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On the Universal Central Extension of Hyperelliptic Current AlgebrasMar 11 2015Jul 20 2015Let $p(t)\in\mathbb C[t]$ be a polynomial with distinct roots and nonzero constant term. We describe, using Fa\'a de Bruno's formula and Bell polynomials, the universal central extension in terms of generators and relations for the hyperelliptic current ... More

Certain families of Polynomials arising in the study of hyperelliptic Lie algebrasFeb 03 2016The associative ring $R(P(t))=\mathbb C[t^{\pm1},u \,|\, u^2=P(t)]$, where $P(t)=\sum_{i=0}^na_it^i=\prod_{k=1}^n(t-\alpha_i)$ with $\alpha_i\in\mathbb C$ pairwise distinct, is the coordinate ring of a hyperelliptic curve. The Lie algebra $\mathcal{R}(P(t))=\text{Der}(R(P(t)))$ ... More

Structure of Intermediate Wakimoto ModulesJan 19 2006We show that our construction of boson type realizations of affine $\mathfrak{sl}(n+1)$ in terms of intermediate Wakimoto modules gives representations that are generically isomorphic to certain Verma type modules. We then use this identification to obtain ... More

Representations of quantum groups defined over commutative rings IIJan 19 2006In this article we study the structure of highest weight modules for quantum groups defined over a commutative ring with particular emphasis on the structure theory for invariant bilinear forms on these modules.

$\mathfrak F$-categories and $\mathfrak F$-functors in Representation Theory IIFeb 06 2018This is a partial derivative of \cite{MR94g:17044}. We give a list of examples/problems that some will find amusing.

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.

Mesh density functions based on local bandwidth applied to moving mesh methodsDec 13 2016Moving mesh methods provide an efficient way of solving partial differential equations for which large, localised variations in the solution necessitate locally dense spatial meshes. In one-dimension, meshes are typically specified using the arclength ... More

DJKM algebras I: Their Universal Central ExtensionSep 05 2010The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak g\otimes \mathbb C[t,t^{-1},u|u^2=(t^2-b^2)(t^2-c^2)]$, appearing in the work ... More

Intermediate Wakimoto modules for Affine sl(n+1)Aug 13 2003We construct certain boson type realizations of affine sl(n+1) that depend on a parameter r. When r=0 we get a Fock space realization of Imaginary Verma modules appearing in the work of the first author and when r=n they are the Wakimoto modules described ... More

Families of orthogonal Laurent polynomials, hyperelliptic Lie algebras and elliptic integralsAug 03 2015We describe a family of polynomials discovered via a particular recursion relation, which have connections to Chebyshev polynomials of the first and the second kind, and the polynomial version of Pell's equation. Many of their properties are listed in ... More

Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category $\mathcal O^q_{\text{red,im}}$Dec 04 2018Recently we defined imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$- modules in category $\mathcal O^q_{\text{red,im}}$ and showed the existence of such bases for reduced quantized imaginary Verma modules for $U_q(\widehat{\mathfrak{sl}(2)})$. ... More

Free Field Realizations of the Elliptic Affine Lie Algebra sl(2,R)+Ω_R/dRFeb 07 2009May 23 2009In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2,R) + \Omega_R/dR, where R=C[t,t^{-1},u|u^2=t^3 - 2b t^2 + t]. The first realization gives an analogue of Wakimoto's construction for Affine Kac-Moody algebras, ... More

Imaginary Verma modules and Kashiwara algebras for $U_q(\widehat{\mathfrak{sl}(2)})$Mar 05 2009We consider imaginary Verma modules for quantum affine algebra $U_q(\hat{\mathfrak{sl}(2)})$ and construct Kashiwara type operators and the Kashiwara algebra $\mathcal K_q$. We show that a certain quotient $\mathcal N_q^-$ of $U_q(\hat{\mathfrak{sl}(2)})$ ... More

Kashiwara Algebras and Imaginary Verma Modules for $U_q(\hat{\mathfrak{g}})$Aug 08 2013Aug 15 2013We consider imaginary Verma modules for quantum affine algebra $U_q(\hat{\mathfrak{g}})$, where $\hat{\mathfrak{g}}$ is of type 1 i.e. of non-twisted type, and construct Kashiwara type operators and the Kashiwara algebra $\mathcal K_q$. We show that a ... More

$N$-point locality for vertex operators: normal ordered products, operator product expansions, twisted vertex algebrasJul 18 2013In this paper we study fields satisfying $N$-point locality and their properties. We obtain residue formulae for $N$-point local fields in terms of derivatives of delta functions and Bell polynomials. We introduce the notion of the space of descendants ... More

A Wakimoto type realization of toroidal $\mathfrak{sl}_{n+1}$Jul 07 2010The authors construct a Wakimoto type realization of toroidal $\mathfrak{sl}_{n+1}$ The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor product of two polynomial rings in many commuting variables. ... More

Imaginary Verma Modules for $U_q(\widehat{\mathfrak{sl}(2)})$ and Crystal-like basesSep 02 2015We consider imaginary Verma modules for quantum affine algebraU_q(\widehat{\mathfrak{sl}(2)}) and define a crystal-like base which we call an imaginary crystal basis using the Kashiwara algebra K_q constructed in earlier work of the authors. In particular, ... More

Free field realizations of the Date-Jimbo-Kashiwara-Miwa algebraSep 27 2013We use the description of the universal central extension of the DJKM algebra $\mathfrak{sl}(2, R)$ where $ R=\mathbb C[t,t^{-1},u\,|\,u^2=t^4-2ct^2+1 ]$ given in earlier work to construct realizations of the DJKM algebra in terms of sums of partial differential ... More

The 3-point Virasoro algebra and its action on a Fock spaceFeb 13 2015Jul 20 2015We define a 3-point Virasoro algebra, and construct a representation of it on a previously defined Fock space for the 3-point affine algebra $\mathfrak{sl}(2, \mathcal R) \oplus\left( \Omega_{\mathcal R}/d{\mathcal R}\right)$.

The three point gauge algebra $\mathcal V\ltimes \mathfrak{sl}(2, \mathcal R) \oplus\left(Ω_{\mathcal R}/d{\mathcal R}\right)$ and an action on a Fock spaceFeb 11 2018The three point current algebra $\mathfrak{sl}(2,\mathcal R)$ where $\mathcal R=\mathbb C[t,t^{-1},u\,|\,u^2=t^2+4t ]$ and three-point Virasoro algebra both act on a previously constructed Fock space. In this paper we prove that the semi-direct product, ... More

Representations of $a_{\infty}$ and $d_{\infty}$ with central charge 1 on the single neutral fermion Fock space $\mathit{F^{\otimes \frac{1}{2}}}$Sep 28 2013Nov 29 2013We construct a new representation of the infinite rank Lie algebra $a_{\infty}$ with central charge $c=1$ on the Fock space $\mathit{F^{\otimes \frac{1}{2}}}$ of a single neutral fermion. We show that $\mathit{F^{\otimes \frac{1}{2}}}$ is a direct sum ... More

Realizations of the three point algebra $\mathfrak{sl}(2, \mathcal R) \oplus\left(Ω_{\mathcal R}/d{\mathcal R}\right)$Mar 27 2013Feb 22 2015We describe the universal central extension of the three point current algebra $\mathfrak{sl}(2,\mathcal R)$ where $\mathcal R=\mathbb C[t,t^{-1},u\,|\,u^2=t^2+4t ]$ and construct realizations of it in terms of sums of partial differential operators.

DJKM algebras and non-classical orthogonal polynomialsOct 08 2012Sep 07 2014We describe families of polynomials arising in the study of the universal central extensions of Lie algebras introduced by Date, Jimbo, Kashiwara, and Miwa in their work on the Landau-Lifshitz equations. Two of the families of polynomials we show satisfy ... More

An imaginary PBW basis for quantum affine algebras of type 1Jul 10 2013Mar 28 2014Let $\hat{\mathfrak g}$ be an affine Lie algebra of type 1. We give a PBW basis for the quantum affine algebra $U_q(\hat{\mathfrak g})$ with respect to the triangular decomposition of $\hat{\mathfrak g}$ associated with the imaginary positive root system. ... More

Virasoro action on Imaginary Verma modules and the operator form of the KZ-equationDec 22 2011We define the Virasoro algebra action on imaginary Verma modules for affine sl(2) and construct the analogs of Knizhnik-Zamolodchikov equation in the operator form. Both these results are based on a free field realization of imaginary Verma modules.

A pseudospectral method for solution of the radiative transport equationJan 19 2018The Boltzmann transport equation accurately describes a number of physical phenomena, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently compute numerical solutions to the time-domain transport ... More

Simple superelliptic Lie algebrasDec 25 2014Let $m\in N$, $P(t)\in C[t]$. Then we have the Riemann surfaces (commutative algebras) $R_m(P)=C[t^{\pm1},u | u^m=P(t)]$ and $S_m(P)=C[t , u| u^m=P(t)].$ The Lie algebras $\mathcal{R}_m(P)=Der(R_m(P))$ and $\mathcal{S}_m(P)=Der(S_m(P))$ are called the ... More

Reconstruction-classification method for quantitative photoacoustic tomographyAug 04 2015We propose a combined reconstruction-classification method for simultaneously recovering absorption and scattering in turbid media from images of absorbed optical energy. This method exploits knowledge that optical parameters are determined by a limited ... More

A pseudospectral method for solution of the radiative transport equationJan 19 2018Mar 18 2019The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently compute numerical ... More

On the module structure of the center of hyperelliptic Krichever-Novikov algebras IIDec 02 2018Let $R := R_{2}(p)=\mathbb{C}[t^{\pm 1}, u : u^2 = t(t-\alpha_1)\cdots (t-\alpha_{2n})] $ be the coordinate ring of a nonsingular hyperelliptic curve and let $\mathfrak{g}\otimes R$ be the corresponding current Lie algebra. \color{black} Here $\mathfrak ... More

$N$-point Virasoro Algebras and Their Modules of DensitiesAug 30 2013In this paper we introduce and study $n$-point Virasoro algebras, $\tilde{\W_a}$, which are natural generalizations of the classical Virasoro algebra and have as quotients multipoint genus zero Krichever-Novikov type algebras. We determine necessary and ... More

Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radianceAug 18 2016Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A 2D radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance ... More

A pseudospectral method for solution of the radiative transport equationJan 19 2018Mar 08 2018The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently compute numerical ... More

Molecular simulations of heterogeneous ice nucleation. I. Controlling ice nucleation through surface hydrophilicityJan 08 2015May 29 2015Ice formation is one of the most common and important processes on earth and almost always occurs at the surface of a material. A basic understanding of how the physicochemical properties of a material's surface affect its ability to form ice has remained ... More

Simple superelliptic Lie algebrasDec 25 2014Jul 22 2017Let $m\in N$, $P(t)\in C[t]$. Then we have the Riemann surfaces (commutative algebras) $R_m(P)=C[t^{\pm1},u | u^m=P(t)]$ and $S_m(P)=C[t , u| u^m=P(t)].$ The Lie algebras $\mathcal{R}_m(P)=Der(R_m(P))$ and $\mathcal{S}_m(P)=Der(S_m(P))$ are called the ... More

Molecular simulations of heterogeneous ice nucleation. II. Peeling back the layersJan 08 2015May 29 2015Coarse grained molecular dynamics simulations are presented in which the sensitivity of the ice nucleation rate to the hydrophilicity of a graphene nanoflake is investigated. We find that an optimal interaction strength for promoting ice nucleation exists, ... More

Equations of Parametric Surfaces via SyzygiesOct 11 2000Feb 22 2001The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula for a parametrized surface.

A perturbation result for quasi-linear stochastic differential equations in UMD Banach spacesMar 07 2012We consider the effect of perturbations to a quasi-linear parabolic stochastic differential equation set in a UMD Banach space $X$. To be precise, we consider perturbations of the linear part, i.e. the term concerning a linear operator $A$ generating ... More

Pathwise space approximations of semi-linear parabolic SPDEs with multiplicative noiseDec 18 2018We provide convergence rates for space approximations of semi-linear stochastic differential equations with multiplicative noise in a Hilbert space. The space approximations we consider are spectral Galerkin and finite elements, and the type of convergence ... More

Some remarks on tangent martingale difference sequences in $L^1$-spacesJan 04 2008Let X be a Banach space. Suppose that for all $p\in (1, \infty)$ a constant $C_{p,X}$ depending only on X and p exists such that for any two X-valued martingales f and g with tangent martingale difference sequences one has \[\E\|f\|^p \leq C_{p,X} \E\|g\|^p ... More

Layered posets and Kunen's universal collapseMay 30 2015Jul 16 2016We develop the theory of layered posets, and use the notion of layering to prove a new iteration theorem (Theorem 6): if $\kappa$ is weakly compact then any universal Kunen iteration of $\kappa$-cc posets (each possibly of size $\kappa$) is $\kappa$-cc, ... More

Chang's Conjecture and semiproperness of nonreasonable posetsMay 01 2016Let $\mathbb{Q}$ denote the poset which adds a Cohen real then shoots a club through the complement of $\big( [\omega_2]^\omega \big)^V$ with countable conditions. We prove that the version of Strong Chang's Conjecture from \cite{MR2965421} implies semiproperness ... More

Local Complete Intersections in P^2 and Koszul SyzygiesOct 09 2001We study the syzygies of a codimension two ideal I = <f_1,f_2,f_3> in k[x,y,z]. Our main result is that the module of syzygies vanishing (scheme-theoretically) at the zero locus Z = V(I) is generated by the Koszul syzygies iff Z is a local complete intersection. ... More

Quotients of Strongly Proper Forcings and Guessing ModelsJun 12 2014Jun 05 2015We prove that a wide class of strongly proper forcing posets have quotients with strong properties. Specifically, we prove that quotients of forcing posets which have simple universal strongly generic conditions on a stationary set of models by certain ... More

Prevalence of Generic Laver DiamondMay 12 2014Viale \cite{Viale_GuessingModel} introduced the notion of Generic Laver Diamond at $\kappa$---which we denote $\Diamond_{\text{Lav}}(\kappa)$---asserting the existence of a single function from $\kappa \to H_\kappa$ that behaves much like a supercompact ... More

Least-perimeter partition of the disc into $N$ regions of two different areasJan 02 2019We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected simple cubic graphs ... More

Forcing axioms, approachability, and stationary set reflectionJul 16 2018Apr 07 2019We prove a variety of theorems about stationary set reflection and concepts related to internal approachability. We prove that an implication of Fuchino-Usuba relating stationary reflection to a version of Strong Chang's Conjecture cannot be reversed; ... More

Namba forcing, weak approximation, and guessingOct 02 2016May 25 2018We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle $\textsf{IGMP}$, $\textsf{GMP}$ together with $2^\omega \le \omega_2$ is consistent with the existence of an $\omega_1$-distributive ... More

Vector-valued decoupling and the Burkholder-Davis-Gundy inequalityJul 12 2011Aug 26 2012Let X be a Banach space. We prove p-independence of the one-sided decoupling inequality for X-valued tangent martingales as introduced by Kwapien and Woyczynski. It is known that a Banach space X satisfies the two-sided decoupling inequality if and only ... More

Vector-valued stochastic delay equations - a semigroup approachJun 28 2010Nov 12 2010Let E be a type 2 UMD Banach space, H a Hilbert space and let p be in [1,\infty). Consider the following stochastic delay equation in E: dX(t) = AX(t) + CX_t + b(X(t),X_t)dW_H(t), t>0; X(0) = x_0; X_0 = f_0. Here A : D(A) -> E is the generator of a C_0-semigroup, ... More

Regularity and Segre-Veronese embeddingsMay 29 2008This paper studies the regularity of certain coherent sheaves that arise naturally from Segre-Veronese embeddings of a product of projective spaces. We give an explicit formula for the regularity of these sheaves and show that their regularity is subadditive. ... More

Moment Maps, Strict Linear Precision, and Maximum Likelihood Degree OneOct 08 2018We study the moment maps of a smooth projective toric variety. In particular, we characterize when the moment map coming from the quotient construction is equal to a weighted Fubini-Study moment map. This leads to an investigation into polytopes with ... More

Convergence rates of the splitting scheme for parabolic linear stochastic Cauchy problemsJun 11 2009Feb 25 2010We study the splitting scheme associated with the linear stochastic Cauchy problem dU(t) = AU(t) dt + dW(t), where A is the generator of an analytic C_0-semigroup S={S(t)} on a Banach space E and W={W(t)} is a Brownian motion with values in a fractional ... 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

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

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.

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

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

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

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

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

Positivity for quantum cluster algebrasJan 28 2016Oct 04 2017Building on work by Kontsevich, Soibelman, Nagao and Efimov, we prove the positivity of quantum cluster coefficients for all skew-symmetric quantum cluster algebras, via a proof of a conjecture first suggested by Kontsevich on the purity of mixed Hodge ... 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

Relations between tautological cycles on JacobiansJun 23 2007Jul 09 2007We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results about the structure ... 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.

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

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

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

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

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 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

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

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

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

A simple hierarchical Bayesian model for simultaneous inference of tournament graphs and informant errorApr 29 2013Oct 11 2013The paper presents a hierarchical Bayesian model for simultaneous inference of tournament graphs and informant error. From multiple informant reports or measurement instrument outputs, the model estimates the structure of a criterion (i.e., true) tournament ... More

The Calabi-Yau equation on almost-Kahler four-manifoldsApr 18 2006Mar 26 2007Let (M, \omega) be a compact symplectic 4-manifold with a compatible almost complex structure J. The problem of finding a J-compatible symplectic form with prescribed volume form is an almost-K\"ahler analogue of Yau's theorem and is connected to a programme ... More

Interest Point Detection for Reconstruction in High Granularity Tracking DetectorsJun 15 2010This paper presents an investigation of the use of interest point detection algorithms from image processing applied to reconstruction of interactions in high granularity tracking detectors. Their purpose is to extract keypoints from the data as input ... More

The Kähler-Ricci flow on compact Kähler manifoldsFeb 24 2015These notes are based on a lecture series given at the Park City Math Institute in the summer of 2013. The notes are intended as a leisurely introduction to the K\"ahler-Ricci flow on compact K\"ahler manifolds, aimed at graduate students with some background ... More

Some Optimizations for (Maximal) Multipliers in $L^p$Feb 08 2014We use Oberlin, Nazarov, and Thiele's Multi-Frequency Calder\'{o}n-Zygmund decomposition to lower estimates on maximal multipliers in $L^p$. We also improve on classical multiplier results of Coifman, Rubio de Francia, and Semmes.

Essential dimension and the flats spanned by a point setFeb 25 2016Oct 12 2016Let $P$ be a finite set of points in $\mathbb{R}^d$ or $\mathbb{C}^d$. We answer a question of Purdy on the conditions under which the number of hyperplanes spanned by $P$ is at least the number of $(d-2)$-flats spanned by $P$. In answering this question, ... More

Coxeter groups as Beauville groupsAug 11 2015Apr 21 2016We generalize earlier work of Fuertes and Gonz\'{a}lez-Diez as well as earlier work of Bauer, Catanese and Grunewald to Coxeter groups in general by classifying which of these are strongly real Beauville groups. As a consequence of this we determine which ... More

Recent work on Beauville surfaces, structures and groupsMay 29 2014Beauville surfaces are a class of complex surfaces defined by letting a finite group $G$ act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group $G$. In ... More

Ultraviolet Light from Old Stellar PopulationsNov 29 1996We consider the general theoretical problem of ultraviolet light from old stellar populations (t > 2 Gyr), and the interpretation of galaxy spectra at short wavelengths (lamda < 3200A) The sources believed to be responsible for the observed `ultraviolet ... More

The Far-Ultraviolet Radiation from Elliptical GalaxiesJan 21 1997Since the discovery of the Ultraviolet Upturn Phenomenon (``UVX'') in early-type galaxies it has been clear that the stellar populations of such systems contain an unexpected hot component. Recent work has provided strong circumstantial evidence that ... More