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Majorana Fermion Quantum Mechanics for Higher Rank TensorsMay 15 2019May 20 2019We study quantum mechanical models in which the dynamical degrees of freedom are real fermionic tensors of rank five and higher. They are the non-random counterparts of the Sachdev-Ye-Kitaev (SYK) models where the Hamiltonian couples six or more fermions. ... More

TASI Lectures on Large $N$ Tensor ModelsAug 28 2018Sep 05 2018The first part of these lecture notes is mostly devoted to a comparative discussion of the three basic large $N$ limits, which apply to fields which are vectors, matrices, or tensors of rank three and higher. After a brief review of some physical applications ... More

Prismatic Large $N$ Models for Bosonic TensorsAug 13 2018We study the $O(N)^3$ symmetric quantum field theory of a bosonic tensor $\phi^{abc}$ with sextic interactions. Its large $N$ limit is dominated by a positive-definite operator, whose index structure has the topology of a prism. We present a large $N$ ... More

Merging Nonlinear Optics and Negative-Index MetamaterialsAug 03 2011The extraordinary properties of nonlinear optical propagation processes in double-domain positive/negative index metamaterials are reviewed. These processes include second harmonic generation, three- and four-wave frequency mixing, and optical parametric ... More

Negative-Index Metamaterials: Second-Harmonic Generation, Manley-Rowe Relations and Parametric AmplificationJan 10 2006Second harmonic generation and optical parametric amplification in negative-index metamaterials (NIMs) are studied. The opposite directions of the wave vector and the Poynting vector in NIMs results in a "backward" phase-matching condition, causing significant ... More

The Planck and LHC results and particle physicsDec 15 2013I will discuss the recent LHC and Planck results, which are completely compatible with the Standard Model of particle physics, and the standard cosmological model ($\Lambda$CDM), respectively. It turns out that the extension of the Standard Model is, ... More

Recomposing rational functionsOct 20 2016Let $A$ be a rational function. For any decomposition $A=V\circ U$ of $A$ into a composition of rational functions $U$ and $V$, the rational function $\tilde A=U\circ V$ is called an elementary transformation of $A$, and rational functions $A$ and $B$ ... More

Mirrorless Negative-index Parametric Micro-oscillatorJul 22 2008The feasibility and extraordinary properties of mirrorless parametric oscillations in strongly absorbing negative-index metamaterials are shown. They stem from the backwardness of electromagnetic waves inherent to this type of metamaterials.

Ultraviolet phenomena in AdS self-interacting quantum field theoryFeb 08 2018We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $\phi^4$ field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general ... More

Hawking radiation and secularly growing loop correctionsAug 29 2015Dec 20 2015We study the expectation value of the energy momentum tensor during thin shell collapse for a massive, real, scalar field theory. At tree-level, we find thermal, Hawking-type, behaviour for the energy flux. Using the Schwinger-Keldysh technique, we calculate ... More

Ultraviolet phenomena in AdS self-interacting quantum field theoryFeb 08 2018Mar 19 2018We study the one-loop corrections to the four-point function in the Anti de Sitter space-time for a $\phi^4$ field theory. Our calculation shows the existence of non-local counterterms which however respect the AdS isometry. Our arguments are quite general ... More

Majorana Fermion Quantum Mechanics for Higher Rank TensorsMay 15 2019We study quantum mechanical models in which the dynamical degrees of freedom are real fermionic tensors of rank five and higher. They are the non-random counterparts of the Sachdev-Ye-Kitaev (SYK) models where the Hamiltonian couples six or more fermions. ... More

A way to distinguish very compact stellar objects from black holesJan 15 2016Feb 15 2016We propose a way to distinguish compact stellar object, whose size is very close to its Schwarzschild radius, from the collapsing stars. Namely, we show that {\it massive} fields in the vicinity of a very compact stellar object have discrete energy levels. ... More

Coherent Nonlinear Optics and Quantum Control in Negative-Index MetamaterialsJun 01 2009The extraordinary properties of laser-induced transparency of a negative-index slab and parametric amplification for a backward-wave signal are investigated. The effects of the idler absorption and phase mismatch on the amplification of the signal are ... More

Atomic collapse in graphene and cyclic RG flowDec 28 2013In this Letter we consider the problem of screening of external charge in graphene from the cyclic RG flow viewpoint. The analogy with conformal Calogero model is used to suggest the interpretation of the tower of resonant states as tower of Efimov states. ... More

Lower bounds on the number of closed trajectories of generalized billiardsApr 11 2006Given a domain or, more generally, a Riemannian manifold with boundary, a billiard is the motion of a particle when the field of force is absent. Trajectories of such a motion are geodesics inside the domain; and the particle reflects from the boundary ... More

Silicon-Vacancy Spin Qubit in Diamond: A Quantum Memory Exceeding 10 ms with Single-Shot State ReadoutAug 29 2017Dec 04 2017The negatively-charged silicon-vacancy (SiV$^-$) color center in diamond has recently emerged as a promising system for quantum photonics. Its symmetry-protected optical transitions enable creation of indistinguishable emitter arrays and deterministic ... More

Perfect Matchings as IID Factors on Non-Amenable GroupsOct 31 2009Sep 18 2011We prove that in every bipartite Cayley graph of every non-amenable group, there is a perfect matching that is obtained as a factor of independent uniform random variables. We also discuss expansion properties of factors and improve the Hoffman spectral ... More

Simplicial James-Hopf map and decompositions of the unstable Adams spectral sequence for suspensionsMar 11 2017We use combinatorial group theory methods to extend the definition of a classical James-Hopf invariant to a simplicial group setting. This allow us to realize certain coalgebra idempotents at sSet -level and obtain a functorial decomposition of the spectral ... More

The Gromov--Guth--Whitney embedding theoremMay 16 2018This is an appendix to arXiv:1610.04888, "Quantitative null-cobordism", which improves one of the main results of that paper to a near-sharp one. It is not a self-contained paper.

On uniformly rational varietiesJun 29 2013We investigate basic properties of uniformly rational varieties, i.e. those smooth varieties for which every point has a Zariski open neighborhood isomorphic to an open subset of A^n. It is an open question of Gromov whether all smooth rational varieties ... More

The geometry of dented pentagram mapsAug 24 2013Dec 08 2014We propose a new family of natural generalizations of the pentagram map from 2D to higher dimensions and prove their integrability on generic twisted and closed polygons. In dimension $d$ there are $d-1$ such generalizations called dented pentagram maps, ... More

Non-integrability vs. integrability in pentagram mapsApr 24 2014We revisit recent results on integrable cases for higher-dimensional generalizations of the 2D pentagram map: short-diagonal, dented, deep-dented, and corrugated versions, and define a universal class of pentagram maps, which are proved to possess projective ... More

A simple energy pump for the surface quasi-geostrophic equationJun 22 2011We consider the question of growth of high order Sobolev norms of solutions of the conservative surface quasi-geostrophic equation. We show that if $s>0$ is large then for every given $A$ there is exist small in $H^s$ initial data such that the corresponding ... More

The Connes character formula for locally compact spectral triplesMar 05 2018May 04 2018A fundamental tool in noncommutative geometry is Connes' character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterisation of manifolds. A non-compact space ... More

On Contraction of Algebraic PointsJul 06 2016Mar 08 2017We study contraction of points on $\mathbb{P}^1(\bar{\mathbb{Q}})$ with certain control on local ramification indices, with application to the unramified curve correspondences problem initiated by Bogomolov and Tschinkel.

Coarse equidistribution of the argument of entire functions of finite orderOct 14 2004We present several results that show somewhat surprising equidistribution patterns in the asymptotic behaviour of the argument of entire functions of finite order.

On a number of rational points on a convex curveMar 15 2005Let $\gamma$ be a bounded convex curve on a plane. Then $\sharp (\gamma\cap (\Z/n)^2)=o(n^{2/3})$. It streghtens the classical result of Jarn\'\i k (an upper estimate $O(n^{2/3})$) and disproves a conjecture of Vershik on existence of the so-called {\it ... More

Algorithms and Polynomiography for Solving Quaternion Quadratic EquationsSep 06 2014Solving a quadratic equation $P(x)=ax^2+bx+c=0$ with real coefficients is known to middle school students. Solving the equation over the quaternions is not straightforward. Huang and So \cite{Huang} give a complete set of formulas, breaking it into several ... More

Global Regularity for the Critical Dispersive Dissipative Surface Quasi-Geostrophic EquationAug 06 2009We consider surface quasi-geostrophic equation with dispersive forcing and critical dissipation. We prove global existence of smooth solutions given sufficiently smooth initial data. This is done using a maximum principle for the solutions involving conservation ... More

Improved Description of One- and Two-Hole States after Electron Capture in 163 Holmium and the Determination of the Neutrino MassJan 18 2015Apr 07 2015The atomic pair 163 Holmium and 163 Dysprosium seems due to the small Q value of about 2.3 to 2.8 keV the best case to determine the neutrino mass by electron capture. The bolometer spectrum measures the full deexcitation energy of Dysprosium by X rays, ... More

Why should we care about the top quark Yukawa coupling?Nov 07 2014Mar 12 2015In the cosmological context, for the Standard Model to be valid up to the scale of inflation, the top quark Yukawa coupling $y_t$ should not exceed the critical value $y_t^{crit}$, coinciding with good precision (about 0.02%) with the requirement of the ... More

Lagrangian fibrations for IHS fourfoldsOct 25 2018In this paper we study the Lagrangian fibrations for projective irreducible symplectic fourfolds and exclude the case of non-smooth base. Our method could be extended to the higher-dimensional cases.

Parafermionic algebras, their modules and cohomologiesFeb 27 2014We explore the Fock spaces of the parafermionic algebra introduced by H.S. Green. Each parafermionic Fock space allows for a free minimal resolution by graded modules of the graded 2-step nilpotent subalgebra of the parafermionic creation operators. Such ... More

A variation on a theme of Caffarelli and VasseurAug 06 2009Aug 10 2009Recently, using DiGiorgi-type techniques, Caffarelli and Vasseur showed that a certain class of weak solutions to the drift diffusion equation with initial data in $L^2$ gain H\"older continuity provided that the BMO norm of the drift velocity is bounded ... More

Traversable wormholes in four dimensionsJul 12 2018Aug 29 2018We present a wormhole solution in four dimensions. It is a solution of an Einstein Maxwell theory plus charged massless fermions. The fermions give rise to a negative Casimir-like energy, which makes the wormhole possible. It is a long wormhole that does ... More

All-optical nanoscale thermometry with silicon-vacancy centers in diamondAug 17 2017We demonstrate an all-optical thermometer based on an ensemble of silicon-vacancy centers (SiVs) in diamond by utilizing a temperature dependent shift of the SiV optical zero-phonon line transition frequency, $\Delta\lambda/\Delta T= 6.8\,\mathrm{GHz/K}$. ... More

Symmetric tensors and the geometry of subvarieties of $\Bbb P^N$Sep 18 2006This paper following a geometric approach proves new, and reproves old, vanishing and nonvanishing results on the space of twisted symmetric differentials, $H^0(X,S^m\Omega^1_X\otimes \Cal O_X(k))$ with $k\le m$, on subvarieties $X\subset \Bbb P^N$. The ... More

Controlling Synthesis of Nanostructured Silver Aggregates by LightDec 17 2004The possibilities for control over the size and properties of silver nanoaggregates with incoherent and laser light are investigated. The applications in nanoengineering and for giant enhancement of optical processes at nanoscale are discussed.

Rademacher averages on noncommutative symmetric spacesMar 31 2008Let E be a separable (or the dual of a separable) symmetric function space, let M be a semifinite von Neumann algebra and let E(M) be the associated noncommutative function space. Let $(\epsilon_k)_k$ be a Rademacher sequence, on some probability space ... More

Level curves of rational functions and unimodular points on rational curvesMay 08 2018May 17 2018We obtain an improvement and broad generalisation of a result of N. Ailon and Z. Rudnick (2004) on common zeros of shifted powers of polynomials. Our approach is based on reducing this question to a more general question of counting intersections of level ... More

Local structure of closed symmetric 2-differentialsOct 04 2014In the authors's previous work on symmetric differentials and their connection to the topological properties of the ambient manifold, a class of symmetric differentials was introduced: closed symmetric differentials ([BoDeO11] and [BoDeO13]). In this ... More

Geometrically induced spectral effects in tubes with a mixed Dirichlet-Neumann boundaryAug 27 2017Dec 30 2017We investigate spectral properties of the Laplacian in $L^2(Q)$, where $Q$ is a tubular region in $\mathbb{R}^3$ of a fixed cross section, and the boundary conditions combined a Dirichlet and a Neumann part. We analyze two complementary situations, when ... More

Congruences on sums of $q$-binomial coefficientsFeb 11 2019We establish a $q$-analogue of Sun--Zhao's congruence on harmonic sums. Based on this $q$-congruence and a $q$-series identity, we prove a congruence conjecture on sums of central $q$-binomial coefficients, which was recently proposed by Guo. We also ... More

Jungles, bundles, and fixed parameter tractabilityDec 07 2011Aug 02 2012We give a fixed-parameter tractable (FPT) approximation algorithm computing the path-width of a tournament, and more generally, of a semi-complete digraph. Based on this result, we prove that topological containment and rooted immersion problems are FPT ... More

Searching for Stopped Gluinos at CMSNov 09 2009We describe plans for a search for long-lived particles which will become stopped by the CMS detector. We will look for the subsequent decay of these particles during time intervals where there are no $pp$ collisions in CMS: during gaps between crossings ... More

Basis entropy in Banach spacesOct 27 2013We introduce and study two notions of entropy in a Banach space X with a normalized Schauder basis . The geometric entropy E(A) of a subset A of X is defined to be the infimum of radii of compact bricks containing A. We obtain several compactness characterizations ... More

Off-line studies of the laser ionization of yttrium at the IGISOL facilitySep 26 2007A laser ion source is under development at the IGISOL facility, Jyvaskyla, in order to address deficiencies in the ion guide technique. The key elements of interest are those of a refractory nature, whose isotopes and isomers are widely studied using ... More

Conditional and uniform quenched CLTs for one-dimensional random walks among random conductancesNov 04 2010Oct 04 2012We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) ... More

Finite subgroups of diffeomorphism groupsOct 24 2013Jan 06 2014We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite simple subgroups ... More

Statefinder analysis of the superfluid Chaplygin gas modelMay 22 2011Dec 05 2011The statefinder indices are employed to test the superfluid Chaplygin gas (SCG) model describing the dark sector of the universe. The model involves Bose-Einstein condensate (BEC) as dark energy (DE) and an excited state above it as dark matter (DM). ... More

Invariants of isospectral deformations and spectral rigidityJun 02 2009Dec 15 2010We introduce a notion of weak isospectrality for continuous deformations. Consider the Laplace-Beltrami operator on a compact Riemannian manifold with boundary with Robin boundary conditions. Given a Kronecker invariant torus $\Lambda$ of the billiard ... More

Total flooding time and rumor propagation on graphsJan 26 2016We study a model of rumor propagation in discrete time where each site in the graph has initially a distinct information; we are interested in the number of "conversations" before the entire graph knows all informations. This problem can be described ... More

Algebraic conesAug 08 2009A characterization of algebraic cones in terms of actions of the one-dimensional multiplicative algebraic monoid ${\bf M}_{\rm m}$ and the algebraic group ${\bf G}_{\rm m}$ are given.

Biased random walk on the interlacement setOct 10 2016Apr 24 2017We study a biased random walk on the interlacement set of $\mathbb{Z}^d$ for $d\geq 3$. Although the walk is always transient, we can show, in the case $d=3$, that for any value of the bias the walk has a zero limiting speed and actually moves slower ... More

Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiardsAug 31 2010Jun 18 2011We consider a random walk in a stationary ergodic environment in $\mathbb Z$, with unbounded jumps. In addition to uniform ellipticity and a bound on the tails of the possible jumps, we assume a condition of strong transience to the right which implies ... More

Shape and local growth for multidimensional branching random walks in random environmentSep 18 2007Nov 13 2007We study branching random walks in random environment on the $d$-dimensional square lattice, $d \geq 1$. In this model, the environment has finite range dependence, and the population size cannot decrease. We prove limit theorems (laws of large numbers) ... More

Generic algebras: rational parametrization and normal formsNov 24 2014Jan 19 2015For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to isomorphism, ... More

Hasq Hash ChainsDec 14 2014This paper describes a particular hash-based records linking chain scheme. This scheme is simple conceptually and easy to implement in software. It allows for a simple and secure way to transfer ownership of digital objects between peers.

Integration of Flexible Web Based GUI in I-SOASNov 14 2010It is necessary to improve the concepts of the present web based graphical user interface for the development of more flexible and intelligent interface to provide ease and increase the level of comfort at user end like most of the desktop based applications. ... More

On pairs, triples and quadruples of points on a cubic surfaceOct 13 2018Apr 22 2019Let $X^{(n)}$ denote $n$-th symmetric power of a cubic surface $X$. We show that $X^{(4)}\times X$ is stably birational to $X^{(3)}\times X$, despite examples when $X^{(4)}$ is not stably birational to $X^{(3)}$.

A Calderon Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of BourgainDec 15 2009We introduce a Calderon Zygmund decomposition such that the bad function has vanishing integral against a number of pure frequencies. Then we prove a variation norm variant of a maximal inequality for several frequencies due to Bourgain. To obtain the ... More

Two weight inequalities for individual Haar multipliers and other well localized operatorsFeb 26 2007In this paper we are proving that Sawyer type condition for boundedness work for the two weight estimates of individual Haar multipliers, as well as for the Haar shift and other "well localized" operators.

The power law for the Buffon needle probability of the four-corner Cantor setJan 18 2008Let $C_n$ be the $n$-th generation in the construction of the middle-half Cantor set. The Cartesian square $K_n$ of $C_n$ consists of $4^n$ squares of side-length $4^{-n}$. The chance that a long needle thrown at random in the unit square will meet $K_n$ ... More

Virtual continuity of the measurable functions of several variables, and Sobolev embedding theoremsJul 12 2013Jul 16 2013Classical Luzin's theorem states that the measurable function of one variable is "almost" continuous. This is not so anymore for functions of several variables. The search of right analogue of the Luzin theorem leads to a notion of virtually continuous ... More

Global estimates for kernels of Neumann series and Green's functionsMar 16 2014We obtain global pointwise estimates for kernels of the resolvents $(I-T)^{-1}$ of integral operators \[Tf(x) = \int_{\Omega} K(x, y) f(y) d \omega(y)\] on $L^2(\Omega, \omega)$ under the assumptions that $||T||_{L^2(\omega) \rightarrow L^2 (\omega)} ... More

Convolutions of Cantor measures without resonanceMay 23 2009Denote by $\mu_a$ the distribution of the random sum $(1-a) \sum_{j=0}^\infty \omega_j a^j$, where $P(\omega_j=0)=P(\omega_j=1)=1/2$ and all the choices are independent. For $0<a<1/2$, the measure $\mu_a$ is supported on $C_a$, the central Cantor set ... More

Fermionic structure in the sine-Gordon model: form factors and null-vectorsMay 31 2011The form factor bootstrap in integrable quantum field theory allows one to capture local fields in terms of infinite sequences of Laurent polynomials called `towers'. For the sine-Gordon model, towers are systematically described by fermions introduced ... More

On stable cohomology of central extensions of elementary abelian groupsSep 28 2018We study when kernels of inflation maps associated to extraspecial p-groups in stable group cohomology are generated by their degree two components. This turns out to be true if the prime is large enough compared to the rank of the elementary abelian ... More

Gelfand-type problem for turbulent jetsMay 27 2019We consider the model of auto-ignition (thermal explosion) of a free round reactive turbulent jet. This model falls into the general class of Gelfand-type problems and constitutes a boundary value problem for a certain semi-linear elliptic equation that ... More

On the distinction between the classes of Dixmier and Connes-Dixmier tracesOct 11 2012In the present paper we prove that the classes of Dixmier and Connes-Dixmier traces differ even on the Dixmier ideal $\mathcal M_{1,\infty}$. We construct a Marcinkiewicz space $\mathcal M_\psi$ and a positive operator $T\in \mathcal M_\psi$ which is ... More

A Polynomial kernel for Proper Interval Vertex DeletionApr 22 2012It is known that the problem of deleting at most k vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we answers this ... More

Lower bounds for uncentered maximal functions in any dimensionFeb 18 2016In this paper we address the following question: given $ p\in (1,\infty)$, $n \geq 1$, does there exists a constant $A(p,n)>1$ such that $\| M f\|_{L^{p}}\geq A(n,p) \| f\|_{L^{p}}$ for any nonnegative $f \in L^{p}(\mathbb{R}^{n})$, where $Mf$ is a maximal ... More

Quantum Nonlinear Optics with a Germanium-Vacancy Color Center in a Nanoscale Diamond WaveguideDec 09 2016Jun 01 2017We demonstrate a quantum nanophotonics platform based on germanium-vacancy (GeV) color centers in fiber-coupled diamond nanophotonic waveguides. We show that GeV optical transitions have a high quantum efficiency and are nearly lifetime-broadened in such ... More

Spectra of Eigenstates in Fermionic Tensor Quantum MechanicsFeb 28 2018Jul 31 2018We study the $O(N_1)\times O(N_2)\times O(N_3)$ symmetric quantum mechanics of 3-index Majorana fermions. When the ranks $N_i$ are all equal, this model has a large $N$ limit which is dominated by the melonic Feynman diagrams. We derive an integral formula ... More

Spectrum of Majorana Quantum Mechanics with $O(4)^3$ SymmetryAug 22 2018Feb 11 2019We study the quantum mechanics of 3-index Majorana fermions $\psi^{abc}$ governed by a quartic Hamiltonian with $O(N)^3$ symmetry. Similarly to the Sachdev-Ye-Kitaev model, this tensor model has a solvable large $N$ limit dominated by the melonic diagrams. ... More

Bellman approach to the one-sided bumping for weighted estimates of Calderón--Zygmund operatorsJun 11 2013Jan 18 2014We give again (see also arXiv:1112.0676) a proof of weighted estimate of any Calder\'on-Zygmund operator. This is under a universal sharp sufficient condition that is weaker than the so-called bump condition. Bump conjecture was recently solved independently ... More

A simple Online Fair Division problemMar 25 2019A fixed set of $n$ agents share a random object: the distribution $\mu$ of the profile of utilities is IID across periods, but arbitrary across agents. We consider a class of online division rules that learn the realized utility profile, and only know ... More

Structure of the two-neutrino double-$β$ decay matrix elements within perturbation theoryJun 02 2015The two-neutrino double-$\beta$ Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It ... More

Holomorphic functional calculus on upper triangular forms in finite von Neumann algebrasOct 09 2013The decompositions of an element of a finite von Neumann algebra into the sum of a normal operator plus an s.o.t.-quasinilpotent operator, obtained using the Haagerup--Schultz hyperinvariant projections, behave well with respect to holomorphic functional ... More

Blow up and regularity for fractal Burgers equationApr 22 2008The paper is a comprehensive study of the existence, uniqueness, blow up and regularity properties of solutions of the Burgers equation with fractional dissipation. We prove existence of the finite time blow up for the power of Laplacian $\alpha < 1/2,$ ... More

A $C^*$-algebraic approach to the principal symbol IIJun 19 2018We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings important in ... More

Dixmier traces generated by exponentiation invariant generalised limitsOct 11 2012We define a new class of singular positive traces on the ideal $\mathcal M_{1,\infty}$ of $B(H)$ generated by exponentiation invariant generalized limits. We prove that this new class is strictly contained in the class of all Dixmier traces. We also prove ... More

The Riesz transform, rectifiability, and removability for Lipschitz harmonic functionsDec 21 2012Dec 05 2013We show that, given a set $E\subset \mathbb R^{n+1}$ with finite $n$-Hausdorff measure $H^n$, if the $n$-dimensional Riesz transform $$R_{H^n|E} f(x) = \int_{E} \frac{x-y}{|x-y|^{n+1}} f(y) dH^n(y)$$ is bounded in $L^2(H^n|E)$, then $E$ is $n$-rectifiable. ... More

On the uniform rectifiability of AD regular measures with bounded Riesz transform operator: the case of codimension 1Dec 20 2012Dec 21 2012We prove that if $\mu$ is a d-dimensional Ahlfors-David regular measure in $\R^{d+1}$, then the boundedness of the $d$-dimensional Riesz transform in $L^2(\mu)$ implies that the non-BAUP David-Semmes cells form a Carleson family. Combined with earlier ... More

Unirationality and existence of infinitely transitive modelsApr 04 2012Oct 17 2012We study unirational algebraic varieties and the fields of rational functions on them. We show that after adding a finite number of variables some of these fields admit an infinitely transitive model. The latter is an algebraic variety with the given ... More

Anomalous acoustoelectric effect in La_{0.67}Ca_{0.33}MnO_{3} filmsOct 19 2001We have studied acoustoelectric (AE) effect produced by surface acoustic waves (SAW) in a monolithic layered structure, composed of piezodielectric LiNbO_{3} substrate and La_{0.67}Ca_{0.33}MnO_{3} film. The experiments unexpectedly revealed in the longitudinal ... More

Krein's trace theorem revisitedDec 14 2016We supply the first proof of Krein's Trace Theorem which does not use complex analysis. Our proof holds for~$\sigma$-finite von Neumann algebras $\mathcal{M}$ of type II and unbounded perturbations from the predual of~$\mathcal{M}$.

The fractional Riesz transform and an exponential potentialApr 10 2012Oct 09 2012In this paper we study the $s$-dimensional Riesz transform of a finite measure $\mu$ in $\mathbf{R}^d$, with $s\in (d-1,d)$. We show that the boundedness of the Riesz transform of $\mu$ implies that a nonlinear potential of exponential type is finite ... More

Criteria for the Absence and Existence of Bounded Solutions at the Threshold Frequency in a Junction of Quantum WaveguidesMay 30 2017Dec 07 2017In the junction $\Omega$ of several semi-infinite cylindrical waveguides we consider the Dirichlet Laplacian whose continuous spectrum is the ray $[\lambda_\dagger, +\infty)$ with a positive cut-off value $\lambda_\dagger$. We give two different criteria ... More

Notes on derivations of Murray--von Neumann algebrasJun 01 2019Let $\mathcal{M}$ be a type II$_1$ von Neumann factor and let $S(\mathcal{M})$ be the associated Murray-von Neumann algebra of all measurable operators affiliated to $\mathcal{M}.$ We extend a result of Kadison and Liu \cite{KL} by showing that any derivation ... More

Self-derived localizations of groupsMay 18 2019We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most interesting class is the class of localizations which coincide with their zero derived functors. We call them ... More

New coins from old, smoothlyAug 14 2008Jan 25 2010Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be random. The work ... More

Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structureMay 17 2010Feb 27 2012The SU(4)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion manifolds of the form M x G/H, with G/H a coset space and M a product of a torus with Euclidean space. ... More

Every operator has almost-invariant subspacesAug 29 2012We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we show that the ... More

Intuitive dyadic calculus: the basicsAug 23 2015This book is a short introduction into dyadic analysis with applications to classical weighted norm inequalities.

Minimum Degree of the Difference of Two Polynomials over $\mathbb Q$. Part II: Davenport-Zannier pairsSep 26 2015Oct 24 2015In this paper we study pairs of polynomials with a given factorization pattern and such that the degree of their difference attains its minimum. We call such pairs of polynomials Davenport--Zannier pairs, or DZ-pairs for short. The paper is devoted to ... More

Discovery of optical flickering from the symbiotic star EF AquilaeFeb 27 2017We report optical CCD photometry of the recently identified symbiotic star EF Aql. Our observations in Johnson V and B bands clearly show the presence of stochastic light variations with an amplitude of about 0.2 mag on a time scale of minutes. The observations ... More

Cherenkov Detectors Fast Simulation Using Neural NetworksMar 28 2019We propose a way to simulate Cherenkov detector response using a generative adversarial neural network to bypass low-level details. This network is trained to reproduce high level features of the simulated detector events based on input observables of ... More

Noncommutative Geometry for Symmetric Non-Self-Adjoint OperatorsAug 06 2018Jan 06 2019We introduce the notion of a pre-spectral triple, which is a generalisation of a spectral triple $(\mathcal{A}, H, D)$ where $D$ is no longer required to be self-adjoint, but closed and symmetric. Despite having weaker assumptions, pre-spectral triples ... More