April 2003 arXiv papers — page 10

K. L. Luhman, Cesar Briceno, John R. Stauffer, Lee Hartmann

Briceno et al. recently used optical imaging, data from the Two-Micron All-Sky Survey (2MASS), and follow-up spectroscopy to search for young low-mass stars and brown dwarfs in 8 square degrees of the Taurus star-forming region. By the end of that study, there remained candidate members of Taurus that lacked the spectroscopic observations needed to measure s

Lee Samuel Finn, Badri Krishnan, Patrick J. Sutton

The currently accepted model for gamma-ray burst phenomena involves the violent formation of a rapidly rotating solar-mass black hole. Gravitational waves should be associated with the black-hole formation, and their detection would permit this model to be tested. Even upper limits on the gravitational-wave strength associated with gamma-ray bursts could con

O. G. Benvenuto, M. A. De Vito

We present a numerical code intended for calculating stellar evolution in close binary systems. In doing so, we consider that mass transfer episodes occur when the stellar size overflows the corresponding Roche lobe. In such situation we equate the radius of the star with the equivalent radius of the Roche lobe. This equation is handled implicitly together w

L. Rizzi, E. V. Held, G. Bertelli, I. Saviane

The thin red giant branch (RGB) of the Carina dwarf spheroidal galaxy appears at first sight quite puzzling and seemingly in contrast with the presence of several distinct bursts of star formation. In this Letter, we provide a measurement of the color spread of red giant stars in Carina based on new BVI wide-field observations, and model the width of the RGB

D. M. Neumann, M. Arnaud, C. Benoist, L. da Costa

We present here a study of XMM-Newton data of two distant galaxy cluster candidates. One of these was discovered serendipitously in near infrared data, CL J0533-2411, the other one corresponds to the cluster EIS J0533-2412 part of the EIS cluster survey. The estimated redshift of CL J0533-2411 is z=1.2-1.7. EIS J0533-2412 is a rich system (Lambda_cl=299), wi

Jayaram N. Chengalur, Nissim Kanekar

We present Giant Meterwave Radio Telescope images of the 1065 MHz emission from the 1_11 -> 1_10 rotational transition of acetaldehyde (CH3CHO) in the molecular cloud complex Sgr B2. Our observations are unique in that they have a high spatial resolution (~4"), while still being sensitive to large-scale emission. Most complex organic molecules in this cl

Naoyuki Tamura, Kouji Ohta

We performed B and R band surface photometry for E/S0 galaxies in a nearby rich cluster ABELL 2199 to investigate their B-R color gradients (d(B-R)/dlogr). Our aims are to study statistical properties of the color gradients and, by comparing them with those in less dense environments, to examine environmental dependence of color gradients in elliptical galax

Tomislav Ivezic

In this paper it is exactly proved by using the Clifford algebra formalism that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not the Lorentz transformations of well-defined quantities from the 4D spacetime but the 'apparent' transformations of the 3D quantities. Thence the usual Ma

B. McKernan, T. Yaqoob, I. M. George, T. J. Turner

We observed the Seyfert 1 galaxy NGC 4593 with the Chandra high energy transmission gratings and present a detailed analysis of the soft X-ray spectrum. We measure strong absorption lines from He-like O, Ne, Mg, Si, H-like N, O, Ne, Mg, Si and highly ionized Fe XIX-XXV. Only the NLya, OLya and MgLya lines appear to be marginally resolved. We identify a spect

Karen L. Masters, Riccardo Giovanelli, Martha P. Haynes

In order to study the effects of internal extinction in spiral galaxies we search for correlations of near infrared (NIR) photometric parameters with inclination. We use data from the 2 Micron All-Sky Survey (2MASS) Extended Source Catalog (XSC) on 15,224 spiral galaxies for which we also have redshifts. For 3035 of the galaxies, I-band photometry is availab

Tanmay Vachaspati, Arthur Lue

Rapid progress has been made in observations of the temperature anisotropies of the Cosmic Microwave Background (CMB). These observations have enabled cosmologists to characterize the state of the universe at recombination, and observational efforts are now being directed towards obtaining the polarization map of the CMB. Here we draw an analogy between the

Alison J. Farmer, E. S. Phinney

We use a population synthesis approach to characterise, as a function of cosmic time, the extragalactic close binary population descended from stars of low to intermediate initial mass. The unresolved gravitational wave (GW) background due to these systems is calculated for the 0.1-10 mHz frequency band of the planned Laser Interferometer Space Antenna (LISA

Ailin Zhang, T. G. Steele

Instanton effects and three-loop perturbative contributions are incorporated into QCD sum-rule analyses of pseudoscalar ($J^{PC}=0^{-+}$) gluonium. Gaussian sum-rules are shown to be superior to Laplace sum-rules in optimized predictions for pseudoscalar gluonium states in the presence of instanton contributions. The Gaussian sum-rule analysis yields a pseud

Levon Pogosian, S. -H. Henry Tye, Ira Wasserman, Mark Wyman

Overall, brane inflation is compatible with the recent analysis of the WMAP data. Here we explore the constraints of WMAP and 2dFGRS data on the various brane inflationary scenarios. Brane inflation naturally ends with the production of cosmic strings, which may provide a way to distinguish these models observationally. We argue that currently available data

E. M. Lipmanov

The absolute neutrino masses are obtained in terms of the atmospheric and solar mass-squared differences within the framework of low energy phenomenology by suggestion of a quantitative analogy between the hierarchies of the neutrino and charged lepton mass ratios. It points to a quasi-degenerate three neutrino mass pattern with the neutrino mass scale likel

Marta Volonteri, Piero Madau, Francesco Haardt

We investigate a hierarchical structure formation scenario in which galaxy stellar cores are created from the binding energy liberated by shrinking supermassive black hole (SMBH) binaries. The binary orbital decay heats the surrounding stars, eroding a preexisting 1/r^2 stellar cusp. We follow the merger history of dark matter halos and associated SMBHs via

Aparna Venkatesan, James W. Truran

We investigate whether a single population of first stars could have influenced both the metal enrichment and reionization of the high-redshift intergalactic medium (IGM), by calculating the generated ionizing radiation per unit metal yield as a function of the metallicity of stellar populations. We examine the relation between the ionizing radiation and car

M. Choudhury, A. R. Rao, S. V. Vadawale, A. K. Jain

We present results of our study of correlated radio and X-ray emission in two black hole candidates and Galactic microquasars GRS 1915+105 and Cygnus X-1 in their steady long term hard states, along with Cygnus X-3 (using data obtained from RXTE-ASM, CGRO-BATSE and GBI). We detect a pivotal behavior in the X-ray spectrum of GRS 1915+105, correlated to the ra

Takanori Sugihara

We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation of the fermion propagator

Roberto A. Sussman, Xavier Hernandez

We examine isothermal dark matter halos in hydrostatic equilibrium with a cosmological constant Lambda =Omega_Λrho_{crit}c^2, where Omega_Λ=0.7, and rho_{crit} is the present value of the critical density with h=0.65. The Newtonian limit of General Relativity yields equilibrium equations that are different from those arising by merely coupling an ``isotherma

Valeri Frolov, Martin Snajdr, Dejan Stojkovic

We study the interaction of an n-dimensional topological defect (n-brane) described by the Nambu-Goto action with a higher-dimensional Schwarzschild black hole moving in the bulk spacetime. We derive the general form of the perturbation equations for an n-brane in the weak field approximation and solve them analytically in the most interesting cases. We spec

Chong-Sun Chu, Konstantinos Kyritsis

In this letter, we determine the particle and the string light cone in the pp-wave background. The result is a deformed version of the flat one. We point out the light cone exhibits an intriguing periodicity in the light cone time direction x^+ with a period \sim 1/ μ. Our results also suggest that a quantum theory in the pp-wave background can be formulated

C. Pappas, F. Mezei, G. Ehlers, P. Manuel

We present new Neutron Spin Echo (NSE) results and a revisited analysis of historical data on spin glasses, which reveal a pure power-law time decay of the spin autocorrelation function $s(Q,t) = S(Q,t)/S(Q)$ at the glass temperature $T_g$, each power law exponent being in excellent agreement with that calculated from dynamic and static critical exponents de

A. Omont, G. Gilmore, C. Alard, B. Aracil

The ISOGAL project is an infrared survey of specific regions sampling the Galactic Plane selected to provide information on Galactic structure,stellar populations,stellar mass-loss and the recent star formation history of the inner disk and Bulge of the Galaxy. ISOGAL combines 7 and 15 micron ISOCAM observations - with a resolution of 6'' at worst -

Sadhan K. Adhikari

We predict the loss of superfluidity in a Bose-Einstein condensate in an axially symmetric harmonic trap alone during resonant collective oscillations via a classical dynamical transition. The forced resonant oscillation can be initiated by (a) a periodic modulation of the atomic scattering length with a frequency that equals twice the radial trapping freque

Gilles Chabrier

We review recent determinations of the present day and initial mass functions in various components of the Galaxy, disk, spheroid, young and globular clusters. As a general feature, the IMF is well described by a power-law form for $m\ga 1 \msol$ and a lognormal form below. The extension of the disk IMF into the brown dwarf (BD) regime is in good agreement w

Benjamin Doyon

A result from Palmer, Beatty and Tracy suggests that the two-point function of certain spinless scaling fields in a free Dirac theory on the Poincare disk can be described in terms of Painleve VI transcendents. We complete and verify this description by fixing the integration constants in the Painleve VI transcendent describing the two-point function, and by

G. M. Falco, R. A. Duine, H. T. C. Stoof

The Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. We show that a bosonic version of the Kondo effect can occur in degenerate atomic Fermi gases near the Feshbach resonance. We also discuss how this bosonic Kondo effect can be obser

Luc Blanchet

We look for physically realistic initial data in numerical relativity which are in agreement with post-Newtonian approximations. We propose a particular solution of the time-symmetric constraint equation, appropriate to two momentarily static black holes, in the form of a conformal decomposition of the spatial metric. This solution is isometric to the post-N

Runyao Duan, Zhengfeng Ji, Yuan Feng, Mingsheng Ying

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its comple

Yoshimasa Hidaka, Osamu Morimatsu, Tetsuo Nishikawa, Munehisa Ohtani

We study the effect of thermal width of $π$ on the spectral function of $σ$ applying a resummation technique called optimized perturbation theory at finite temperature ($T$) to ${\cal O}(4)$ linear sigma model. In order to take into account finite thermal width of $π$, we replace the internal pion mass in the self-energy of $σ$ with that of complex pole foun

Alberto Manrique, Andreu Raig, Eduard Salvador-Sole, Teresa Sanchis

We calculate by means of the Press-Schechter formalism the density profile developed by dark-matter halos during accretion, i.e., the continuous aggregation of small clumps. We find that the shape of the predicted profile is similar to that shown by halos in high-resolution cosmological simulations. Furthermore, the mass-concentration relation is correctly r

J. Striet, F. A. Bais

In this paper we present new results on the core instability of the 't Hooft Polyakov monopoles we reported on before. This instability, where the spherical core decays in a toroidal one, typically occurs in models in which charge conjugation is gauged. In this paper we also discuss a third conceivable configuration denoted as ``split core'', whi

M. Sami, N. Dadhich, Tetsuya Shiromizu

We discuss a model in which high energy brane corrections allow a single scalar field to describe inflation at early epochs and quintessence at late times. The reheating mechanism in the model originates from Born-Infeld matter whose energy density mimics cosmological constant at very early times and manifests itself as radiation subsequently. For most of th

F. A. Bais, J. Striet

Alice electrodynamics (AED) is a theory of electrodynamics in which charge conjugation is a local gauge symmetry. In this paper we investigate a charge instability in alice electrodynamics in (2+1)-dimensions due to this local charge conjugation. The instability manifests itself through the creation of a pair of alice fluxes. The final state is one in which

Tomo Munehisa, Yasuko Munehisa

We propose a new type of Monte Carlo approach in numerical studies of quantum systems. Introducing a probability function which determines whether a state in the vector space survives or not, we can evaluate expectation values of powers of the Hamiltonian from a small portion of the full vector space. This method is free from the negative sign problem becaus

Ken-ichi Nakao, Yoshiyuki Morisawa

We construct approximate solutions that will describe the last stage of cylindrically symmetric gravitational collapse of dust fluid. Just before the spacetime singularity formation, the speed of the dust fluid might be almost equal to the speed of light by gravitational acceleration. Therefore the analytic solution describing the dynamics of cylindrical nul

Takashi Nagatani, Dirk Helbing

Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as "bull-whip effect". Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management fu

Giuseppe Tormen, Lauro Moscardini, Naoki Yoshida

We analyze the dynamical and thermal evolution of dark matter and ICM in hydrodynamical Tree-SPH simulations of galaxy clusters. Starting from a sample of 17 high-resolution objects, with virial mass ranging from 3 10^{14} to 1.7 10^{15} M_sun, we follow the build-up of the systems in dark matter and hot gas through the repeated merging of satellites along t

Todd A. Oliynyk

In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of desirable properties: they agree with the standard quantum mechanical ones if the observables commute, they also depend con

Qing-yu Cai

We show a deterministic secure direct communication protocol using single qubit in mixed state. The security of this protocol is based on the security proof of BB84 protocol. It can be realized with current technologies.

Toshihiro Kawaguchi

Super-Eddington accretion onto black holes (BHs) may occur at ultraluminous compact X-ray sources in nearby galaxies, Galactic microquasars and narrow-line Seyfert 1 galaxies (NLS1s). Effects of electron scattering (opacity and Comptonization) and the relativistic correction (gravitational redshift and transverse Doppler effect) on the emergent spectra from

A. Ya. Maltsev, S. P. Novikov

New observable integer-valued numbers of the topological origin were revealed by the present authors studying the conductivity theory of single crystal 3D normal metals in the reasonably strong magnetic field ($B \leq 10^{3} Tl$). Our investigation is based on the study of dynamical systems on Fermi surfaces for the motion of semi-classical electron in magne

H. C. Rosu

A short review of Schroedinger hamiltonians for which the spectral problem has been related in the literature to the distribution of the prime numbers is presented here. We notice a possible connection between prime numbers and centrifugal inversions in black holes and suggest that this remarkable link could be directly studied within trapped Bose-Einstein c

David A. Levin, Yuval Peres

Suppose that attached to each site z in Z is a coin with bias theta(z), and only finitely many of these coins have non-zero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {theta(z) : z in Z}, using only the outcomes of these coin tosses and no i

B. F. Samsonov, M. L. Glasser, L. M. Nieto

Time-dependent supersymmetry allows one to delete quasienergy levels for time-periodic Hamiltonians and to create new ones. We illustrate this by examining an exactly solvable model related to the simple harmonic oscillator with a time-varying frequency. For an interesting nonharmonic example we present the change of the Berry phase due to a supersymmetry tr

J. M. Isidro

The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space C, but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a complex structure on C. When the latter is a complex-analytic manifold admitting just one complex structure, there is a

N. K. Solovarov

We show that the von Neumann's algorithm of reduction (i.e. the algorithm of calculating the density matrix of the observable subsystem from the density matrix of the closed quantum system) corresponds to the special approximation at which the unobservable subsystem is supposed to be in the steady state of minimum information (infinite temperature). We f

U. I. Safronova, I. M. Savukov, M. S. Safronova, W. R. Johnson

Energies of 5l_j (l= s, p, d, f, g) and 4f_j states in neutral Ag and Ag-like ions with nuclear charges Z = 48 - 100 are calculated using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates and lifetimes are calculated for the 17 possible 5l_j-5l'_{j'} and 4f_j-5l_{j'} electric-dipole transi

Mario Rabinowitz

This paper is intended to provide an insight into physics and engineering that can modernize electric power systems. Topics covered are Flexible ac transmission systems (FACTS), Custom Power, Greatly improved Capacitors, Electrical Insulation, Distribution Cables, Improved Polymeric Insulation, Underground Vault Explosions, Fault Location, Smart Cables, Neut

Saeed. Otarod

The conditions under which, the continuity equation can be substituted by an ordinary non differential equation, will be discussed. Since continuity equation is a fundamental equation, this result will be applicable in a vast area of Physics.

A. S. Jensen, D. V. Fedorov

The conditions for occurrence of the Efimov effect is briefly described using hyperspherical coordinates. The strength of the effective hyperradial $ρ^{-2}$ potential appearing for two or three large scattering lengths is computed and discussed as function of two independent mass ratios of the three constituent particles. The effect is by far most pronounced

Jean-Philippe Laval, James C. McWilliams

Numerical simulations are made for forced turbulence at a sequence of increasing values of Reynolds number, R, keeping fixed a strongly stable, volume-mean density stratification. At smaller values of R, the turbulent velocity is mainly horizontal, and the momentum balance is approximately cyclostrophic and hydrostatic. This is a regime dominated by so-calle

I. Y. Dodin, N. J. Fisch, G. M. Fraiman

The Lagrangian and Hamiltonian functions describing average motion of a relativistic particle under the action of a slightly inhomogeneous intense laser field are obtained. In weak low-frequency background fields, such a particle on average drifts with an effective, relativistically invariant mass, which depends on the laser intensity. The essence of the pro

Colm Connaughton, Sergey Nazarenko

A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is presented. This equation respects the scaling properties of the original Navier-Stokes equations and it has the Kolmogorov -5/3 cascade and the thermodynamic equilibrium spectra as exact steady state solutions. The general steady state in this model conta

Rudolph C. Hwa, C. B. Yang

The medium effect on the pion distribution at high $p_T$ in $AA$ collisions is compared to that of the pion distribution at high $p_L$ in $pA$ collisions. Both the suppression of the spectra and the energy losses of the measured pions are studied. Although the medium effect on $p_T$ is larger than on $p_L$, the difference is found surprisingly to be not as b

N. E. Ligterink

We give a full kinematical classification of all the tree-level two-pion photoproduction processes on the nucleon, which consists of seventeen diagrams. It suggests a method of analysis of two-pion data with little model bias.

P. Mohr

The cross sections of the 8Li(n,gamma)9Li and 8B(p,gamma)9C capture reactions have been analyzed using the direct capture model. At low energies which is the astrophysically relevant region the capture process is dominated by E1 transitions from incoming s-waves to bound p-states. The cross sections of both mirror reactions can be described simultaneously wi

S. Ishikawa, M. Tanifuji, Y. Iseri

Contributions of three-nucleon forces (3NF) to proton-deuteron scattering observables at energies below the deuteron breakup threshold are studied by solving the Faddeev equation that includes the Coulomb interaction. At E_p=3.0 MeV, we find that the central part of a two-pion exchange 3NF removes the discrepancy between measured cross sections and the calcu

I. B. Khriplovich, A. I. Milstein

We consider the corrections to deuterium hyperfine structure originating from the two-photon exchange between electron and deuteron, with the deuteron excitations in the intermediate states. In particular, the motion of the two intermediate nucleons as a whole is taken into account. The problem is solved in the zero-range approximation. The result is in good

A. A. Shkalikov

A model problem of the form -iεy''+q(x)y=λy, y(-1)=y(1)=0, is associated with well-known in hydrodynamics Orr--Sommerfeld operator. Here (λ) is the spectral parameter, (ε) is the small parameter which is proportional to the viscocity of the liquid and to the reciprocal of the Reynolds number, and (q(x)) is the velocity of the stationary flow of the l

Miloslav Znojil, Denis Yanovich, Vladimir P. Gerdt

A new type of exact solvability is reported. We study the general central polynomial potentials (with 2q anharmonic terms) which satisfy the Magyari's partial exact solvability conditions (this means that they possess a harmonic-oscillator-like wave function proportional to a polynomial of any integer degree N). Working in the space of a very large dimen

Sever Silvestru Dragomir

In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Renyi's entropy mappings are also given.

Rafał Latała

We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.

Vincent Lafforgue

The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group $C^*$-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy and the exhaustion by Atiyah and Schmid of the discrete series representations of connected semi-simple Lie groups.

Liming Ge

This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some of the key ideas and results in free probability theory. Last section states some of the important applications of free

Dietmar Bisch

An inclusion of II$_1$ factors $N \subset M$ with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones' pictorial description of the standard invariant of a subfactor as a so-called planar algebra and show how this point of view leads to new structure results fo

Philippe Biane

A combinatorial approach to free probability theory has been developped by Roland Speicher, based on the notion of noncrossing cumulants, a free analogue of the classical theory of cumulants in probability theory. We review this theory, and explain the connections between free probability theory and random matrices. We relate noncrossing cumulants to classic

Semyon Alesker

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincaré duality and hard Lefschetz theorem), and their relations and applications to integral geometry.

Xiangyu Zhou

In this talk, we'll present some recent results related to group actions in several complex variables. We'll not aim at giving a complete survey about the topic but giving some our own results and related ones. We'll divide the results into two cases: compact and noncompact transformation groups. We emphasize some essential differences between th

Christophe Thiele

Many concepts of Fourier analysis on Euclidean spaces rely on the specification of a frequency point. For example classical Littlewood Paley theory decomposes the spectrum of functions into annuli centered at the origin. In the presence of structures which are invariant under translation of the spectrum (modulation) these concepts need to be refined. This wa

Nicolas Lerner

In 1957, Hans Lewy constructed a counterexample showing that very simple and natural differential equations can fail to have local solutions. A geometric interpretation and a generalization of this counterexample were given in 1960 by L.Hörmander. In the early seventies, L.Nirenberg and F.Treves proposed a geometric condition on the principal symbol, the so-

Carlos E. Kenig

We will review work with Tatiana Toro yielding a characterization of those domains for which the harmonic measure has a density whose logarithm has vanishing mean oscillation.

Juha Heinonen

We discuss the issue of branching in quasiregular mapping, and in particular the relation between branching and the problem of finding geometric parametrizations for topological manifolds. Other recent progress and open problems of a more function theoretic nature are also presented.

Alexandre Eremenko

We describe some results of value distribution theory of holomorphic curves and quasiregular maps, which are obtained using potential theory. Among the results discussed are: extensions of Picard's theorems to quasiregular maps between Riemannian manifolds, a version of the Second Main Theorem of Nevanlinna for curves in projective space and non-linear d

Hans-Christian v. Bothmer, Klaus Hulek

We show that the linear syzygy spaces of elliptic normal curves, their secant varieties and of bielliptic canonical curves are spanned by geometric syzygies.

Marie-France Vignéras

I will survey some results in the theory of modular representations of a reductive $p$-adic group, in positive characteristic $\ell \neq p$ and $\ell=p$.

Freydoon Shahidi

This is a report on the global aspects of the Langlands-Shahidi method which in conjunction with converse theorems of Cogdell and Piatetski-Shapiro has recently been instrumental in establishing a significant number of new and surprising cases of Langlands Functoriality Conjecture over number fields. They have led to striking new estimates towards Ramanujan

Eckhard Meinrenken

This article summarizes joint work with A. Alekseev (Geneva) on the Duflo isomorphism for quadratic Lie algebras. We describe a certain quantization map for Weil algebras, generalizing both the Duflo map and the quantization map for Clifford algebras. In this context, Duflo's theorem generalizes to a statement in equivariant cohomology.

Vikram Bhagvandas Mehta

In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic $p$. We quickly review the notions of stable and semistable vector bundles and principal $G$-bundles, where $G$ is any semisimple group. We define the notion of a low height representation in characteris

Toshiyuki Kobayashi

The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs discretely with finite multiplicity (admissible restrictions). Basic theory and new perspectives of admissible restrictions are

Alexander Klyachko

This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.

Michael Harris

The local Langlands correspondence for GL(n) of a non-Archimedean local field $F$ parametrizes irreducible admissible representations of $GL(n,F)$ in terms of representations of the Weil-Deligne group $WD_F$ of $F$. The correspondence, whose existence for $p$-adic fields was proved in joint work of the author with R. Taylor, and then more simply by G. Hennia

Yael Fregier

We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.

Patrick Delorme

Let $G$ be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over $\R$. Let $σ$ be an involution of the Lie group $G$, $H$ an open subgroup of the subgroup of fixed points of $σ$. One decomposes the elements of $L^2(G/H)$ with th

Mikhail Grinenko

We describe the set of Mori structures for a Fano 3-fold of index 2 and degree 1 (the double cone over the Veronese surface). In partiular, it is proved that such a Fano variety is not rational, the group of birational automorphisms coincides with the group of biregular automorphisms, and there are no structures of conic bundle.

Yuri Berest, George Wilson

In this survey article we discuss the question: to what extent is an algebraic variety determined by its ring of differential operators? In the case of affine curves, this question leads to a variety of mathematical notions such as the Weyl algebra, Calogero-Moser spaces and the adelic Grassmannian. We give a fairly detailed overview of this material.

K. J. Dykema, N. J. Kalton

Let M be a factor of type II_\infty or II_1 having separable predual and let M-bar be the algebra of affiliated τ-measureable operators. We characterize the commutator space [I,J] for sub-(M,M)-bimodules I and J of M-bar.

Alexander Borichev, Hakan Hedenmalm, Alexander Volberg

In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate nontrivial bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces of sequences.

K. Srinivasa Rao, G. Vanden Berghe, Christian Krattenthaler

Example 7, after Entry 43, in Chapter XII of the first Notebook of Srinivasa Ramanujan is proved and, more generally, a summation theorem for $_3F_2(a,a,x;1+a,1+a+N;1)$, where $N$ is a non-negative integer, is derived.

Alastair Hamilton

In this paper we will study deformations of A-infinity algebras. We will also answer questions relating to Moore algebras which are one of the simplest nontrivial examples of an A-infinity algebra. We will compute the Hochschild cohomology of odd Moore algebras and classify them up to a unital weak equivalence. We will construct miniversal deformations of pa

C. DeConcini, C. Procesi, N. Reshetikhin, M. Rosso

We study the restriction of representations of Cayley-Hamilton algebras to subalgebras. This theory is applied to determine tensor products and branching rules for representations of quantum groups at roots of 1.

Thomas Eckl

Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kaehler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji's numerically trivial fibration and the Iitaka fibration. Using almost positive singular hermitian metrics with analytic

Mihail N. Kolountzakis

This is a survey on the subject of the title corresponding to three lectures I gave in June 2001 at the Workshop on Fourier Analysis and Convexity, at the Universita di Milano-Biccoca.

Lewis Bowen

We prove the existence of an automorphism-invariant coupling for the wired and the free uniform spanning forests on Cayley graphs of finitely generated residually amenable groups.

Palle E. T. Jorgensen, Anna Paolucci

We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from this multiresolution analysis are contained as a special case in the Fock Space construction.

Graham J. Leuschke, Roger Wiegand

Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will classify these rings up to analytic isomorphism (under the additional hypothesis that the ring contains an infinite field)

Graham J. Leuschke, Roger Wiegand

Let R = k[[x_0,...,x_d]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x_0,...,x_d]]. We investigate the question of which rings of this form have bounded Cohen--Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen--Macaulay modules. As with finite Cohen--Macaulay type, if th

Peter Saveliev

We consider sufficient conditions of local removability of coincidences of maps f,g:N->M, where M,N are manifolds with dimensions dimN>dimM. The coincidence index is the only obstruction to the removability for maps with fibers either acyclic or homeomorphic to spheres of certain dimensions. We also address the normalization property of the index and coincid

Andrew Kresch, Harry Tamvakis

We propose a theory of double Schubert polynomials P_w(X,Y) for the Lie types B, C, D which naturally extends the family of Lascoux of Schutzenberger in type A. These polynomials satisfy positivity, orthogonality, and stability properties, and represent the classes of Schubert varieties and degeneracy loci of vector bundles. When w is a maximal Grassmannian