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Complex Relations in a Deep Structured Prediction Model for Fine Image SegmentationMay 24 2018Many deep learning architectures for semantic segmentation involve a Fully Convolutional Neural Network (FCN) followed by a Conditional Random Field (CRF) to carry out inference over an image. These models typically involve unary potentials based on local ... More

The G Dwarf Problem Exists in Other GalaxiesJun 04 1996Stellar population models with abundance distributions determined from the analytic Simple model of chemical evolution fail to match observations of the nuclei of bulge-dominated galaxies in three respects. First, the spectral energy distribution in the ... More

A model for interpreting social interactions in local image regionsDec 26 2017Understanding social interactions (such as 'hug' or 'fight') is a basic and important capacity of the human visual system, but a challenging and still open problem for modeling. In this work we study visual recognition of social interactions, based on ... More

Minimal Images in Deep Neural Networks: Fragile Object Recognition in Natural ImagesFeb 08 2019The human ability to recognize objects is impaired when the object is not shown in full. "Minimal images" are the smallest regions of an image that remain recognizable for humans. Ullman et al. 2016 show that a slight modification of the location and ... More

Structured learning and detailed interpretation of minimal object imagesNov 29 2017We model the process of human full interpretation of object images, namely the ability to identify and localize all semantic features and parts that are recognized by human observers. The task is approached by dividing the interpretation of the complete ... More

Quark-Squark Alignment RevisitedJun 06 2002We re-examine the possibility that the solution to the supersymmetric flavor problem is related to small mixing angles in gaugino couplings induced by approximate horizontal Abelian symmetries. We prove that, for a large class of models, there is a single ... More

New Physics and Future B FactoriesFeb 13 2002Further experimental and theoretical studies of the physics of flavor and CP violation are well motivated. Within the supersymmetric framework, higher precision measurements will allow to explore classes of models with stronger degree of universality: ... More

Phenomenological Constraints on $\barΛ$ and $λ_1$Jan 13 1994Combining the experimental data on the inclusive decays $D\to X\,e\,\nu$, $B\to X\,e\,\nu$ and $B\to X\,\tau\,\nu$, we find severe constraints on the $\bar\Lambda$ and $\lambda_1$ parameters of the Heavy Quark Effective Theory. In particular, we get $\bar\Lambda<0.7\,$GeV. ... More

On the accuracy of solving confluent Prony systemsJun 06 2011Jun 26 2012In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation ... More

Geometry and Singularities of the Prony mappingJan 07 2013Prony mapping provides the global solution of the Prony system of equations \[ \Sigma_{i=1}^{n}A_{i}x_{i}^{k}=m_{k},\ k=0,1,...,2n-1. \] This system appears in numerous theoretical and applied problems arising in Signal Reconstruction. The simplest example ... More

Zeroes and rational points of analytic functionsAug 08 2016Dec 16 2017For an analytic function $f(z)=\sum_{k=0}^\infty a_kz^k$ on a neighbourhood of a closed disc $D\subset {\bf C}$, we give assumptions, in terms of the Taylor coefficients $a_k$ of $f$, under which the number of intersection points of the graph $\Gamma_f$ ... More

On algebraic properties of low rank approximations of Prony systemsMar 25 2018We consider the reconstruction of spike train signals of the form $$F(x) = \sum_{i=1}^d a_i \delta(x-x_i),$$ from their moments measurements $m_k(F)=\int x^k F(x) dx = \sum_{i=1}^d a_ix^k$. When some of the nodes $x_i$ near collide the inversion becomes ... More

SU(3) Relations and the CP Asymmetry in $B \to K_S K_S K_S$May 23 2005The CP asymmetry in the $B \to K_S K_S K_S$ decay is being measured by the two B factories. A large deviation of the CP asymmetry $S_{K_S K_S K_S}$ from $-S_{\psi K_S}$ and/or of $C_{K_S K_S K_S}$ from zero would imply new physics in $b \to s$ transitions. ... More

Gaussian Mixture Generative Adversarial Networks for Diverse Datasets, and the Unsupervised Clustering of ImagesAug 30 2018Generative Adversarial Networks (GANs) have been shown to produce realistically looking synthetic images with remarkable success, yet their performance seems less impressive when the training set is highly diverse. In order to provide a better fit to ... More

Implications of Horizontal Symmetries on Baryon Number Violation in Supersymmetric ModelsAug 18 1994The smallness of the quark and lepton parameters and the hierarchy between them could be the result of selection rules due to a horizontal symmetry broken by a small parameter. The same selection rules apply to baryon number violating terms. Consequently, ... More

Constraining the Phase of B_s - \bar{B}_s MixingMay 02 2006Jul 27 2006New physics contributions to B_s-\bar{B}_s mixing can be parametrized by the size (r_s^2) and the phase (2\theta_s) of the total mixing amplitude relative to the Standard Model amplitude. The phase has so far been unconstrained. We first use the D0 measurement ... More

Relating leptogenesis parameters to light neutrino massesFeb 15 2007We obtain model independent relations among neutrino masses and leptogenesis parameters. We find exact relations that involve the CP asymmetries $\epsilon_{N_\alpha}$, the washout parameters $\tilde m_\alpha$ and $\theta_{\alpha\beta}$, and the neutrino ... More

Accuracy of Algebraic Fourier Reconstruction for Shifts of Several SignalsNov 14 2013Apr 14 2014We consider the problem of "algebraic reconstruction" of linear combinations of shifts of several known signals $f_1,\ldots,f_k$ from the Fourier samples. Following \cite{Bat.Sar.Yom2}, for each $j=1,\ldots,k$ we choose sampling set $S_j$ to be a subset ... More

Extra-Large Remnant Recoil Velocities and Spins from Near-Extremal-Bowen-York-Spin Black-Hole BinariesMar 04 2008Jul 17 2008We evolve equal-mass, equal-spin black-hole binaries with specific spins of a/mH 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counter-aligned and pointing ... More

A New Stability Result for Viscosity Solutions of Nonlinear Parabolic Equations with Weak Convergence in TimeJan 06 2006We present a new stability result for viscosity solutions of fully nonlinear parabolic equations which allows to pass to the limit when one has only weak convergence in time of the nonlinearities.

Sub-Gaussian tails for the number of triangles in G(n,p)Sep 13 2009Let X be the random variable that counts the number of triangles in the random graph G(n,p). We show that for some absolute constant c, the probability that X deviates from its expectation by at least \lambda \var(X)^{1/2} is at most e^{-c\lambda^2}, ... More

Some large polyominoe's perimeter: a stochastic analysisJul 29 2018Aug 30 2018In this paper, we analyze the stochastic properties of some large size (area) polyominoe's perimeter such that the directed column-convex polyomino, the column-convex polyomino, the directed diagonally-convex polyomino, the staircase (or parallelogram) ... More

Weak Identification and Estimation of Social Interaction ModelsFeb 16 2019The identification of the network effect is based on either group size variation, the structure of the network or the relative position in the network. I provide easy-to-verify necessary conditions for identification of undirected network models based ... More

Comparing an analytical spacetime metric for a merging binary to a fully non-linear numerical evolution using curvature scalarsFeb 08 2018We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling black-hole binaries ... More

Can an evolving Universe host a static event horizon?Oct 02 2012Nov 09 2012We prove the existence of general relativistic perfect fluid black hole solutions, and demonstrate the phenomenon for the $P=w\rho$ class of equations of state. While admitting a local time-like Killing vector on the event horizon itself, the various ... More

Contraction of a Generalized Metric StructureDec 10 2008In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we introduce a ... More

Leibniz Homology of the Affine Indefinite Orthogonal Lie AlgebraJan 04 2013In this paper, we compute the Leibniz (co)homology of the affine indefinite orthogonal Lie algebra. This calculation generalizes a result \cite[corollary 4.5]{JL} obtained by Jerry Lodder. We construct several indefinite orthogonal invariants in terms ... More

The perimeter of uniform and geometric words: a probabilistic analysisAug 21 2017May 12 2018Let a word be a sequence of $n$ i.i.d. integer random variables. The perimeter $P$ of the word is the number of edges of the word, seen as a polyomino. In this paper, we present a probabilistic approach to the computation of the moments of $P$. This is ... More

A local description of 2-dimensional almost minimal sets bounded by a curveJan 29 2019We study the local regularity of sliding almost minimal sets of dimension 2 in $R^n$ , bounded by a smooth curve $L$. These are a good way to model soap films bounded by a curve, and their definition is similar to Almgren's. We aim for a local description, ... More

Multifractal Properties of Price Fluctuations of Stocks and CommoditiesAug 01 2003We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal ... More

Future prospects of B physicsApr 27 2009Jul 09 2009In recent years, the CKM picture of flavor and CP violation has been confirmed, mainly due to B decay data. Yet, it is likely that there are small corrections to this picture. We expect to find new physics not much above the weak scale. This new physics ... More

Reconstruction of Planar Domains from Partial Integral MeasurementsMay 25 2012We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear differential equation ... More

Geometry and Singularities of Prony varietiesJun 05 2018We start a systematic study of the topology, geometry and singularities of the Prony varieties $S_q(\mu)$, defined by the first $q+1$ equations of the classical Prony system $$\sum_{j=1}^d a_j x_j^k = \mu_k, \ k= 0,1,\ldots \ .$$ Prony varieties, being ... More

Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of viewJan 07 2018Apr 22 2018This is a survey paper discussing one specific (and classical) system of algebraic equations - the so called "Prony system". We provide a short overview of its unusually wide connections with many different fields of Mathematics, stressing the role of ... More

Prony Scenarios and Error Amplification in a Noisy Spike-Train ReconstructionFeb 25 2018Mar 08 2018The paper is devoted to the characterization of the geometry of Prony curves arising from spike-train signals. We give a sufficient condition which guarantees the blowing up of the amplitudes of a Prony curve S in case where some of its nodes tend to ... More

Towards Unstructured Mesh Generation Using the Inverse Poisson ProblemFeb 17 2008A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical relation between ... More

Simulation Study Comparing Two Tests of Second-order Stationarity and Confidence Intervals for Localized AutocovarianceMar 21 2016This report compares two tests of second-order stationarity through simulation. It also provides several examples of localised autocovariances and their approximate confidence intervals on different real and simulated data sets. An empirical verification ... More

Two applications of polylog functions and Euler sumsSep 25 2017Sep 30 2017Let $I(n):=\int_0^1 [x^n+(1-x)^n]^\frac1n dx.$ In this paper, we show that $I(n)= \sum_0^\infty \frac{I_i}{n^i},n\rightarrow \infty$ and we compute $I_i, i =0..5$, obtained by polylog functions and Euler sums. As a corollary, we obtain explicit expressions ... More

Triangle-free Subgraphs at the Triangle-Free ProcessMar 10 2009Jul 06 2009We consider the triangle-free process: given an integer n, start by taking a uniformly random ordering of the edges of the complete n-vertex graph K_n. Then, traverse the ordered edges and add each traversed edge to an (initially empty) evolving graph ... More

Einstein-Weyl structures corresponding to diagonal Kähler Bianchi IX metricsDec 05 1996Jun 13 1997We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal K\"ahler Bianchi IX metric. In particular, we show that the subclass of Einstein-Weyl structures with a constant conformal scalar curvature is the one with ... More

Extended QED with CPT violation : clarifying some controversiesNov 01 2006We rediscuss the controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term. We analyse some consequences of the division of the Lagrangian density between "free part" and "interaction part". ... More

Non linear $σ$ models : renormalisability versus geometryJul 17 1999After some recalls on the standard (non)-linear $\sigma$ model, we discuss the interest of B.R.S. symmetry in non-linear $\sigma$ models renormalisation. We also emphasise the importance of a correct definition of a theory through physical constraints ... More

Solution to Rubel's question about differentially algebraic dependence on initial valuesOct 31 2002Nov 28 2002We prove that, for generic systems of polynomial differential equations, the dependence of the solution on the initial conditions is not differentially algebraic. This answers, in the negative, a question posed by L.A. Rubel.

New Approaches in designing a Zeeman-SlowerDec 10 2012Jan 17 2013We present two new approaches for the design of a Zeeman-Slower, which rely on optimal compliance with the adiabatic following condition and are applicable to a wide variety of systems. The first approach is an analytical one, based on the assumption ... More

Progress in the Development of Plasma Panel Radiation DetectorsDec 30 2010Plasma Display Panels (PDP), the underlying engine of panel plasma television displays, are being investigated for their utility as radiation detectors called Plasma Panel Sensors (PPS). The PPS a novel variant of a micropattern radiation detector, is ... More

The Pattern of CP Asymmetries in $b\to s$ TransitionsMar 16 2005Oct 06 2005New CP violating physics in $b\to s$ transitions will modify the CP asymmetries in B decays into final CP eigenstates ($\phi K_S$, $\eta^\prime K_S$, $\pi^0 K_S$, $\omega K_S$, $\rho^0 K_S$ and $\eta K_S$) from their Standard Model values. In a model ... More

Time Variations in the Scale of Grand UnificationSep 12 2002Oct 08 2002We study the consequences of time variations in the scale of grand unification, $M_U$, when the Planck scale and the value of the unified coupling at the Planck scale are held fixed. We show that the relation between the variations of the low energy gauge ... More

The importance of N2 leptogenesisDec 15 2006Sep 17 2007We argue that fast interactions of the lightest singlet neutrino $N_1$ would project part of a preexisting lepton asymmetry $L_p$ onto a direction that is protected from $N_1$ washout effects, thus preventing it from being erased. In particular, we consider ... More

Climate network suggests enhanced El Niño global impacts in localized areasSep 02 2016We construct directed and weighted climate networks based on near surface air temperature to investigate the global impacts of El Nino and La Nina. We find that regions which are characterized by higher positive or negative network in weighted links, ... More

Implications of the CP asymmetry in semileptonic B decayFeb 04 2002Apr 29 2002Recent experimental searches for $A_{SL}$, the CP asymmetry in semileptonic B decay, have reached an accuracy of order one percent. Consequently, they give meaningful constraints on new physics. We find that cancellations between the Standard Model (SM) ... More

High Energy Collisions of Black Holes Numerically RevisitedJun 19 2015Aug 24 2016We use fully nonlinear numerical relativity techniques to study high energy head-on collision of nonspinning, equal-mass black holes to estimate the maximum gravitational radiation emitted by these systems. Our simulations include improvements in the ... More

Evolutions of unequal mass, highly spinning black hole binariesNov 22 2017We evolve a binary black hole system bearing a mass ratio of $q=m_1/m_2=2/3$ and individual spins of $S^z_1/m_1^2=0.95$ and $S^z_2/m_2^2=-0.95$ in a configuration where the large black hole has its spin antialigned with the orbital angular momentum, $L^z$, ... More

Kac-Moody Lie algebras graded by Kac-Moody root systemsJul 20 2012We look to gradations of Kac-Moody Lie algebras by Kac-Moody root systems with finite dimensional weight spaces. We extend, to general Kac-Moody Lie algebras, the notion of C-admissible pair as introduced by H. Rubenthaler and J. Nervi for semi-simple ... More

Exotic colored scalars at the LHCOct 20 2016We study the phenomenology of exotic color-triplet scalar particles $X$ with charge $|Q|=2/3, 4/3,5/3,7/3,8/3$ and $10/3$. If $X$ is a non-singlet of $SU(2)_W$ representation, mass splitting within the multiplet allows for cascade decays of the members ... More

Stability of partial Fourier matrices with clustered nodesSep 03 2018We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary "off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the nodes on the unit circle), in the case when some of the nodes are separated ... More

Spline functions, the discrete biharmonic operator and approximate eigenvaluesFeb 27 2017Nov 30 2017The biharmonic operator plays a central role in a wide array of physical models, notably in elasticity theory and the streamfunction formulation of the Navier-Stokes equations. The need for corresponding numerical simulations has led, in recent years, ... More

SU(3) Relations and the CP Asymmetries in B Decays to $η' K_S$, $φ K_S$ and $K^+ K^- K_S$Mar 20 2003Jun 05 2003We consider CP asymmetries in neutral $B$ meson decays to $\eta' K_S$, $\phi K_S$, and $K^+ K^- K_S$. We use SU(3) relations to estimate or bound the contributions to these amplitudes proportional to $V_{ub}^*V_{us}$. Such contributions induce a deviation ... More

An exact method to compute a $p$-value for the beyond-pairwise correlations among cancer gene mutationsMay 18 2015The increasing observation of mutual exclusivity correlations among cancer gene mutations is a key component for identifying driver events or pathways in cancer genome analysis. Here we report a rigorous statistical method to compute an exact $p$-value ... More

Scalar field "mini--MACHOs": a new explanation for galactic dark matterJul 12 2004We examine the possibility that galactic halos are collisionless ensembles of scalar field ``massive compact halo objects'' (MACHOs). Using mass constraints from MACHO microlensing and from theoretical arguments on halos made up of massive black holes, ... More

Comparison of Numerical and Post-Newtonian Waveforms for Generic Precessing Black-Hole BinariesAug 05 2008Jan 01 2009We compare waveforms and orbital dynamics from the first long-term, fully non-linear, numerical simulations of a generic black-hole binary configuration with post-Newtonian predictions. The binary has mass ratio q~0.8 with arbitrarily oriented spins of ... More

Cascading Failures in Networks with Proximate Dependent NodesOct 21 2013We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an initial attack. We ... More

A deep generative model for single-cell RNA sequencing with application to detecting differentially expressed genesOct 13 2017Oct 17 2017We propose a probabilistic model for interpreting gene expression levels that are observed through single-cell RNA sequencing. In the model, each cell has a low-dimensional latent representation. Additional latent variables account for technical effects ... More

Information Constraints on Auto-Encoding Variational BayesMay 22 2018Nov 29 2018Parameterizing the approximate posterior of a generative model with neural networks has become a common theme in recent machine learning research. While providing appealing flexibility, this approach makes it difficult to impose or assess structural constraints ... 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Stabilization phenomena in Kac-Moody algebras and quiver varietiesMay 30 2005Aug 29 2006Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X_0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X, we show that if we expand X by extending X_0, the branching ... 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

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

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

A compactness result in approach theory with an application to the continuity approach structureApr 28 2015Jun 17 2015We establish a compactness result in approach theory which we apply to obtain a generalization of Prokhorov's Theorem for the continuity approach structure.

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

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

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