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Eigenvalues of Large Sample Covariance Matrices of Spiked Population ModelsAug 12 2004We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample ... More

Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samplesFeb 25 2009The detection problem in statistical signal processing can be succinctly formulated: Given m (possibly) signal bearing, n-dimensional signal-plus-noise snapshot vectors (samples) and N statistically independent n-dimensional noise-only snapshot vectors, ... More

The Random Matrix Regime of Maronna's M-estimator with elliptically distributed samplesNov 27 2013This article demonstrates that the robust scatter matrix estimator $\hat{C}_N\in {\mathbb C}^{N\times N}$ of a multivariate elliptical population $x_1,\ldots,x_n\in {\mathbb C}^N$ originally proposed by Maronna in 1976, and defined as the solution (when ... More

On the signal-to-interference ratio of CDMA systems in wireless communicationsFeb 28 2007Let $\{s_{ij}:i,j=1,2,...\}$ consist of i.i.d. random variables in $\mathbb{C}$ with $\mathsf{E}s_{11}=0$, $\mathsf{E}|s_{11}|^2=1$. For each positive integer $N$, let $\mathbf{s}_k={\mathbf{s}}_k(N)=(s_{1k},s_{2k},...,s_{Nk})^T$, $1\leq k\leq K$, with ... More

Robust Estimates of Covariance Matrices in the Large Dimensional RegimeApr 24 2012Apr 14 2014This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using tools from random ... More

Eigen-Inference for Energy Estimation of Multiple SourcesJan 22 2010Oct 24 2010In this paper, a new method is introduced to blindly estimate the transmit power of multiple signal sources in multi-antenna fading channels, when the number of sensing devices and the number of available samples are sufficiently large compared to the ... More

A CLT for Information-theoretic statistics of Non-centered Gram random matricesJul 01 2011In this article, we study the fluctuations of the random variable: $$ {\mathcal I}_n(\rho) = \frac 1N \log\det(\Sigma_n \Sigma_n^* + \rho I_N),\quad (\rho>0) $$ where $\Sigma_n= n^{-1/2} D_n^{1/2} X_n\tilde D_n^{1/2} +A_n$, as the dimensions of the matrices ... More

Gaussian fluctuations for non-Hermitian random matrix ensemblesFeb 18 2005Feb 28 2007Consider an ensemble of $N\times N$ non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded densities and finite ... More

Singular values of large non-central random matricesFeb 08 2018We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It provides a decomposition ... More

A Deterministic Equivalent for the Analysis of Correlated MIMO Multiple Access ChannelsJun 19 2009Oct 24 2010In this article, novel deterministic equivalents for the Stieltjes transform and the Shannon transform of a class of large dimensional random matrices are provided. These results are used to characterise the ergodic rate region of multiple antenna multiple ... More

A note on the CLT of the LSS for sample covariance matrix from a spiked population modelApr 23 2013Jul 05 2013In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance structure. ... More

Separation of the largest eigenvalues in eigenanalysis of genotype data from discrete subpopulationsJan 18 2013We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of subpopulations represented ... More

TASI lectures on cosmological observables and string theoryJun 11 2016These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of ... More

Backdraft: String Creation in an Old Schwarzschild Black HoleFeb 06 2014Feb 21 2014We analyze string production in the background of a Schwarzschild black hole, after developing first quantized methods which capture string-theoretic nonadiabatic effects which can exceed naive extrapolations of effective field theory. Late-time infalling ... More

Inflation in string theory confronts data/Les modèles d'inflation en théorie des cordes face aux observationsDec 07 2015Following the 2015 Planck release, we briefly comment on the status and some ongoing opportunities in the interface between inflationary cosmology, string theory, and CMB data. The constraints in the $r$-$n_s$ plane introduce a new parameter into inflationary ... More

The dangerous irrelevance of string theoryJun 08 2017We comment on the relation between string theory and empirical science, grounding our discussion in cosmology, a subject with increasingly precise data in which this connection operates at several levels. It is important to take into account the phenomenon ... More

Cosmological Numerical Simulations of Radio Relics in Galaxy Clusters: Insights for Future ObservationsJan 18 2011The acceleration of electrons at shock fronts is thought to be responsible for radio relics, extended radio features in the vicinity of merging galaxy clusters. By combining high resolution Adaptive Mesh Refinement Hydro/N-body cosmological simulations ... More

Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolutionAug 23 2000A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing a set of additional, ... More

String-theoretic breakdown of effective field theory near black hole horizonsApr 21 2015We investigate the validity of the equivalence principle near horizons in string theory, analyzing the breakdown of effective field theory caused by longitudinal string spreading effects. An experiment is set up where a detector is thrown into a black ... More

4d Conformal Field Theories and Strings on OrbifoldsFeb 25 1998Mar 16 1998We propose correspondences between 4d quantum field theories with N=2,1,0 (super)conformal invariance and Type IIB string theory on various orbifolds. We argue using the spacetime string theory, and check using the beta functions (exactly for N=2,1 and ... More

Chirality Changing Phase Transitions in 4d String VacuaApr 25 1997May 12 1997We provide evidence that some four-dimensional N=1 string vacua with different numbers of generations are connected through phase transitions. The transitions involve going through a point in moduli space where there is a nontrivial fixed point governing ... More

On Vanishing Two Loop Cosmological Constants in Nonsupersymmetric StringsOct 16 1998It has recently been suggested that in certain special nonsupersymmetric type II string compactifications, at least the first two perturbative contributions to the cosmological constant $\Lambda$ vanish. Support for perturbative vanishing beyond 1-loop ... More

Singularities, Gauge Dynamics, and Nonperturbative Superpotentials in String TheoryAug 29 1996Aug 30 1996We describe a class of 4d N=1 compactifications of the $SO(32)$ heterotic/type I string theory which are destabilized by nonperturbatively generated superpotentials. In the type I description, the destabilizing superpotential is generated by a one instanton ... More

Global U(1) R-Symmetry And Conformal Invariance Of (0,2) ModelsMar 08 1994We derive a condition under which (0,2) linear sigma models possess a ``left-moving'' conformal stress tensor in $\bq$ cohomology (i.e. which leaves invariant the ``right-moving'' ground states) even away from their critical points. At the classical level ... More

Tensor valuations on lattice polytopesApr 24 2017The Ehrhart polynomial and the reciprocity theorems by Ehrhart \& Macdonald are extended to tensor valuations on lattice polytopes. A complete classification is established of tensor valuations of rank up to eight that are equivariant with respect to ... More

Galaxy Clusters at the Edge: Temperature, Entropy, and Gas Dynamics at the Virial RadiusApr 20 2010Recently, Suzaku has produced temperature and entropy profiles, along with profiles of gas density, gas fraction, and mass, for multiple galaxy clusters out to ~r_200 (~= virial radius). In this paper, we compare these novel X-ray observations with results ... More

Longitudinal nonlocality in the string S-matrixApr 21 2015Apr 30 2015We analyze four and five-point tree-level open string S-matrix amplitudes in the Regge limit, exhibiting some basic features which indicate longitudinal nonlocality, as suggested by light cone gauge calculations of string spreading. Using wavepackets ... More

Dark Ages Radio Explorer Mission: Probing the Cosmic DawnDec 05 2014The period between the creation of the cosmic microwave background at a redshift of ~1000 and the formation of the first stars and black holes that re-ionize the intergalactic medium at redshifts of 10-20 is currently unobservable. The baryonic component ... More

Astrophysics Conducted by the Lunar University Network for Astrophysics Research (LUNAR) and the Center for Lunar Origins (CLOE)Sep 11 2012[Abridged] The Moon is a unique platform from and on which to conduct astrophysical measurements. The Lunar University Network for Astrophysics Research (LUNAR) and the Center for Lunar Origins and Evolution (CLOE) teams within the NASA Lunar Science ... More

Graphs with three eigenvalues and second largest eigenvalue at most 1Jun 08 2015We classify the connected graphs with precisely three distinct eigenvalues and second largest eigenvalue at most 1.

Collective Motion in the Interfacial and Interior Regions of Supported Polymer Films and its Relation to RelaxationFeb 12 2019To understand the role of collective motion in the often large changes in interfacial molecular mobility observed in polymer films, we investigate the extent of collective motion in the interfacial regions of a thin supported polymer film and within the ... More

Double Ionisation in R-Matrix Theory Using a 2-electron Outer RegionJul 03 2015We have developed a two-electron outer region for use within R-matrix theory to describe double ionisation processes. The capability of this method is demonstrated for single-photon double ionisation of He in the photon energy region between 80 eV to ... More

Closed String Tachyons, AdS/CFT, and Large N QCDMar 26 2001Apr 06 2001We find that tachyonic orbifold examples of AdS/CFT have corresponding instabilities at small radius, and can decay to more generic gauge theories. We do this by computing a destabilizing Coleman-Weinberg effective potential for twisted operators of the ... More

Large-density field theory, viscosity, and "$2k_F$" singularities from string dualsMar 05 2012Mar 15 2012We analyze systems where an effective large-N expansion arises naturally in gauge theories without a large number of colors: a sufficiently large charge density alone can produce a perturbative string ('tHooft) expansion. One example is simply the well-known ... More

Long-Range Nonlocality in Six-Point String Scattering: simulation of black hole infallersMar 29 2017May 10 2017We set up a tree-level six point scattering process in which two strings are separated longitudinally such that they could only interact directly via a non-local spreading effect such as that predicted by light cone gauge calculations and the Gross-Mende ... More

Probing spacetime foam with extragalactic sourcesAug 29 2005Dec 30 2005Due to quantum fluctuations, spacetime is probably ``foamy'' on very small scales. We propose to detect this texture of spacetime foam by looking for core-halo structures in the images of distant quasars. We find that the Very Large Telescope interferometer ... More

Probing Planck-scale Physics with Extragalactic Sources?Feb 18 2003May 26 2003At Planck-scale, spacetime is "foamy" due to quantum fluctuations predicted by quantum gravity. Here we consider the possibility of using spacetime foam-induced phase incoherence of light from distant galaxies and gamma-ray bursters to probe Planck-scale ... More

Searching For the Physical Drivers of Eigenvector 1: Influence of Black Hole Mass and Eddington RatioJul 21 2003[Abridged] We compute the virial mass of the central black hole (M) and the luminosity-to-mass (L/M) ratio of ~ 300 low-z quasars and luminous Seyfert 1 nuclei. We analyze: (1) whether radio-quiet and radio-loud objects show systematic differences in ... More

Energy conservation for the Euler equations on $\mathbb{T}^2\times \mathbb{R}_+$ for weak solutions defined without reference to the pressureJun 01 2018We study weak solutions of the incompressible Euler equations on $\mathbb{T}^2\times \mathbb{R}_+$; we use test functions that are divergence free and have zero normal component, thereby obtaining a definition that does not involve the pressure. We prove ... More

Energy conservation in the 3D Euler equations on $\mathbb{T}^2\times \mathbb{R}_+$Nov 01 2016Jun 30 2017The aim of this paper is to prove energy conservation for the incompressible Euler equations in a domain with boundary. We work in the domain $\mathbb{T}^2\times\mathbb{R}_+$, where the boundary is both flat and has finite measure. However, first we study ... More

Don't Panic! Closed String Tachyons in ALE SpacetimesAug 10 2001Sep 07 2001We consider closed string tachyons localized at the fixed points of noncompact nonsupersymmetric orbifolds. We argue that tachyon condensation drives these orbifolds to flat space or supersymmetric ALE spaces. The decay proceeds via an expanding shell ... More

Self-tuning flat domain walls in 5d gravity and string theoryJan 31 2000We present Poincare invariant domain wall (``3-brane'') solutions to some 5-dimensional effective theories which can arise naturally in string theory. In particular, we find theories where Poincare invariant solutions exist for arbitrary values of the ... More

De Sitter Holography and Entanglement EntropyApr 23 2018Jul 06 2018We propose a new example of entanglement knitting spacetime together, satisfying a series of checks of the corresponding von Neumann and Renyi entropies. The conjectured dual of de Sitter in d+1 dimensions involves two coupled CFT sectors constrained ... More

Varying dilaton as a tracer of classical string interactionsApr 09 2017Apr 27 2017We analyze tree-level string amplitudes in a linear dilaton background, motivated by its use as a gauge-invariant tracer of string interactions in scattering experiments and its genericity among simple perturbative string theory limits. A simple case ... More

Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic RaysJun 09 2008Aug 21 2008We present new results characterizing cosmological shocks within adaptive mesh refinement N-Body/hydrodynamic simulations that are used to predict non-thermal components of large-scale structure. This represents the first study of shocks using adaptive ... More

Vacuum Energy Cancellation in a Non-supersymmetric StringJul 10 1998Dec 21 1998We present a nonsupersymmetric orbifold of type II string theory and show that it has vanishing cosmological constant at the one and two loop level. We argue heuristically that the cancellation persists at higher loops.

New N=1 Superconformal Field Theories in Four Dimensions from D-brane ProbesOct 27 1996We present several new examples of nontrivial 4d N=1 superconformal field theories. Some of these theories exhibit exotic global symmetries, including non-simply laced groups (such as $F_4$). They are obtained by studying threebrane probes in F-theory ... More

dS/dS and $T\bar T$Nov 19 2018The $T\bar T$ deformation of a conformal field theory has a dual description as a cutoff $AdS_3$ spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk $dS_3$ spacetime instead. ... More

Tate cohomology of circle actions as a Heisenberg groupFeb 16 2001Sep 13 2001We study the Madsen-Tillman spectrum \CP^\infty_{-1} as a quotient of the Mahowald pro-object \CP^\infty_{-\infty}, which is closely related to the Tate cohomology of circle actions. That theory has an associated symplectic structure, whose symmetries ... More

Projective Model Structures for Exact CategoriesMar 21 2016In this article we provide sufficient conditions on weakly idempotent complete exact categories $E$ which admit an abelian embedding, such that various categories of chain complexes in $E$ are equipped with projective model structures. In particular we ... More

Weak semiprojectivity for purely infinite C*-algebrasJun 18 2002Apr 13 2005We prove that a simple, separable, nuclear, purely infinite classifiable $C^*$-algebra is weakly semiprojective if and only if its $K$-groups are direct sums of cyclic groups.

Braids, trees, and operadsSep 13 2001The space of unordered configurations of distinct points in the plane is aspherical, with Artin's braid group as its fundamental group. Remarkably enough, the space of ordered configurations of distinct points on the real projective line, modulo projective ... More

P-adic Line Integrals and Cauchy's TheoremsMay 20 2016Jun 16 2016Working in the p-adic analog of the complex numbers, we'll define a line integral on a small arc of a circle. This allows new versions of the Residue Theorem, the Cauchy-Goursat Theorem on discs with and without holes, Cauchy's Integral Formula and the ... More

Moduli of Singular CurvesNov 28 2010The purpose of this note is to prove that there is an algebraic stack U parameterizing all curves. The curves that appear in the algebraic stack U are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also prove the boundedness ... More

New Dimensions for Wound Strings: The Modular Transformation of Geometry to TopologyDec 13 2006Jan 03 2007We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative ... More

Ehrhart tensor polynomialsJun 06 2017The notion of Ehrhart tensor polynomials, a natural generalization of the Ehrhart polynomial of a lattice polytope, was recently introduced by Ludwig and Silverstein. We initiate a study of their coefficients. In the vector and matrix cases, we give Pick-type ... More

Bounds on curved domain walls in 5d gravityFeb 15 2000Feb 17 2000We discuss maximally symmetric curved deformations of the flat domain wall solutions of five-dimensional dilaton gravity that appeared in a recent approach to the cosmological constant problem. By analyzing the bulk field configurations and the boundary ... More

New Sources of Gravitational Waves during InflationSep 02 2011Sep 25 2014We point out that detectable inflationary tensor modes can be generated by particle or string sources produced during inflation, consistently with the requirements for inflation and constraints from scalar fluctuations. We show via examples that this ... More

The Markov approximation for the atomic output couplerOct 30 1998The regions of validity of the Markov approximation for the coupling of atoms out of an atomic trap are determined. We consider radio-frequency output coupling in the presence of gravity and collisional repulsion, and Raman output coupling. The Markov ... More

CIV 1549 as an Eigenvector 1 Parameter for Active Galactic NucleiMay 14 2007[Abridged] We have been exploring a spectroscopic unification for all known types of broad line emitting AGN. The 4D Eigenvector 1 (4DE1) parameter space shows promise as a unification capable of organizing quasar diversity on a sequence primarily governed ... More

How Much Can We Learn From A Merging Cold Front Cluster? : Insights From X-ray Temperature and Radio Maps of Abell 3667Aug 21 2014The galaxy cluster Abell 3667 is an ideal laboratory to study the plasma processes in the intracluster medium (ICM). High resolution Chandra X-ray observations show a cold front in Abell 3667. At radio wavelengths, Abell 3667 reveals a double radio-relic ... More

Topological gravity in Minkowski spaceJul 07 2004May 22 2006The two-category with three-manifolds as objects, h-cobordisms as morphisms, and diffeomorphisms of these as two-morphisms, is extremely rich; from the point of view of classical physics it defines a nontrivial topological model for general relativity. ... More

The tangent bundle of an almost-complex free loopspaceSep 13 2001Apr 06 2003The main construction of this paper contains a serious error, and I am withdrawing it. I owe Andrew Stacey and Ralph Cohen thanks for seeing the problem; in particular, Stacey has shown that the projections constructed in \S 3.1 will fail in general to ... More

Homotopy-theoretically enriched categories of noncommutative motivesFeb 15 2014Mar 22 2015Waldhausen's $K$-theory of the sphere spectrum (closely related to the algebraic $K$-theory of the integers) is a naturally augmented $S^0$-algebra, and so has a Koszul dual. Classic work of Deligne and Goncharov implies an identification of the rationalization ... More

Complex orientations for THH of some perfectoid fieldsAug 16 2016This sketch argues that work of Hesselholt [8] on the topological Hochschild homology of $\Cp$ extends, using work of Scholze [15, 23] on flat descent, to define complex orientations for a version of topological Hochschild homology for rings of integers ... More

A functorial approach to the C*-algebras of a graphFeb 27 2001Oct 05 2001A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to the category ... More

Birational geometry of moduli spaces of sheaves and Bridgeland stabilityJun 08 2016Jun 23 2016Moduli spaces of sheaves and Hilbert schemes of points have experienced a recent resurgence in interest in the past several years, due largely to new techniques arising from Bridgeland stability conditions and derived category methods. In particular, ... More

Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundlesOct 24 2012Oct 29 2013We compute the cone of effective divisors on the Hilbert scheme of points in the projective plane. We show the sections of many stable vector bundles satisfy a natural interpolation condition, and that these bundles always give rise to the edge of the ... More

An algebraic analog of the Virasoro groupSep 13 2001The group of diffeomorphisms of a circle is not an infinite-dimensional algebraic group, though in many ways it behaves as if it were. Here we construct an algebraic model for this object, and discuss some of its representations, which appear in the Kontsevich-Witten ... More

Topological gravity in dimensions two and fourAug 01 1999Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].

C*-algebras for categories of paths asociated to the Baumslag-Solitar groupsNov 29 2011Nov 15 2012In this paper we describe the C*-algebras associated to the Baumslag-Solitar groups with the ordering defined by the usual presentations. These are Morita equivalent to the crossed product C*-algebras obtained by letting the group act on its directed ... More

Semiprojectivity for certain purely infinite C*-algebrasFeb 28 2001Jun 18 2002It is proved that classifiable simple separable nuclear purely infinite C*-algebras having finitely generated K-theory and torsion-free K_1 are semiprojective. This is accomplished by exhibiting these algebras as C*-algebras of infinite directed graphs. ... More

On the Complexity of Properties of Transformation SemigroupsOct 31 2018We investigate the computational complexity for determining various properties of a finite transformation semigroup $S$ given by generators. In particular, we show that checking whether an element of $S$ is regular is PSPACE-complete. We give polynomial ... More

The Spectral Kuznetsov Formula on SL(3)Nov 28 2014The $SL(3)$ Kuznetsov formula exists in several versions, and has been employed with some success to study automorphic forms on $SL(3)$. In each version, the weight functions on the geometric side are given by multiple integrals with complicated oscillating ... More

Techniques for Profile Binning and Analysis of Eigenvector Composite Spectra: Comparing Hbeta and MgII 2800 as Virial EstimatorsOct 16 2013We review the basic techniques for extracting information about quasar structure and kinematics from the broad emission lines in quasars. We consider which lines can most effectively serve as virial estimators of black hole mass. At low redshift the Balmer ... More

Structural Signatures of Vitrification in Hard Core FluidsAug 18 2003Computer simulations of hard spheres and disks are used to estimate the most probable cavity size, $\xi_{\rm cavity}$, and a ``rattle'' size, $\xi_{\rm rattle}$, over which a particle can translate holding all other particles fixed. Both of these measures ... More

Effects Of The Ionosphere On Ground-Based Detection Of The Global 21 CM Signal From The Cosmic Dawn And The Dark AgesSep 01 2014Mar 09 2016Detection of the global HI 21 cm signal from Cosmic Dawn and Epoch of Reionization is the key science driver for several ongoing ground-based and future ground/space-based experiments. The crucial spectral features in the global 21 cm signal (turning ... More

The Santa Fe Light Cone Simulation Project: II. The Prospects for Direct Detection of the WHIM with SZE SurveysMar 18 2009Detection of the Warm-Hot Intergalactic Medium (WHIM) using Sunyaev-Zeldovich effect (SZE) surveys is an intriguing possibility, and one that may allow observers to quantify the amount of "missing baryons" in the WHIM phase. We estimate the necessary ... More

On the Origin of Cool Core Galaxy Clusters: Comparing X-Ray Observations with Numerical SimulationsMar 24 2009To better constrain models of cool core galaxy cluster formation, we have used X-ray observations taken from the Chandra and ROSAT archives to examine the properties of cool core and non-cool core clusters, especially beyond the cluster cores. We produced ... More

Biregular graphs with three eigenvaluesDec 22 2014Apr 12 2016We consider nonregular graphs having precisely three distinct eigenvalues. The focus is mainly on the case of graphs having two distinct valencies and our results include constructions of new examples, structure theorems, valency constraints, and a classification ... More

The Design of EzWindows: A Graphics API for an Introductory Programming CourseOct 03 1998Teaching object-oriented programming in an introductory programming course poses considerable challenges to the instructor. An often advocated approach to meeting this challenge is the use of a simple, object-oriented graphics library. We have developed ... More

Moonshine elements in elliptic cohomologyDec 06 2007This is a historical talk about the recent confluence of two lines of research in equivariant elliptic cohomology, one concerned with connected Lie groups, the other with the finite case. These themes come together in (what seems to me remarkable) work ... More

Largeness of LERF and 1-relator groupsMar 26 2008We consider largeness of groups given by a presentation of deficiency 1, where the group is respectively free-by-cyclic, LERF or 1-relator. We give the first examples of (finitely generated free)-by-(infinite cyclic) word hyperbolic groups which are large, ... More

Techniques for classifying nonnegatively curved left-invariant metrics on compact Lie groupsAug 14 2006We provide techniques for studying the nonnegatively curved left-invariant metrics on a compact Lie group. For "straight" paths of left-invariant metrics starting at bi-invariant metrics and ending at nonnegatively curved metrics, we deduce a nonnegativity ... More

Complex orientations for THH of some perfectoid fieldsAug 16 2016Oct 14 2016This sketch argues that work of Hesselholt [8] on the topological Hochschild homology of $\Cp$ extends, using work of Scholze [15, 23] on flat descent, to define complex orientations for a version of topological Hochschild homology for rings of integers ... More

Schur Q-functions and a Kontsevich-Witten genusJul 11 1998The Virasoro operations in Witten's theory of two-dimensional topological gravity have a homotopy-theoretic interpretation as endomorphisms of an ordinary cohomology theory with coefficients in a localization of I. Schur's ring \Delta of Q-functions. ... More

A catalogue of spectroscopic binary candidate stars derived from a comparison of Gaia DR2 with other radial velocity cataloguesJan 25 2019Using the recently published Gaia second data release which includes measurements of the mean radial velocity of about 7.2 million stars, we performed a systematic comparison with other existing radial velocity catalogues in order to search for variations ... More

Geometric Tate-Swan cohomology of equivariant spectraOct 15 2012Nov 21 2012We sketch a quick and dirty geometric approach to the Tate-Swan cohomology of equivariant spectra, illustrating it with conjectural applications to Atiyah-Segal $K$-theory of circle actions, and a possible geometric model for the topological cyclic homology ... More

Maximal Cocliques in $\operatorname{PSL}_2(q)$Feb 26 2018Jan 14 2019The generating graph of a finite group is a structure which can be used to encode certain information about the group. It was introduced by Liebeck and Shalev and has been further investigated by Lucchini, Mar\'oti, Roney-Dougal and others. We investigate ... More

Kuznetsov, Petersson and Weyl on GL(3), I: The principal series formsMar 28 2017May 31 2018The Kuznetsov and Petersson trace formulae for $GL(2)$ forms may collectively be derived from Poincar\'e series in the space of Maass forms with weight. Having already developed the spherical spectral Kuznetsov formula for $GL(3)$, the goal of this series ... More

On the category of finitely presented mod $p$ representations of $GL_2(F)$, $F/\mathbb{Q}_p$ finiteOct 16 2017Let $F$ be a finite extension of $\mathbb{Q}_p$, and let $\mathbb{F}$ be a finite field of characteristic $p$. A smooth representation of $GL_2(F)$ over $\mathbb{F}$ is finitely presented if it can be written as the cokernel of a map between representations ... More

Kuznetsov, Petersson and Weyl on $GL(3)$, II: The generalized principal series formsJun 27 2017Jan 22 2018This paper initiates the study by analytic methods of the generalized principal series Maass forms on $GL(3)$. These forms occur as an infinite sequence of one-parameter families in the two-parameter spectrum of $GL(3)$ Maass forms, analogous to the relationship ... More

Quantum cohomology and closed-string mirror symmetry for toric varietiesFeb 01 2018Dec 17 2018We give a short new computation of the quantum cohomology of an arbitrary smooth toric variety $X$, by showing directly that the Kodaira-Spencer map of Fukaya-Oh-Ohta-Ono defines an isomorphism onto a suitable Jacobian ring. The proof is based on the ... More

Categories of orbit types for proper Lie groupoidsMay 17 2014It is widely understood that the quotient space of a topological group action can have a complicated combinatorial structure, indexed somehow by the sotropy groups of the action, but how best to record this structure seems unclear. This sketch defines ... More

Abelian varieties and the Kervaire invariantMay 03 2011Notes from a talk at the April 2011 ICMS (Edinburgh) conference on the recent solution of the Kervaire invariant problem. This is an entirely expository account, emphasizing connections with the theory of topological automorphic forms.

Graph-Based Models for Kirchberg AlgebrasApr 14 2005We give a construction of Kirchberg algebras from graphs. By using product graphs in the construction we are able to provide models for general (UCT) Kirchberg algebras while maintaining the explicit generators and relations of the underlying graphs.

Interpolation on surfaces in P^3Jun 24 2010Jan 04 2011Given a surface S in P^3 and a collection of general points on it, how many surfaces of a given degree intersect S in a curve with prescribed multiplicities at the points? We formulate two natural conjectures which would answer this question, and we show ... More

GAGA theoremsApr 05 2018We prove a new and unified GAGA theorem for proper schemes and algebraic spaces. This recovers all analytic and formal GAGA results in the literature, and is also valid in the non-noetherian setting.

The arithmetic Kuznetsov formula on $GL(3)$, I: The Whittaker caseAug 31 2017Jun 02 2018The original formulae of Kuznetsov for $SL(2,\mathbb{Z})$ allowed one to study either a spectral average via Kloosterman sums or to study an average of Kloosterman sums via a spectral interpretation. In previous papers, we have developed the spectral ... More

Complex orientations for THH of some perfectoid fieldsAug 16 2016Oct 02 2016This sketch argues that work of Hesselholt [8] on the topological Hochschild homology of $\Cp$ extends, using work of Scholze [15, 23] on flat descent, to define complex orientations for a version of topological Hochschild homology for rings of integers ... More