Self-dual configurations in a generalized Abelian Chern-Simons-Higgs model with explicit breaking of the Lorentz covariance - Casana, Rodolfo et al. D91 no. Noncommutative phenomena in flat and curved space-times - Millner, Anthony. Lumpy cosmic strings - Lake, Matthew J. Maxwell—Higgs self-dual solitons on an infinite cylinder - Casana, Rodolfo et al. A30 no. Vortex solutions in a Witten-type model - Itaya, Satoru et al. Vortex solutions of an Abelian Higgs model with visible and hidden sectors - Arias, Paola et al.

D90 no. Note on vortices from Lorentz-violating models - Sourrouille, Lucas Phys. D89 no. D87 no. PoS ConfinementX arXiv Three lectures on noncommutative field theories - Schaposnik, F. C71 D15 COO Peristaltic modes of single vortex in the Abelian Higgs model - Kojo, Toru et al. Instabilities of Twisted Vortices - Forgacs, Peter et al. Topological contributions to fermionic correlators and nonperturbative aspects of QCD in two-dimensions - Christiansen, Hugo R. Zero modes and conformal anomaly in Liouville vortices - Nardelli, G.

D83 arXiv Nagaraja et al. D19 CU-TP Construction of topological defect networks with complex scalar fields - Afonso, V. Generalized self-dual Chern-Simons vortices - Bazeia, D.

D81 arXiv Selfdual Chern-Simons solitons in noncommutative space - Lozano, G. Born-Infeld action and supersymmetry - Silva, G. An Argument for unsuppressed anomalous fermion number violation in high-energy collisions? One loop corrections to the mass of self-dual semi-local planar topological solitons - Izquierdo, A. Alonso et al. Threshold bound states and zero modes of fermions in a selfdual Chern-Simons vortex background - Grignani, G. Scattering of low-energy fermions by a background of Chern-Simons vortices - Grignani, G. Effective string theory of vortices and Regge trajectories of hybrid mesons with zero mass quarks - Baker, M.

Domain walls in a generalized Chern-Simons model - dos Santos, C.

C70 Bogomolny type equations for gravitating gauged sigma models - Forgacs, P. Effective theory on non-Abelian vortices in six dimensions - Eto, Minoru et al. Quantum fluctuations around low-dimensional topological defects - Mateos Guilarte, Juan et al. The Self - gravitating gas in the presence of dark energy - de Vega, H. A concept of strong necessary condition in nonlinear field theory - Sokalski, K. B32 Multi-vortices are wall vortices: A Numerical proof - Bolognesi, Stefano et al. Quantum mass and central charge of supersymmetric monopoles: Anomalies, current renormalization, and surface terms - Rebhan, Anton et al.

Weyl invariant formulation of flux tube solution in the dual Ginzburg-Landau theory - Koma, Yoshiaki et al. B78 arXiv D78 arXiv Gluodynamics in external field: A Test of the dual superconductor picture - Chernodub, M. Classical string solutions in effective infrared theory of SU 3 gluodynamics - Chernodub, M.

## A Classical Vortex Solution of the Abelian Higgs Model - INSPIRE-HEP

Effective string theory of vortices and Regge trajectories - Baker, M. Lectures on abelian Chern-Simons vortices - Horvathy, P. D85 arXiv D82 On polynomial approximation of the static vortex in Abelian Higgs model - Karkowski, J. NonAbelian string conductivity - Kibble, T. Transmogrifying fuzzy vortices - Murugan, Jeff et al. A Topological model for two-dimensional gravity coupled to matter - Cugliandolo, L. Generalized Noninteracting Vortices - Lohe, M.

D61 D43 Bogomolny limit for nontopological solitons in a Chern-Simons model with anomalous magnetic moment - Torres, M. D46 RR Korean Phys. New developments in the quantization of supersymmetric solitons kinks, vortices and monopoles - Rebhan, Anton et al. Vortices - Schaposnik, F. Analogies between self-duality and stealth matter source - Hassaine, Mokhtar J.

On the supermassive U 1 gauge cosmic strings - Linet, B. A Topologically nontrivial sectors in the Abelian Higgs model with massless fermions - Cabra, D. D44 Simple models with Alice fluxes - Striet, J. Casimir scaling in a dual superconducting scenario of confinement - Koma, Y.

The String equation and solitons - Novikov, S. NATO Sci. Gluodynamics in external field in dual superconductor approach - Chernodub, M. D73 , Erratum: Phys. Multiflavor correlation functions in nonAbelian gauge theories at finite fermion density in two-dimensions - Christiansen, H.

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In this paper, we show that the same is true within a smaller and simpler class of functions, which we call rigid systems. As a consequence, the problem of describing the joint spectrum of a family of exponents of Diophantine approximation is reduced to combinatorial analysis. This paper describes a characterization of tightness of closed contact 3-manifolds in terms of supporting open book decompositions. The main result is that tightness of a closed contact 3-manifold is preserved under Legendrian surgery.

In this article, we solve the strong openness conjecture on the multiplier ideal sheaf associated to any plurisubharmonic function, which was posed by Demailly. This has a wide range of important consequences. Another one is an improvement in the range for the discrete restriction theorem for lattice points on the sphere.

Our argument relies on the interplay between linear and multilinear restriction theory. We use the method of interlacing polynomials introduced in our previous article to prove two theorems known to imply a positive solution to the Kadison— Singer problem. The second is a formulation due to Casazza et al. We do this by proving a variant of a conjecture of Bilu and Linial about the existence of good 2-lifts of every graph. Such families were conjectured to exist by Linial and others.

In particular, this shows the existence of simply connected surfaces of general type arbitrarily close to the Bogomolov -Miyaoka-Yau line. We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure constants of two-step flag varieties. This formula gives an expression for the structure constants that is positive in the sense of Graham. The construction involves a superposition of weakly interacting perturbed Beltrami flows on infinitely many scales.

An obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field. In this paper we give a shorter proof of this final result, adhering more to the original scheme of the second and fourth authors and introducing some new devices. We prove the positivity conjecture for all skew-symmetric cluster algebras. We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces.

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Combined with our previous work on the Surface Subgroup Theorem, this yields a proof of the Ehrenpreis Conjecture. We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature.

The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques. This partially answers a long standing question of A. Katok regarding zero entropy Hamiltonian systems in low dimensions. Our approach uses pseudoholomorphic curve techniques from symplectic geometry. In principle, this gives informations on the transcendence properties of series of periods. Our main result is reminiscent to the Kontsevich- Zagier conjecture on periods in a modified form. This was predicted by a classical conjecture, originally stated by Brieskorn for complexified real reflection groups.

The complexified real case follows from a theorem of Deligne and, after contributions by Nakamura and Orlik-Solomon, only six exceptional cases remained open. In addition to solving these six cases, our approach is applicable to most previously known cases, including complexified real groups for which we obtain a new proof, based on new geometric objects. We prove that these conjectures are compatible with fibrations, for fibrations into rationally connected varieties over a curve.

In particular, they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers. We prove the analogous result for rational points, conditionally on a conjecture on locally split values of polynomials which a recent work of Matthiesen establishes in the case of linear polynomials over the rationals.

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The results in the positive case parallel those in the smooth case. We also establish that solutions of this problem are polyhomogeneous , i. The proof of this theorem relies on the construction of a family of sheaves of locally analytic overconvergent modular forms. We use this result to show that the average size of the 3-Selmer group of all elliptic curves, when ordered by height , is equal to 4.

This implies that the average rank of all elliptic curves, when ordered by height , is less than 1. Combining our counting techniques with a recent result of Dokchitser and Dokchitser, we prove that a positive proportion of all elliptic curves have rank 0. Assuming the finiteness of the Tate—Shafarevich group , we also show that a positive proportion of elliptic curves have rank 1. Finally, combining our counting results with the recent work of Skinner and Urban, we show that a positive proportion of elliptic curves have analytic rank 0; i.

It follows that a positive proportion of all elliptic curves satisfy BSD. We show that the base complex manifold of an effectively parametrized holomorphic family of compact canonically polarized complex manifolds admits a smooth invariant Finsler metric whose holomorphic sectional curvature is bounded above by a negative constant. As a consequence, we show that such a base manifold is Kobayashi hyperbolic. Similar results hold also for the system PCR the natural common extension of Polynomial Calculus and Resolution when the characteristic of the ground field is different from 2.

As a byproduct, we also improve on the small restriction switching lemma due to Segerlind , Buss and Impagliazzo by removing a square root from the final bound. We apply automorphy lifting techniques to establish new cases of symmetric power functoriality for Hilbert modular forms of regular algebraic weight. The proof is based on a novel application of an automorphy lifting theorem for residually reducible Galois representations. Our techniques are quite general and may be applied to counting integral orbits in other representations of algebraic groups.

We follow the setup of Elekes and Sharir which, in the spirit of the Erlangen program , allows us to study the problem in the group of rigid motions of the plane. This converts the problem to one of point-line incidences in space. We introduce two new ideas in our proof. In order to control points where many lines are incident, we create a cell decomposition using the polynomial ham sandwich theorem.

This creates a dichotomy: either most of the points are in the interiors of the cells, in which case we immediately get sharp results or, alternatively, the points lie on the walls of the cells, in which case they are in the zero-set of a polynomial of suprisingly low degree , and we may apply the algebraic method. In order to control points incident to only two lines, we use the flecnode polynomial of the Rev. George Salmon to conclude that most of the lines lie on a ruled surface. Then we use the geometry of ruled surfaces to complete the proof. This paper is the fifth and final in a series on embedded minimal surfaces.

The first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely-oriented double spiral staircases.

## Lecture Notes

The second gives a pair of pants decomposition of any such surface when there are small necks, cutting the surface along a collection of short curves. After the cutting , we are left with graphical pieces that are defined over a disk with either one or two sub-disks removed a topological disk with two sub-disks removed is called a pair of pants. Both of these structures occur as different extremes in the two-parameter family of minimal surfaces known as the Riemann examples.

We construct an initial data for the two-dimensional Euler equation in a disk for which the gradient of vorticity exhibits double exponential growth in time for all times. This estimate is known to be sharp — the double exponential growth is the fastest possible growth rate. We present a positive solution to the so-called Bernoulli Conjecture concerning the characterization of sample boundedness of Bernoulli processes.

We also discuss some applications and related open problems. We deduce that Kazhdan- Lusztig polynomials have positive coefficients for arbitrary Coxeter systems. Using results of Soergel one may deduce an algebraic proof of the Kazhdan- Lusztig conjecture.

By the relative trace formula approach of Jacquet—Rallis, we prove the global Gan — Gross —Prasad conjecture for unitary groups under some local restrictions for the automorphic representations. We construct a Euler system in the cohomology of the tensor product of the Galois representations attached to two modular forms, using elements in the higher Chow groups of products of modular curves. We introduce a new compactification of the space of relative stable maps. This approach uses logarithmic geoemetry in the sense of Kato-Fontaine-Illusie without taking expansions of the target.

The underlying structures of the stable logarithmic maps are stable in the usual sense. This is an erratum to the paper The quantitative behaviour of polynomial orbits on nilmanifolds by the authors, published as Ann.

The proof of Theorem 8. We provide two fixes for this issue here. This is the same basic mode of argument we attempted originally , though the details are different. The equal sides case is the only one required in applications such as the proof of the inverse conjectures for the Gowers norms due to the authors and Ziegler. A major ingredient of the proof is a stronger version of the Bombieri- Vinogradov theorem that is applicable when the moduli are free from large prime divisors only, but it is adequate for our purpose.

We show that every holomorphic one-form on a smooth complex projective variety of general type must vanish at some point. The proof uses generic vanishing theory for Hodge modules on abelian varieties. We describe the vanishing threshold and show that it is sharp. We classify truncations of level 1 and describe their specialization behavior.

In the last section we relate our invariant to the Ekedahl-Oort stratification of the Siegel moduli space and to generalizations to other PEL Shimura varieties. Thus, our theory subsumes the well-known regularity theory for codimension 1 area minimizing rectifiable currents and settles the long standing question as to which weakest size hypothesis on the singular set of a stable minimal hypersurface guarantees the validity of the above regularity conclusions. An optimal strong maximum principle for stationary codimension 1 integral varifolds follows from our regularity and compactness theorems.

However, our construction of the ideal is very different from that of Haiman, using the formalism of divided powers rather than representation theory. We show that the conjecture of Oort on lifting covers of curves is true. A kind of boundedness result is given as well.

We prove a critical case of this conjecture. Moreover, we can prove that the Donaldson-Futaki invariants of the appearing models decrease. In , T. We prove this conjecture using the min-max theory of minimal surfaces. Skip to content. Rectifiable- Reifenberg and the regularity of stationary and minimizing harmonic maps. Cyclic surfaces and Hitchin components in rank 2. Pages by Assaf Naor From volume Geometric invariants for real quadratic fields. Pages by W. Pages by Reiko Miyaoka From volume Finite time singularity for the modified SQG patch equation.

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