteq \mathbb{F}^d$ be a finite set of points, and let $\alpha,\beta \in \mathbb{F} \setminus \{0\}$. We study the quantity \[|\Pi_{\alpha, \beta}| = \{(p,q,r) \in P \times P \times P \mid p \cdot q = \alpha, p ... More

A Useful Algebraic System of Statistical ModelsFeb 09 2015This paper proposes a single form for statistical models that accommodates a broad range of models, from ordinary least squares to agent-based microsimulations. The definition makes it almost trivial to define morphisms to transform and combine existing ... More

1-bounded entropy and regularity problems in von Neumann algebrasMay 25 2015Oct 07 2016We investigate the singular subspace of an inclusion of tracial von Neumann algebras. The singular subspace is a canonical N-N subbimodule of L^{2}(M) and it contains the quasinormalizer introduced by Popa, one-sided quasinormalizer introduced by Fang-Gao-Smith, ... More

Measuring photometric redshifts using galaxy images and Deep Neural NetworksApr 27 2015Jun 15 2016We propose a new method to estimate the photometric redshift of galaxies by using the full galaxy image in each measured band. This method draws from the latest techniques and advances in machine learning, in particular Deep Neural Networks. We pass the ... More

Energy and Information Near Black Hole HorizonsJan 21 2014Jul 21 2014The central challenge in trying to resolve the firewall paradox is to identify excitations in the near-horizon zone of a black hole that can carry information without injuring a freely falling observer. By analyzing the problem from the point of view ... More

Lie algebra configuration pairingOct 22 2010We give a new description of the configuration pairing of Sinha and Walter by showing that it computes coefficients in the associative, preLie, or graph polynomial of a Lie bracket expression. We also connect the graph complexes of Sinha and Walter with ... More

On Higher-Dimensional Oscillation in Ergodic TheorySep 09 2013Feb 25 2015We extend the results of Jones, Rosenblatt, and Wierdl concerning higher-dimensional oscillation in ergodic theory in a variety of ways. We do so by transference to the integer lattice, where we employ technique from (discrete) harmonic analysis.

The cosmological singularity problemJan 25 2010Despite impressive phenomenological successes, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Depending on the model, one would like to understand how appropriate initial conditions were selected ... More

Higher K-energy functionals and higher Futaki invariantsApr 23 2002May 01 2002This note discusses the higher K-energy functionals which were defined by Bando and Mabuchi, and integrate higher Futaki invariants. Two new formulas for the higher K-energy functionals are given, and the second K-energy is shown to be related to Donaldson's ... More

Horizontal Branch Stellar EvolutionNov 09 1995I review aspects of the evolution of horizontal branch (HB) stars. I start by discussing current topics in the study of HB stellar evolution, including a brief review of the main determinants of the structure of low-mass core helium burning stars and ... More

An infinite family of Legendrian torus knots distinguished by cube numberDec 20 2010For a knot $K$ the cube number is a knot invariant defined to be the smallest $n$ for which there is a cube diagram of size $n$ for $K$. There is also a Legendrian version of this invariant called the \emph{Legendrian cube number}. We will show that the ... More

Koszul duality between Higgs and Coulomb categories $\mathcal{O}$Nov 20 2016Feb 13 2019We prove a Koszul duality theorem between the category of weight modules over the quantized Coulomb branch (as defined by Braverman, Finkelberg and Nakajima) attached to a group $G$ and representation $V$ and a category of $G$-equivariant D-modules on ... More

Centers of KLR algebras and cohomology rings of quiver varietiesApr 16 2015Aug 22 2015Attached to a weight space in an integrable highest weight representation of a simply-laced Kac-Moody algebra $\mathfrak{g}$, there are two natural commutative algebras: the cohomology ring of a quiver variety and the center of a cyclotomic KLR algebra. ... More

Weighted Khovanov-Lauda-Rouquier algebrasSep 11 2012Mar 20 2017In this paper, we define a generalization of Khovanov-Lauda-Rouquier algebras which we call weighted Khovanov-Lauda-Rouquier algebras. We show that these algebras carry many of the same structures as the original Khovanov-Lauda-Rouquier algebras, including ... More

Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebraSep 18 2016Dec 19 2018We give an alternate presentation of the cyclotomic rational Cherednik algebra, which has the useful feature of compatibility with the Opdam-Dunkl subalgebra. This presentation has a diagrammatic flavor, and it provides a simple explanation of several ... More

Comparison of canonical bases for Schur and universal enveloping algebrasMar 30 2015Aug 13 2015We show that canonical bases in $\dot{U}(\mathfrak{sl}_n)$ and the Schur algebra are compatible; in fact we extend this result to $p$-canonical bases. This follows immediately from a fullness result from a functor categorifying this map. In order to prove ... More

On generalized category $\mathcal{O}$ for a quiver varietySep 15 2014Aug 22 2016In this paper, we give a method for relating the generalized category $\mathcal{O}$ defined by the author and collaborators to explicit finitely presented algebras, and apply this to quiver varieties. This allows us to describe combinatorially not just ... More

On the Hausdorff measure of non-compactness for the parametrized Prokhorov metricApr 13 2016Jul 29 2016We quantify Prokhorov's Theorem by establishing an explicit formula for the Hausdorff measure of non-compactness (HMNC) for the parametrized Prokhorov metric on the set of Borel probability measures on a Polish space. Furthermore, we quantify the Arzel\`a-Ascoli ... More

A note on multiplicative functions on progressions to large moduliApr 15 2016Apr 23 2018Let $f : \mathbf{N} \rightarrow \mathbf{C}$ be a bounded multiplicative function. Let $a$ be a fixed integer (say $a = 1$). Then $f$ is well-distributed on the progression $n \equiv a \pmod{q} \subset \{1,\dots, X\}$, for almost all primes $q \in [Q,2Q]$, ... More

On (not) computing the Mobius function using bounded depth circuitsMar 25 2011Jun 01 2012Any function F : {0,...,N-1} -> {-1,1} such that F(x) can be computed from the binary digits of x using a bounded depth circuit is orthogonal to the Mobius function mu in the sense that E_{0 <= x <= N-1} mu(x)F(x) = o(1). The proof combines a result of ... More

On a variant of the large sieveJul 31 2008Aug 01 2008We introduce a variant of the large sieve and give an example of its use in a sieving problem. Take the interval [N] = {1,...,N} and, for each odd prime p <= N^{1/2}, remove or ``sieve out'' by all n whose reduction mod p lies in some interval I_p of ... More

An l^{p}-Version of von-Neumann Dimension For Banach Space Representations of Sofic GroupsOct 25 2011Sep 30 2013A. Gournay defined a notion of $l^{p}$-dimension for subspaces of the l^{q}-left-regular representation of an amenable discrete group. We give an alternative definition that works for sofic groups and a different notion for groups satisfying the Connes ... More

An l^{p}-Version of von Neumann Dimension for Representations of Equivalence RelationsFeb 10 2013Mar 27 2013In our previous paper, "l^{p}-Version of von Neumann Dimension for Banach Space Representations of Sofic Groups," we define an extended version of von Neumann dimension for actions of a sofic group on a Banach space. This dimension was studied especially ... More

Generalizations of Joints ProblemJun 28 2016We generalize the joints problem to sets of varieties and prove almost sharp bound on the number of joints. As a special case, given a set of $N$ $2$-planes in $\mathbb{R}^6$, the number of points at which three $2$-planes intersect and span $\mathbb{R}^6$ ... More

The dark matter crisisMar 07 2001Mar 08 2001I explore several possible solutions to the ``missing satellites'' problem that challenges the collisionless cold dark matter model.

Quantum Satake in type A: part IMar 21 2014Jan 05 2017We give an interpretation of sl_n webs as morphisms between certain singular Soergel bimodules. We explain how this is a combinatorial, algebraic version of the geometric Satake equivalence (in type A). We then q-deform the construction, giving an equivalence ... More

A Diagrammatic Temperley-Lieb CategorificationMar 17 2010Mar 05 2016The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of ... More

Computing Tree Decompositions with FlowCutter: PACE 2017 SubmissionSep 26 2017We describe the algorithm behind our PACE 2017 submission to the heuristic tree decomposition computation track. It was the only competitor to solve all instances and won a tight second place. The algorithm was originally developed in the context of accelerating ... More

Collective Resonances in Nanoparticle OligomersSep 26 2017The study of nanostructured artificial media for optics has expanded rapidly over the last few decades, coupled with improvements of fabrication technology that have enabled investigation of previously unrealisable optical scattering systems. Such development ... More

Positively curved surfaces in the three-sphereApr 18 2003In this talk I will discuss an example of the use of fully nonlinear parabolic flows to prove geometric results. I will emphasise the fact that there is a wide variety of geometric parabolic equations to choose from, and to get the best results it can ... More

The exact spread of M12 is 9Sep 11 2009Apr 13 2010Let G be a group. We say that G has spread r if for any set of distinct non-trivial elements {x1,...,xr}\subset G there exists an element y\in G with the property that <xi, y> = G for every 1 0<i<r+1. The group G has exact spread r if it has spread r ... More

TLS 1.3 for engineers: An exploration of the TLS 1.3 specification and Oracle's Java implementationJan 22 2019The Internet delivered in excess of forty terabytes per second in 2017 (Cisco, 2018), and over half of today's Internet traffic is encrypted (Sandvine, 2018); enabling trade worth trillions of dollars (Statista, 2017). Yet, the underlying encryption technology ... More

A Non-Linear Roth Theorem for Sets of Positive DensityJan 05 2019Suppose that $A \subset \mathbb{R}$ has positive upper density, \[ \limsup_{|I| \to \infty} \frac{|A \cap I|}{|I|} = \delta > 0,\] and $P(t) \in \mathbb{R}[t]$ is a polynomial with no constant or linear term, or more generally a non-flat curve: a locally ... More

Nonparametric Instrumental Variables Estimation Under MisspecificationJan 04 2019Jun 25 2019Nonparametric instrumental variables estimators are highly sensitive to the failure of instrumental validity. An arbitrarily small deviation from instrumental validity can lead to large asymptotic bias for many NPIV estimators. Imposing strong smoothness ... More

Local weak$^{*}$-Convergence, algebraic actions, and a max-min principleSep 19 2018Nov 14 2018We continue our study of when topological and measure-theoretic entropy agree for algebraic action of sofic groups. Specifically, we provide a new abstract method to prove that an algebraic action is strongly sofic. The method is based on passing to a ... More

The Namer-Claimer gameAug 31 2018In each round of the Namer-Claimer game, Namer names a distance d, then Claimer claims a subset of [n] that does not contain two points that differ by d. Claimer wins once they have claimed sets covering [n]. I show that the length of this game is of ... More

A distributed simulation framework for quantum networks and channelsAug 21 2018We introduce the Simulator for Quantum Networks and Channels ($\texttt{SQUANCH}$), an open-source Python library for creating parallelized simulations of distributed quantum information processing. The framework includes many features of a general-purpose ... More

Deep In-GPU Experience ReplayJan 09 2018Experience replay allows a reinforcement learning agent to train on samples from a large amount of the most recent experiences. A simple in-RAM experience replay stores these most recent experiences in a list in RAM, and then copies sampled batches to ... More

Discrete Fractional Integration Operators Along the PrimesMay 07 2019We prove that the discrete fractional integration operators along the primes \[ T^{\lambda}_{\mathbb{P}}f(x) := \sum_{p} \frac{f(x-p)}{p^{\lambda}} \cdot \log p \] are bounded $\ell^p\to \ell^{p'}$ whenever $ \frac{1}{p'} < \frac{1}{p} - (1-\lambda), ... More

A Non-Linear Roth Theorem for Fractals of Sufficiently Large DimensionApr 23 2019May 19 2019Suppose that $d \geq 2$, and that $A \subset [0,1]$ has sufficiently large dimension, $1 - \epsilon_d < \dim_H(A) < 1$. Then for any polynomial $P$ of degree $d$ with no constant term, there exists a point configuration $\{ x, x-t,x-P(t) \} \subset A$ ... More

Spectral gap for the interchange process in a boxMay 05 2008We show that the spectral gap for the interchange process (and the symmetric exclusion process) in a $d$-dimensional box of side length $L$ is asymptotic to $\pi^2/L^2$. This gives more evidence in favor of Aldous's conjecture that in any graph the spectral ... More

Special subvarieties arising from families of cyclic covers of the projective lineJun 17 2010Oct 12 2010We consider families of cyclic covers of the projective line, where we fix the covering group and the local monodromies and we vary the branch points. We prove that there are precisely twenty such families that give rise to a special subvariety in the ... More

CM liftings of Supersingular Elliptic CurvesApr 09 2009Assuming GRH, we present an algorithm which inputs a prime $p$ and outputs the set of fundamental discriminants $D<0$ such that the reduction map modulo a prime above $p$ from elliptic curves with CM by $\order_{D}$ to supersingular elliptic curves in ... More

Reconstruction of singularities on orbifold del Pezzo surfaces from their Hilbert seriesAug 29 2018The Hilbert series of a polarised algebraic variety $(X,D)$ is a powerful invariant that, while it captures some features of the geometry of $(X,D)$ precisely, often cannot recover much information about its singular locus. This work explores the extent ... More

The constant angle problem for mean curvature flow inside rotational toriJul 18 2012We flow a hypersurface in Euclidean space by mean curvature flow with a Neumann boundary condition, where the boundary manifold is any torus of revolution. If we impose the conditions that the initial manifold is compatible and does not contain the rotational ... More

A new presentation of the cyclotomic Cherednik algebraSep 18 2016We give an alternate presentation of the cyclotomic rational Cherednik algebra. This presentation has a diagrammatic flavor, and it provides a simple explanation of several surprising facts about this algebra. It allows direct proof of the connection ... More

Big Bang Models in String TheoryMay 19 2006Dec 20 2006These proceedings are based on lectures delivered at the "RTN Winter School on Strings, Supergravity and Gauge Theories", CERN, January 16 - January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a ... More

Dimension-free Maximal Inequalities for Spherical Means in the HypercubeSep 17 2013Dec 08 2014We extend the main result of \cite{HKS} -- the existence of dimension-free $L^2$-bounds for the spherical maximal function in the hypercube -- to all $L^p, p > 1$. Our approach is motivated by the spectral technique developed in \cite{S} and \cite{NS} ... More

Improved mixing time bounds for the Thorp shuffle and L-reversal chainFeb 04 2008We prove a theorem that reduces bounding the mixing time of a card shuffle to verifying a condition that involves only pairs of cards, then we use it to obtain improved bounds for two previously studied models. E. Thorp introduced the following card shuffling ... More

Singularity formation in the Yang-Mills flowOct 08 2002May 31 2003This paper studies rapidly forming singularities in the Yang-Mills flow. It is shown that a sequence of blow-ups near the singular point converges, modulo the gauge group, to a homothetically shrinking soliton with non-zero curvature. The proof uses Hamilton's ... More

Renormalization Group and Black Hole Production in Large Extra DimensionsJul 31 2007Aug 22 2007It has been suggested that the existence of a non-Gaussian fixed point in general relativity might cure the ultraviolet problems of this theory. Such a fixed point is connected to an effective running of the gravitational coupling. We calculate the effect ... More

Construction of Maximal Hypersurfaces with Boundary ConditionsAug 22 2014Oct 07 2016We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of ... More

The chart based approach to studying the global structure of a spacetime induces a coordinate invariant boundaryJan 07 2014Feb 25 2014I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism is a chart independent ... More

Relative entropy and the Pinsker product formula for sofic groupsMay 05 2016We continue our study of the outer Pinsker factor for probability measure-preserving actions of sofic groups. Using the notion of doubly quenched convergence developed by Austin, we prove that in many cases the outer Pinsker factor of a product action ... More

Infinite-dimensional $\ell^1$ minimization and function approximation from pointwise dataMar 09 2015Jun 23 2016We consider the problem of approximating a smooth function from finitely-many pointwise samples using $\ell^1$ minimization techniques. In the first part of this paper, we introduce an infinite-dimensional approach to this problem. Three advantages of ... More

Subelliptic Resolvent Estimates for Non-self-adjoint Semiclassical Schrodinger OperatorsSep 02 2016Oct 01 2016In this paper we prove a subelliptic resolvent estimate for a class of semiclassical non-self-adjoint Schr\"odinger operators with purely imaginary potentials when the spectral parameter is in a parabolic neighborhood of the imaginary axis.

A new infinite family of non-abelian strongly real Beauville $p$-groups for every odd prime $p$Aug 02 2016We prove that there exist infinitely many a non-abelian strongly real Beauville $p$-group for every prime $p$. Previously only finitely many in the case $p=2$ have been constructed.

The Deligne-Mostow list and special families of surfacesJul 14 2016We study whether there exist infinitely many surfaces with given discrete invariants for which the H^2 is of CM type. This is a surface analogue of a conjecture of Coleman about curves. We construct a large number of examples of families of surfaces with ... More

Strongly Real Beauville GroupsMay 29 2014A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent groups. We ... More

Sarkozy's theorem in function fieldsMay 24 2016Jun 02 2016S\'ark\"ozy proved that dense sets of integers contain two elements differing by a $k$th power. The bounds in quantitative versions of this theorem are rather weak compared to what is expected. We prove a version of S\'ark\"ozy's theorem for polynomials ... More

Sparse 3D convolutional neural networksMay 12 2015Aug 25 2015We have implemented a convolutional neural network designed for processing sparse three-dimensional input data. The world we live in is three dimensional so there are a large number of potential applications including 3D object recognition and analysis ... More

A Data Science Course for Undergraduates: Thinking with DataMar 18 2015Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the increasingly sophisticated ... More

The critical CoHA of a quiver with potentialNov 27 2013Oct 27 2016Pursuing the similarity between the Kontsevich--Soibelman construction of the cohomological Hall algebra of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the inetgrality conjecture ... More

Invariance of orientation data for ind-constructible Calabi-Yau $A_{\infty}$ categories under derived equivalenceJun 28 2010Oct 25 2011We study orientation data, as introduced by Kontsevich and Soibelman in order to define well-behaved integration maps from the motivic Hall algebra of 3-dimensional Calabi-Yau categories to rings of motives. We start with an example that demonstrates ... More

Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropyFeb 18 2019We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an algebraic action of $G$ on $X,$ there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly ... More

Long arithmetic progressions of primesAug 02 2005This is an article for a general mathematical audience on the author's work, joint with Terence Tao, establishing that there are arbitrarily long arithmetic progressions of primes. It is based on several one hour lectures, chiefly given at British universities. ... More

Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and SarnakNov 17 2009Nov 18 2009This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer science. We ... More

Sum-product phenomena in F_p: a brief introductionApr 14 2009These notes arose from my Cambridge Part III course on Additive Combinatorics, given in Lent Term 2009. The aim was to understand the simplest proof of the Bourgain-Glibichuk-Konyagin bounds for exponential sums over subgroups. As a byproduct one obtains ... More

Independence Tuples and Deninger's ProblemFeb 12 2015Apr 27 2016Motivated by our results in "Polish Models and Sofic Entropy," we define modified version of the independence tuples for sofic entropy developed by Kerr and Li. These modified version essentially require that the independence sequences give rise to representations ... More

Polish Models and Sofic EntropyNov 06 2014Dec 31 2015For actions of a sofic group on probability spaces, the entropy has been defined by Bowen, with an extension by Kerr-Li. In particular, when the action is by homeomorphisms of a compact space preserving a given measure, Kerr-Li show one can compute the ... More

Evolutionary processes in clustersJun 27 2003Are the morphologies of galaxies imprinted during an early and rapid formation epoch or are they due to environmental processes that subsequently transform galaxies between morphological classes? Recent numerical simulations demonstrate that the cluster ... More

Caustic Rings and Cold Dark MatterMar 06 2001The hierarchical cold dark matter (CDM) model for structure formation is a well defined and testable model. Direct detection is the best technique for confirming the model yet predictions for the energy and density distribution of particles on earth remain ... More

The Nature Of Dark MatterFeb 03 1994Collisionless particles, such as cold dark matter, interact only by gravity and do not have any associated length scale, therefore the dark halos of galaxies should have negligible core radii. This expectation has been supported by numerical experiments ... More

Thick Soergel calculus in type ASep 10 2010Mar 05 2016Let R be the polynomial ring in n variables, acted on by the symmetric group S_n. Soergel constructed a full monoidal subcategory of R-bimodules which categorifies the Hecke algebra, whose objects are now known as Soergel bimodules. Soergel bimodules ... More

New Upper Bounds on the Spreads of Some Large Sporadic GroupsJul 12 2009May 03 2011Let G be a group. We say that G has spread r if for any set of distinct elements {x1,..., xr}\subset G there exists an element y\in G with the property that <xi, y>=G for every 0<i<r+1. Few bounds on the spread of finite simple groups are known. In this ... More

Moving surfaces by non-concave curvature functionsFeb 17 2004Feb 14 2010A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed ... More

The 1-2-3 Conjecture and related problems: a surveyNov 21 2012The 1-2-3 Conjecture, posed in 2004 by Karonski, Luczak, and Thomason, is as follows: "If G is a graph with no connected component having exactly 2 vertices, then the edges of G may be assigned weights from the set {1,2,3} so that, for any adjacent vertices ... More

Lie algebra configuration pairingOct 22 2010Dec 29 2016We give an algebraic construction of the topological graph-tree configuration pairing of Sinha and Walter beginning with the classical presentation of Lie coalgebras via coefficients of words in the associative Lie polynomial. Our work moves from associative ... More

Some properties of a Subclass of Univalent FunctionsOct 05 2012We give some coefficient bounds and distortion theorems for a subclass of univalent functions in the unit disk, and defined using the S\^{a}l\^{a}gean differential operator. The results generalize and unify some well known results for several subclasses ... More

Module structure of the center of the universal central extension of a genus zero Krichever-Novikov algebraFeb 20 2016Jun 24 2016We describe how the center of the universal central extension of the genus zero Krichever-Novikov current algebra decomposes as a direct sum of irreducible modules for automorphism group of the coordinate ring of this algebra.

Nonparametric Estimation and Identification in Non-Separable Models Using Panel DataSep 30 2018We present non-parametric identification results for panel models in the presence of a vector of unobserved heterogeneity that is not additively separable in the structural function. We exploit the time-invariance and finite dimension of the heterogeneity ... More

Quantum Mechanics in Technicolor; Analytic Expressions for a Spin-Half Particle Driven by Polychromatic LightMay 15 2018Jul 23 2018A vast collection of light-matter interactions are described by the single-frequency Rabi model. However, the physical world is polychromatic, and until now there is no general method to find analytic solutions to the multi-frequency Rabi model. We present ... More

A Topological Characterization of the Middle Perversity Intersection Complex for Arbitrary Complex Algebraic VarietiesMay 29 2019For an arbitrary complex algebraic variety which is not necessarily pure dimensional, the intersection complex can be defined as the direct sum of the Deligne-Goresky-Macpherson intersection complexes of each irreducible component. We give two axiomatic ... More

Critical $\bar{\partial}$ problems in one complex dimension and some remarks on conformally invariant variational problems in two real dimensionsJan 11 2013Sep 18 2013We will study a linear first order system, a connection $\db$ problem, on a vector bundle equipped with a connection, over a Riemann surface. We show optimal conditions on the connection forms which allow one to find a holomorphic frame, or in other words ... More

Improved mixing time bounds for the Thorp shuffleDec 14 2009E. Thorp introduced the following card shuffling model. Suppose the number of cards $n$ is even. Cut the deck into two equal piles. Drop the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then drop from ... More

Burnside graphs, algebras generated by sets of matrices, and the Kippenhahn ConjectureJul 21 2017Nov 24 2017Given a set of matrices, it is often of interest to determine the algebra they generate. Here we exploit the concept of the Burnside graph of a set of matrices, and show how it may be used to deduce properties of the algebra they generate. We prove two ... More

Consistency conditions for brane tilingsDec 22 2008Jun 09 2011Given a brane tiling on a torus, we provide a new way to prove and generalise the recent results of Szendroi, Mozgovoy and Reineke regarding the Donaldson-Thomas theory of the moduli space of framed cyclic representations of the associated algebra. Using ... More

The flush statistic on semistandard Young tableauxJan 06 2014In this note, a statistic on Young tableaux is defined which encodes data needed for the Casselman-Shalika formula.