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Persistent Markov partitions and hyperbolic components of rational mapsAug 03 2016Markov partitions persisting in a neighbourhood of hyperbolic components of rational maps were constructed under the condition that closures of Fatou components are disjoint in \cite{R1}. Given such a partition, we characterize all nearby hyperbolic components ... More

Persistent Markov partitions for rational mapsJun 26 2013Sep 30 2016A construction is given of Markov partitions for some rational maps, which persist over regions of parameter space, not confined to single hyperbolic components. The set on which the Markov partition exists, and its boundary, are analysed.

The Ending Laminations Theorem direct from Teichmuller geodesicsApr 01 2004Jul 18 2007A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.

A Curvature Flow and Applications to an Isoperimetric InequalityOct 19 2016Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the warp potential of the surface). This curvature flow preserves the area ... More

Quantum Cluster CharactersSep 29 2011Aug 13 2012Let $\FF$ be a finite field and $(Q,\bfd)$ an acyclic valued quiver with associated exchange matrix $\tilde{B}$. We follow Hubery's approach \cite{hub1} to prove our main conjecture of \cite{rupel}: the quantum cluster character gives a bijection from ... More

The Fully Quantized Axion and Dark EnergyDec 17 2012This letter reviews the exact evolution equation for the axion effective potential with the axion scale factor f and phenomenological consequences of the flat effective potential solution are discussed. It is shown that the corresponding vacuum energy ... More

Power operations for $\text{H}\underline{\mathbb{F}}_2$ and a cellular construction of $\text{BP}\mathbf{R}$Nov 21 2016Jul 02 2017We study some power operations for ordinary $C_2$-equivariant homology with coefficients in the constant Mackey functor $\underline{\mathbb{F}}_2$. In addition to a few foundational results, we calculate the action of these power operations on a $C_2$-equivariant ... More

Rank Two Non-Commutative Laurent Phenomenon and Pseudo-PositivityJul 10 2017Feb 24 2019We study polynomial generalizations of the Kontsevich automorphisms acting on the skew-field of formal rational expressions in two non-commuting variables. Our main result is the Laurentness and pseudo-positivity of iterations of these automorphisms. ... More

Proof of the Kontsevich Non-Commutative Cluster Positivity ConjectureJan 17 2012Feb 01 2012We extend the Lee-Schiffler Dyck path model to give a proof of the Kontsevich non-commutative cluster positivity conjecture with unequal parameters.

Non-perturbative Treatments of the Bosonic String and the Axion with Cosmological ImplicationsJun 28 2012This paper is about the use of a novel, exact functional quantization method as applied to two commonly studied actions in theoretical physics. The functional method in question has its roots in the exact renormalisation group flow techniques pioneered ... More

On categories of slicesNov 09 2017In this paper we give an algebraic description of the category of $n$-slices for an arbitrary group $G$, in the sense of Hill-Hopkins-Ravenel. Specifically, given a finite group $G$ and an integer $n$, we construct an explicit $G$-spectrum $W$ (called ... More

Second Order Backward Stochastic Differential Equations under Monotonicity ConditionJan 03 2012Apr 11 2014In a recent paper, Soner, Touzi and Zhang [20] have introduced a notion of second order backward stochastic differential equations (2BSDEs for short), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness ... More

An algorithm for enumerating difference setsJul 05 2018Mar 13 2019The DifSets package for GAP implements an algorithm for enumerating all difference sets in a group up to equivalence and provides access to a library of results. The algorithm functions by finding difference sums, which are potential images of difference ... More

The Feigin TetrahedronJan 17 2014Mar 19 2015The first goal of this note is to extend the well-known Feigin homomorphisms taking quantum groups to quantum polynomial algebras. More precisely, we define generalized Feigin homomorphisms from a quantum shuffle algebra to quantum polynomial algebras ... More

Greedy bases in rank 2 generalized cluster algebrasSep 10 2013In this note we extend the notion of greedy bases developed by Lee, Li, and Zelevinsky to rank two generalized cluster algebras, i.e. binomial exchange relations are replaced by polynomial exchange relations. In the process we give a combinatorial construction ... More

Why is the CMB fluctuation level 10^{-5}?Sep 08 1997Dec 12 1997We explore the qualitative changes that would occur if the amplitude Q ~ 10^{-5} of cosmological density fluctuations were different. If is less than about 10^{-6}, the cosmological objects that form would have so low virial temperatures that they may ... More

Holographic renormalization for irrelevant operators and multi-trace countertermsFeb 10 2011We investigate the structure of holographic renormalization in the presence of sources for irrelevant operators. By working perturbatively in the sources we avoid issues related to the non-renormalizability of the dual field theory. We find new classes ... More

Positivity in Quantum Cluster Algebras and Flags of Valued Quiver RepresentationsApr 04 2011Apr 05 2011In this paper we give a direct proof of the positivity conjecture for adapted quantum cluster variables. Moreover, our process allows one to explicitly compute formulas for all adapted cluster monomials and certain ordered products of adapted cluster ... More

Boundary Regularity for Conformally Compact Einstein Metrics in Even DimensionsMay 18 2007Apr 08 2008We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system of equations ... More

Coefficients of Gaussian Polynomials Modulo $N$Dec 30 2017The $q$-analogue of the binomial coefficient, known as a $q$-binomial coefficient, is typically denoted $\left[{n \atop k}\right]_q$. These polynomials are important combinatorial objects, often appearing in generating functions related to permutations ... More

Weighted Power Counting and Perturbative UnitarityDec 10 2010Feb 28 2011We consider the relationship between renormalizability and unitarity at a Lifshitz point in d dimensions. We test tree unitarity for theories containing only scalars and fermions, and for pure gauge theory. In both cases, we find the requirement of weighted ... More

On Quantum Analogue of The Caldero-Chapoton FormulaMar 12 2010Apr 24 2010Let $Q$ be any invertible valued quiver without oriented cycles. We study connections between the category of valued representations of $Q$ and expansions of cluster variables in terms of the initial cluster in quantum cluster algebras. We show that an ... More

Bach flow on homogeneous productsMar 21 2018Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group structure. The resulting ... More

Biautomatic structures in systolic Artin groupsJul 06 2018We examine the construction of Huang and Osajda that was used in their proof of the biautomaticity of Artin groups of almost large type. We describe a slightly simpler variant of that biautomatic structure, with explicit descriptions of a few small examples, ... More

Rewriting systems in sufficiently large Artin-Tits groupsNov 09 2015Jul 16 2016A conjecture of Dehornoy claims that, given a presentation of an Artin-Tits group, every word that represents the identity can be transformed into the trivial word using the braid relations, together with certain rules (between pairs of words that are ... More

Omega from Velocities in VoidsAug 23 1993We propose a method for deriving a dynamical lower bound on $\Omega$ from diverging flows in low-density regions, based on the fact that large outflows are not expected in a low-$\Omega$ universe. The velocities are assumed to be induced by gravity from ... More

Counting Hyperbolic ComponentsMar 31 2010Apr 11 2012We give formulas for the numbers of type II and type IV hyperbolic components in the space of quadratic rational maps, for all fixed periods of attractive cycles.

Using administrative data to improve the estimation of immigration to local areas in EnglandMar 03 2009Aug 24 2009International migration is now a significant driver of population change across Europe but the methods available to estimate its true impact upon sub-national areas remain inconsistent, constrained by inadequate systems of measurement and data capture. ... More

Education Stats Made Visible: Helping School District Managers Write Better Three-Year PlansSep 28 2016Problem: School district leaders in California are awash in a sea of data, but are often unable to find it, query it, or relate it with other data. Districts are islands, leaving district managers able to see only their own data. A state education agency ... More

Quasars at z=6: the survival of the fittestJul 05 2006The Sloan Digital Sky survey detected luminous quasars at very high redshift, z>6. Follow-up observations indicated that at least some of these quasars are powered by supermassive black holes (SMBHs) with masses in excess of billion solar masses. SMBHs, ... More

Massive Black Holes as Population III RemnantsJan 13 2001Mar 09 2001Recent numerical simulations of the fragmentation of primordial molecular clouds in hierarchical cosmogonies have suggested that the very first stars (the so-called Population III) may have been rather massive. Here we point out that a numerous population ... More

Dissipative Photosphere Models of Gamma-ray Bursts and X-ray FlashesDec 31 2004Apr 08 2005We consider dissipative effects occurring in the optically thick inner parts of the relativistic outflows producing gamma-ray bursts and X-ray flashes, emphasizing specially the Comptonization of the thermal radiation flux that is advected from the base ... More

Refreshed Shocks and Afterglow Longevity in GRBDec 18 1997We consider fireball models where the ejecta have a range of bulk Lorentz factors, so that the inner (lower $\Gamma$) parts may carry most of the mass, or even most of the energy. The outer shock and contact discontinuity decelerate as the fireball sweeps ... More

Capture of stellar--mass compact objects by massive black holes in galactic cuspsAug 14 1996A significant fraction of the stellar population in the cusp around central black holes of galaxies consists of compact remnants of evolved stars, such as white dwarfs, neutron stars and stellar mass black holes. We estimate the rate of capture of compact ... More

Rapid growth of high redshift black holesJun 02 2005Jul 26 2005We discuss a model for the early assembly of supermassive black holes (SMBHs) at the center of galaxies that trace their hierarchical build-up far up in the dark halo `merger tree'. Motivated by the observations of luminous quasars around redshift z=6 ... More

The Earliest Luminous Sources and the Damping Wing of the Gunn-Peterson TroughJun 20 2000Aug 18 2000Recent observations of high-redshift galaxies and quasars indicate that the hydrogen component of the intergalactic medium (IGM) must have been reionized at some redshift z>6. Prior to complete reionization, sources of ultraviolet radiation will be seen ... More

Optical and Long Wavelength Afterglow from Gamma-Ray BurstsJun 06 1996We discuss the evolution of cosmological gamma-ray burst remnants, consisting of the cooling and expanding fireball ejecta together with any swept-up external matter, after the gamma-ray event. We show that significant optical emission is predicted which ... More

GRB 990123: Reverse and Internal Shock Flashes and Late AfterglowFeb 25 1999The prompt $(t \siml 0.16$ days) light curve and initial 9-th magnitude optical flash from GRB 990123 can be attributed to a reverse external shock, or possibly to internal shocks. We discuss the time decay laws and spectral slopes expected under various ... More

Population III Gamma Ray BurstsApr 12 2010We discuss a model of Poynting-dominated gamma-ray bursts from the collapse of very massive first generation (pop. III) stars. From redshifts of order 20, the resulting relativistic jets would radiate in the hard X-ray range around 50 keV and above, followed ... More

The Edge of a Gamma Ray Burst AfterglowJun 12 1998Jul 16 1998We discuss the formation of spectral features in the decelerating ejecta of gamma-ray bursts, including the possible effect of inhomogeneities. These should lead to blueshifted and broadened absorption edges and resonant features, especially from H and ... More

Classical and quantum chaos in a circular billiard with a straight cutJul 09 1998We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. This system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos, as we vary the size of the cut. We use a quantum web to show ... More

Steep Slopes and Preferred Breaks in GRB Spectra: the Role of Photospheres and ComptonizationAug 11 1999Oct 27 1999The role of a photospheric component and of pair breakdown is examined in the internal shock model of gamma-ray bursts. We discuss some of the mechanisms by which they would produce anomalously steep low energy slopes, X-ray excesses and preferred energy ... More

Gamma-Ray Bursts: Multiwaveband Spectral Predictions for Blast Wave ModelsSep 09 1993In almost any scenario for 'cosmological' gamma-ray bursts (and in many models where they originate in our own Galaxy), the initial energy density is so large that the resulting relativistic plasma expands with $v\sim c$ producing a blast wave ahead of ... More

Iron K-alpha Emission from a Decaying Magnetar Model of Gamma-Ray BurstsOct 13 2000The recent report of X-ray Fe features in the afterglow of the gamma-ray burst GRB 991216 may provide important clues for identifying the nature of its progenitor and constraining the burst mechanism. We argue that the strong line emission can be attributed ... More

Multi-GeV Neutrinos from Internal Dissipation in GRB FireballsJul 07 2000Sub-photospheric internal shocks and transverse differences of the bulk Lorentz factor in relativistic fireball models of GRB lead to neutron diffusion relative to protons, resulting in inelastic nuclear collisions. This produces significant fluxes of ... More

Delayed Gev Emission from Cosmological Gamma-Ray Bursts : Impact of a Relativistic Wind on External MatterApr 22 1994Sudden collapse of a compact object, or coalescence of a compact binary, can generate an unsteady relativistic wind that lasts for a few seconds. The wind is likely to carry a high magnetic field; and its Lorentz factor depends on the extent to which ... More

Consistent Anisotropic Repulsions for Simple MoleculesDec 01 2000We extract atom-atom potentials from the effective spherical potentials that suc cessfully model Hugoniot experiments on molecular fluids, e.g., $O_2$ and $N_2$. In the case of $O_2$ the resulting potentials compare very well with the atom-atom potentials ... More

Gamma-Ray Burst Afterglow emission with a decaying magnetic fieldApr 24 2002Nov 06 2002In models for gamma ray burst afterglows, it is normally assumed that the external shock strongly amplifies the magnetic field and that this field maintains a steady value throughout the shocked region. We discuss the effects of modifying this (probably ... More

Tidal Interaction as the origin of early-type dwarf galaxies in group environmentOct 29 2014We present a sample of dwarf galaxies that suffer ongoing disruption by the tidal force of nearby massive galaxies. Analysing structural and stellar population properties using the archival imaging and spectroscopic data from the Sloan Digital Sky Survey ... More

Normality preserving operations for Cantor series expansions and associated fractals part IJul 03 2014Jul 08 2014It is well known that rational multiplication preserves normality in base $b$. We study related normality preserving operations for the $Q$-Cantor series expansions. In particular, we show that while integer multiplication preserves $Q$-distribution normality, ... More

Unexpected distribution phenomenon resulting from Cantor series expansionsMar 12 2014Mar 07 2015We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen known ones.

On the Existence of Finite Type Link Homotopy InvariantsOct 21 2000We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9 components, there must exist finite type homotopy invariants which are ... More

The cluster symplectic double and moduli spaces of local systemsSep 04 2015We prove a conjecture of Fock and Goncharov which provides a birational equivalence of a cluster variety called the cluster symplectic double and a certain moduli space of local systems associated to a surface.

Quantum cluster characters of Hall algebrasAug 13 2013Nov 28 2014The aim of the present paper is to introduce a generalized quantum cluster character, which assigns to each object V of a finitary Abelian category C over a finite field FF_q and any sequence ii of simple objects in C the element X_{V,ii} of the corresponding ... More

Wheeling: A diagrammatic analogue of the Duflo isomorphismJun 11 2000We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras ... More

Pion condensation in holographic QCDJul 20 2010We study pion condensation at zero temperature in a hard-wall holographic model of hadrons with isospin chemical potential. We find that the transition from the hadronic phase to the pion condensate phase is first order except in a certain limit of model ... More

Cluster algebras and triangulated surfaces. Part II: Lambda lengthsOct 20 2012Aug 13 2018For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric side, this requires ... More

Some consequences of categorificationDec 22 2017Several conjectures on acyclic skew-symmetrizable cluster algebras are proven as direct consequences of their categorification via valued quivers. These include conjectures of Fomin-Zelevinsky, Reading-Speyer, and Reading-Stella related to d-vectors, ... More

Reprocessing of radiation by multi-phase gas in Low Luminosity Accretion FlowsJul 24 1998We discuss the role that magnetic fields in low luminosity accretion flows can play in creating and maintaining a multi-phase medium, and show that small magnetically-confined clouds or filaments of dense cold gas can dramatically reprocess the `primary' ... More

Gamma-Ray BurstsJan 13 2014Gamma-ray bursts are the most luminous explosions in the Universe. They appear connected to supernova remnants from massive stars or the merger of their remnants, and their brightness makes them temporarily detectable out to the larges distances yet explored ... More

Gamma-ray bursts as X-ray depth-gauges of the UniverseMay 07 2003May 31 2003We discuss the X-ray flux of gamma-ray burst afterglows at redshifts in the range 3-30, including the effects of the intergalactic He II absorption. We point out that strong X-ray lines may form locally in burst afterglows starting minutes after the trigger. ... More

Poynting Jets from Black Holes and Cosmological Gamma-Ray BurstsSep 07 1996Mar 20 1997We discuss the properties of magnetically dominated jet-like outflows from stellar mass black holes surrounded by debris tori resulting from neutron star disruption. These jets may have narrow cores (along the rotation axis) which are almost free of baryons ... More

GeV Emission from Collisional Magnetized Gamma Ray BurstsApr 26 2011Magnetic fields may play a dominant role in gamma-ray bursts, and recent observations by the Fermi satellite indicate that GeV radiation, when detected, arrives delayed by seconds from the onset of the MeV component. Motivated by this, we discuss a magnetically ... More

Collapsar Jets, Bubbles and Fe LinesApr 25 2001Jun 20 2001In the collapsar scenario, gamma ray bursts are caused by relativistic jets expelled along the rotation axis of a collapsing stellar core. We discuss how the structure and time-dependence of such jets depends on the stellar envelope and central engine ... More

Spectral Features from Ultrarelativistic Ions in Gamma-Ray Bursts?Apr 13 1998Jun 11 1998Gamma ray burst outflows may entrain small blobs or filaments of dense, highly ionized metal rich material. Such inhomogeneities, accelerated by the flow to Lorentz factors in the range 10-100, could have a significant coverage factor, and give rise to ... More

Unsteady Outflow Models for Cosmological Gamma-Ray BurstsApr 18 1994The 'event' that triggers a gamma ray burst cannot last for more than a few seconds. This is, however, long compared with the dynamical timescale of a compact stellar-mass object ($\sim 10^{-3}$ seconds). Energy is assumed to be released as an outflow ... More

Quasars and Galaxy FormationJan 04 1998The formation of massive black holes may precede the epoch that characterises the peak of galaxy formation, as characterized by the star formation history in luminous galaxies. Hence protogalactic star formation may be profoundly affected by quasar-like ... More

A $C_2$-equivariant analog of Mahowald's Thom spectrum theoremJul 09 2017Feb 03 2018We prove that the $C_2$-equivariant Eilenberg-MacLane spectrum associated to the constant Mackey functor $\underline{\mathbb{F}}_2$ is equivalent to a Thom spectrum over ${\Omega^\rho S^{\rho + 1}}$.

Introduction to Cluster AlgebrasMar 23 2018These are notes for a series of lectures presented at the ASIDE conference 2016. The definition of a cluster algebra is motivated through several examples, namely Markov triples, the Grassmannians $Gr_2(\mathbb{C})$, and the appearance of double Bruhat ... More

E-voting in EstoniaJun 28 2016Estonia has one of the most established e-voting systems in the world. Internet voting - remote e-voting using the voter's own equipment - was piloted in 2005 with the first real elections using e-voting being conducted the same year and has been in use ... More

Companion cluster algebras to a generalized cluster algebraApr 25 2015We study the $c$-vectors, $g$-vectors, and $F$-polynomials for generalized cluster algebras satisfying a normalization condition and a power condition recovering classical recursions and separation of additions formulas. We establish a relationship between ... More

Cell Decompositions for Rank Two Quiver GrassmanniansMar 18 2018We prove that all quiver Grassmannians for exceptional representations of a generalized Kronecker quiver admit a cell decomposition. In the process, we introduce a class of regular representations which arise as quotients of consecutive preprojective ... More

Contracting theory with competitive interacting agentsMay 25 2016In a framework close to the one developed by Holmstr\"om and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, ... More

Laminations from the symplectic doubleOct 11 2014Jun 24 2016Let $S$ be a compact oriented surface with boundary together with finitely many marked points on the boundary, and let $S^\circ$ be the same surface equipped with the opposite orientation. We consider the double $S_\mathcal{D}$ obtained by gluing the ... More

Normality of different orders for Cantor series expansionsJul 25 2016Let $S \subseteq \mathbb{N}$ have the property that for each $k \in S$ the set $(S - k) \cap \mathbb{N} \setminus S$ has asymptotic density $0$. We prove that there exists a basic sequence $Q$ where the set of numbers $Q$-normal of all orders in $S$ but ... More

A breakpoint detection error function for segmentation model selection and evaluationSep 01 2015We consider the multiple breakpoint detection problem, which is concerned with detecting the locations of several distinct changes in a one-dimensional noisy data series. We propose the breakpointError, a function that can be used to evaluate estimated ... More

Symplectic groupoids for cluster manifoldsJul 10 2018We construct symplectic groupoids integrating log-canonical Poisson structures on cluster varieties of type $\mathcal{A}$ and $\mathcal{X}$ over both the real and complex numbers. Extensions of these groupoids to the completions of the cluster varieties ... More

Eilenberg-MacLane spectra as equivariant Thom spectraApr 15 2018May 01 2018We prove that the $G$-equivariant mod $p$ Eilenberg--MacLane spectrum arises as an equivariant Thom spectrum for any finite, $p$-power cyclic group $G$, generalizing a result of Behrens and the second author in the case of the group $C_2$. We also establish ... More

On the Hausdorff dimension of some sets of numbers defined through the digits of their $Q$-Cantor series expansionsJul 03 2014Jul 15 2014Following in the footsteps of P. Erd\H{o}s and A. R\'enyi we compute the Hausdorff dimension of sets of numbers whose digits with respect to their $Q$-Cantor series expansions satisfy various statistical properties. In particular, we consider difference ... More

From rubber bands to rational maps: A research reportFeb 09 2015May 19 2016This research report outlines work, partially joint with Jeremy Kahn and Kevin Pilgrim, which gives parallel theories of elastic graphs and conformal surfaces with boundary. One one hand, this lets us tell when one rubber band network is looser than another, ... More

Cyclic vs mixed homologyJul 07 2016The spectral theory of the Karoubi operator due to Cuntz and Quillen is extended to general mixed (duchain) complexes, that is, chain complexes which are simultaneously cochain complexes. Connes' coboundary map B can be viewed as a perturbation of the ... More

Relativistic SpringsMay 13 2012May 15 2012Here we develop a model for the relativistic spring. We examine the effects of revising the simple harmonic oscillator to include relativistic momentum and a delayed force law. These corrections alter two of the most significant features of the simple ... More

Elastic GraphsJul 01 2016An elastic graph is a graph with an elasticity associated to each edge, which may be viewed as a network made out of ideal rubber bands. The rubber bands may be stretched on a target space, giving an elastic energy. We characterize when a homotopy class ... More

Mediation Analysis Without Sequential Ignorability: Using Baseline Covariates Interacted with Random Assignment as Instrumental VariablesSep 06 2011Dec 31 2012In randomized trials, researchers are often interested in mediation analysis to understand how a treatment works, in particular how much of a treatment's effect is mediated by an intermediated variable and how much the treatment directly affects the outcome ... More

General indifference pricing with small transaction costsJan 14 2014Apr 04 2015We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time T, we obtain an asymptotic expansion of the utility ... More

Control Function Instrumental Variable Estimation of Nonlinear Causal Effect ModelsFeb 02 2016The instrumental variable method consistently estimates the effect of a treatment when there is unmeasured confounding and a valid instrumental variable. A valid instrumental variable is a variable that is independent of unmeasured confounders and affects ... More

Uniqueness for Some Higher-Order Geometric FlowsJul 16 2014We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding ... More

GOGMA: Globally-Optimal Gaussian Mixture AlignmentMar 01 2016Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. ... More

From Dominoes to HexagonsMay 25 2004Sep 12 2016There is a natural generalization of domino tilings to tilings of a polygon by hexagons, or, dually, configurations of oriented curves that meet in triples. We show exactly when two such tilings can be connected by a series of moves analogous to the domino ... More

A positive basis for surface skein algebrasOct 07 2013Feb 16 2015We show that the twisted SL(2) skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.

Winding numbers and SU(2)-representations of knot groupsJun 07 2007Given an abelian group $A$ and a Lie group $G$, we construct a bilinear pairing from $A\times\pi_1({\mathcal R})$ to $\pi_1(G)$, where $\mathcal R$ is a subvariety of the variety of representations $A\to G$. In the case where $A$ is the peripheral subgroup ... More

Normal equivalencies for eventually periodic basic sequencesAug 26 2014W. M. Schmidt, A. D. Pollington, and F. Schweiger have studied when normality with respect to one expansion is equivalent to normality with respect to another expansion. Following in their footsteps, we show that when $Q$ is an eventually periodic basic ... More

A duality map for the quantum symplectic doubleMay 05 2016This paper is a continuation of the author's work with Kim (arXiv:1509.01567), which provided a natural $q$-deformation of Fock and Goncharov's canonical basis for the coordinate ring of a cluster variety associated to a punctured surface. Here we consider ... More

Moral hazard under ambiguityOct 26 2015Oct 24 2016In this paper, we extend the Holmstro\"om and Milgrom problem [47] by adding uncertainty about the volatility of the output for both the Agent and the Principal. We study more precisely the impact of the "Nature" playing against the Agent and the Principal ... More

Integral Expressions for the Vassiliev Knot InvariantsJan 25 1999Jan 26 1999It has been folklore for several years in the knot theory community that certain integrals on configuration space, originally motivated by perturbation theory for the Chern-Simons field theory, converge and yield knot invariants. This was proposed independently ... More

The geometry of cluster varieties from surfacesJun 24 2016Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented surfaces with ... More

Degenerate Classical Field Theories and Boundary TheoriesNov 01 2016We introduce a framework for degenerate classical field theories in the BV formalism, which allows us to discuss many interesting examples of theories which do not admit a Lagrangian description. Further, we study phase spaces and boundary conditions ... More

A mathematical treatment of bank monitoring incentivesFeb 09 2012Apr 04 2015In this paper, we take up the analysis of a principal/agent model with moral hazard introduced in [17], with optimal contracting between competitive investors and an impatient bank monitoring a pool of long-term loans subject to Markovian contagion. We ... More

Quotients of even ringsSep 13 2018We prove that if $R$ is an $\mathbb{E}_2$-ring with homotopy concentrated in even degrees, and $\{x_j\}$ is any sequence of elements in $\pi_{2*}(R)$, then $R/(x_1,x_2,\cdots)$ admits the structure of an $\mathbb{E}_1$-$R$-algebra. This removes an assumption, ... More

Degenerate Classical Field Theories and Boundary TheoriesNov 01 2016Jan 04 2017We introduce a framework for degenerate classical field theories in the BV formalism, which allows us to discuss many interesting examples of theories which do not admit a Lagrangian description. Further, we study phase spaces and boundary conditions ... More