In this paper we recover the non-perturbative partition function of 2D Yang–Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang–Mills theory on surfaces with boundaries and corners in the Batalin–Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting–-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces–-building blocks–-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang–Mills theory.

1 aIraso, Riccardo1 aMnev, P. uhttps://doi.org/10.1007/s00220-019-03392-w01022nas a2200121 4500008004100000245005500041210005500096520063900151100002100790700002300811700001800834856004800852 2018 en d00aTransmission conditions obtained by homogenisation0 aTransmission conditions obtained by homogenisation3 aWe study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems.1 aDal Maso, Gianni1 aFranzina, Giovanni1 aZucco, Davide uhttp://preprints.sissa.it/handle/1963/3531001137nas a2200133 4500008004100000245009100041210006900132260001000201520068100211100001600892700002900908700001800937856004800955 2018 en d00aTruncation and convergence issues for bounded linear inverse problems in Hilbert space0 aTruncation and convergence issues for bounded linear inverse pro bSISSA3 aWe present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests.1 aCaruso, Noe1 aMichelangeli, Alessandro1 aNovati, Paolo uhttp://preprints.sissa.it/handle/1963/3532601540nas a2200133 4500008004100000245006000041210005900101520111900160100001301279700002401292700001901316700002301335856004801358 2017 en d00aTime quasi-periodic gravity water waves in finite depth0 aTime quasiperiodic gravity water waves in finite depth3 aWe prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.1 aBaldi, P1 aBerti, Massimiliano1 aHaus, Emanuele1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3529601183nas a2200121 4500008004100000245007100041210006300112260001800175520077400193100002100967700002200988856005101010 2016 en d00aOn the third critical speed for rotating Bose-Einstein condensates0 athird critical speed for rotating BoseEinstein condensates bAIP Publisher3 aWe study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε−4, with ε−2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.1 aDimonte, Daniele1 aCorreggi, Michele uhttp://urania.sissa.it/xmlui/handle/1963/3524601454nas a2200157 4500008004100000245007300041210006900114260003500183300001100218490000700229520093500236100002201171700002501193700002201218856005601240 2016 eng d00aTowards a gauge theory interpretation of the real topological string0 aTowards a gauge theory interpretation of the real topological st bAmerican Physical SocietycMar a0660010 v933 aWe consider the real topological string on certain noncompact toric Calabi-Yau three-folds $\mathbb{X}$, in its physical realization describing an orientifold of type IIA on $\mathbb{X}$ with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol’nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

1 aHayashi, Hirotaka1 aPiazzalunga, Nicolò1 aUranga, Angel, M. uhttps://link.aps.org/doi/10.1103/PhysRevD.93.06600100906nas a2200157 4500008004100000022001400041245004500055210004400100260000800144300001400152490000700166520048600173100002300659700002000682856004600702 2016 eng d a1572-909500at-Structures are Normal Torsion Theories0 atStructures are Normal Torsion Theories cApr a181–2080 v243 aWe characterize $t$-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathcal{t}$ on a stable $\infty$-category $\mathbb{C}$ is equivalent to a normal torsion theory $\mathbf{F}$ on $\mathbb{C}$, i.e. to a factorization system $\mathbf{F} = (\mathcal{\epsilon}, \mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

1 aFiorenza, Domenico1 aLoregian, Fosco uhttps://doi.org/10.1007/s10485-015-9393-z01189nas a2200121 4500008004100000245005100041210004600092260001000138520072900148653011900877100002000996856005101016 2016 en d00at-structures on stable (infinity,1)-categories0 atstructures on stable infinity1categories bSISSA3 aThe present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosický, Tholen, and Cassidy-Hébert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from.10acategory theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra1 aLoregian, Fosco uhttp://urania.sissa.it/xmlui/handle/1963/3520200745nas a2200121 4500008004100000245005600041210005600097260001000153520032000163653003100483100001800514856009100532 2016 en d00aTwo explorations in Dynamical Systems and Mechanics0 aTwo explorations in Dynamical Systems and Mechanics bSISSA3 aThis thesis contains the work done by Paolo Gidoni during the doctorate programme in Matematical Analysis at SISSA, under the supervision of A. Fonda and A. DeSimone. The thesis is composed of two parts: "Avoiding cones conditions and higher dimensional twist" and "Directional friction in bio-inspired locomotion".10aPoincaré-Birkhoff Theorem1 aGidoni, Paolo uhttps://www.math.sissa.it/publication/two-explorations-dynamical-systems-and-mechanics01401nas a2200121 4500008004100000245007200041210006900113260001300182520098700195100002401182700002201206856005101228 2015 en d00aThree-sphere low-Reynolds-number swimmer with a passive elastic arm0 aThreesphere lowReynoldsnumber swimmer with a passive elastic arm bSpringer3 aOne of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers.1 aMontino, Alessandro1 aDeSimone, Antonio uhttp://urania.sissa.it/xmlui/handle/1963/3453000591nas a2200145 4500008004100000245009500041210006900136260003700205300001600242490000600258100002000264700001800284700002200302856012100324 2015 eng d00aA topological join construction and the Toda system on compact surfaces of arbitrary genus0 atopological join construction and the Toda system on compact sur bMathematical Sciences Publishers a1963–20270 v81 aJevnikar, Aleks1 aKallel, Sadok1 aMalchiodi, Andrea uhttps://www.math.sissa.it/publication/topological-join-construction-and-toda-system-compact-surfaces-arbitrary-genus00787nas a2200121 4500008004100000245013000041210006900171260001000240520031200250100002300562700002900585856005100614 2015 en d00aTranslation and adaptation of Birman's paper "On the theory of self-adjoint extensions of positive definite operators" (1956)0 aTranslation and adaptation of Birmans paper On the theory of sel bSISSA3 aThis is an accurate translation from Russian and adaptation to the modern mathematical jargon of a classical paper by M. Sh. Birman published in 1956, which is still today central in the theory of self-adjoint extensions of semi-bounded operators, and for which yet no English version was available so far.1 aKhotyakov, Mikhail1 aMichelangeli, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3444301418nas a2200133 4500008004100000245010100041210006900142260003500211520074700246653011900993100002101112700002101133856013001154 2014 en d00aTopological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene0 aTopological Invariants of Eigenvalue Intersections and Decrease bJournal of Statistical Physics3 aWe investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|≤const |x|^{−2} as |x|→∞, both in monolayer and bilayer graphene.

10aWannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene1 aMonaco, Domenico1 aPanati, Gianluca uhttps://www.math.sissa.it/publication/topological-invariants-eigenvalue-intersections-and-decrease-wannier-functions-graphene00781nas a2200121 4500008004100000245008700041210006900128260003100197520034000228100001800568700002200586856005100608 2014 en d00aThe topology of a subspace of the Legendrian curves on a closed contact 3-manifold0 atopology of a subspace of the Legendrian curves on a closed cont bAdvanced Nonlinear Studies3 aIn this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry.1 aMaalaoui, Ali1 aMartino, Vittorio uhttp://urania.sissa.it/xmlui/handle/1963/3501600364nas a2200109 4500008004100000245004800041210004800089260001000137653004600147100002500193856003600218 2013 en d00aTopology of moduli spaces of framed sheaves0 aTopology of moduli spaces of framed sheaves bSISSA10aModuli spaces, framed sheaves, instantons1 aAbdellaoui, Gharchia uhttp://hdl.handle.net/1963/715201015nas a2200133 4500008004100000245004500041210003400086260001000120520062000130100001800750700001900768700002100787856007300808 2013 en d00aOn the tritronquée solutions of P$_I^2$0 atritronquée solutions of PI2 bSISSA3 aFor equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\to\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\hat u^{(m)}(x,t)$, $m=0,\dots,6$, called {\em tritronqu\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\'ee solutions.

1 aGrava, Tamara1 aKapaev, Andrey1 aKlein, Christian uhttps://www.math.sissa.it/publication/tritronqu%C3%A9e-solutions-pi200562nas a2200109 4500008004100000245004400041210004400085260001900129520024700148100002100395856003600416 2012 en d00aTabulation of Painlevé 6 transcendents0 aTabulation of Painlevé 6 transcendents bIOP Publishing3 aThe critical and asymptotic behaviors of solutions of the sixth Painlev'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/652000948nas a2200121 4500008004100000245006000041210006000101260002200161520056500183100002400748700001800772856003600790 2012 en d00aThermodynamic phase transitions and shock singularities0 aThermodynamic phase transitions and shock singularities bThe Royal Society3 aWe show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed.1 aDe Nittis, Giuseppe1 aMoro, Antonio uhttp://hdl.handle.net/1963/609001511nas a2200145 4500008004100000245007100041210006900112260001000181520099600191653006801187100002001255700002901275700002501304856003601329 2012 en d00aTopological sensitivity analysis for high order elliptic operators0 aTopological sensitivity analysis for high order elliptic operato bSISSA3 aThe topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders.10aTopological derivative, Elliptic operators, Polarization tensor1 aAmstutz, Samuel1 aNovotny, Antonio, André1 aVan Goethem, Nicolas uhttp://hdl.handle.net/1963/634301043nas a2200097 4500008004100000245013400041210006900175520055400244100001800798856012900816 2011 eng d00aThin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity0 aThinwalled beams with a crosssection of arbitrary geometry deriv3 aThe subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

1 aDavoli, Elisa uhttps://www.math.sissa.it/publication/thin-walled-beams-cross-section-arbitrary-geometry-derivation-linear-theories-starting00881nas a2200133 4500008004300000245008900043210007100132260001300203520043200216100001800648700002500666700002000691856003600711 2011 en_Ud 00aThe time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity0 atimedependent von Kármán plate equation as a limit of 3d nonline bSpringer3 aThe asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.1 aAbels, Helmut1 aMora, Maria Giovanna1 aMüller, Stefan uhttp://hdl.handle.net/1963/383500558nas a2200121 4500008004100000245011500041210006900156300000900225490002900234100001900263700002000282856013400302 2011 eng d00aThe Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach0 aTransition between the Gap Probabilities from the Pearcey to the a1-500 vdoi: 10.1093/imrn/rnr0661 aBertola, Marco1 aCafasso, Mattia uhttps://www.math.sissa.it/publication/transition-between-gap-probabilities-pearcey-airy-process%E2%80%93-riemann-hilbert-approach01005nas a2200121 4500008004300000245005700043210005600100520062300156100002000779700002400799700002400823856003600847 2010 en_Ud 00aTaming open/closed string duality with a Losev trick0 aTaming openclosed string duality with a Losev trick3 aA target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual.1 aBonelli, Giulio1 aPrudenziati, Andrea1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/385501029nas a2200157 4500008004100000245008100041210006900122300001000191490000800201520055000209100001800759700001700777700001600794700001800810856004300828 2010 eng d00aA three-dimensional model for the dynamics and hydrodynamics of rowing boats0 athreedimensional model for the dynamics and hydrodynamics of row a51-610 v2243 aThis paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

1 aFormaggia, L.1 aMola, Andrea1 aParolini, N1 aPischiutta, M uhttps://doi.org/10.1243/17543371jset4601175nas a2200133 4500008004300000245008500043210006900128260001300197520072500210100002900935700002000964700002100984856003601005 2010 en_Ud 00aA time-dependent perturbative analysis for a quantum particle in a cloud chamber0 atimedependent perturbative analysis for a quantum particle in a bSpringer3 aWe consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929.1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aTeta, Alessandro uhttp://hdl.handle.net/1963/396901480nas a2200097 4500008004300000245008700043210006900130520112200199100002501321856003601346 2010 en_Ud 00aTwisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model0 aTwisted Covariance as a Non Invariant Restriction of the Fully C3 aWe discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/360501439nas a2200181 4500008004300000245007000043210006800113260001300181300001200194490000700206520090200213100002501115700001701140700002301157700002001180700002101200856003601221 2010 en_Ud 00aTwo-dimensional almost-Riemannian structures with tangency points0 aTwodimensional almostRiemannian structures with tangency points bElsevier a793-8070 v273 aTwo-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

1 aAgrachev, Andrei, A.1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario uhttp://hdl.handle.net/1963/387000841nas a2200121 4500008004300000245007600043210006900119520043200188100002200620700001700642700002400659856003600683 2009 en_Ud 00aTools for the Solution of PDEs Defined on Curved Manifolds with deal.II0 aTools for the Solution of PDEs Defined on Curved Manifolds with 3 aThe deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.1 aDeSimone, Antonio1 aHeltai, Luca1 aManigrasso, Cataldo uhttp://hdl.handle.net/1963/370001000nas a2200121 4500008004300000245006600043210006400109520060600173100002000779700002400799700001900823856003600842 2009 en_Ud 00aTopological branes, p-algebras and generalized Nahm equations0 aTopological branes palgebras and generalized Nahm equations3 aInspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/270200416nas a2200133 4500008004100000022001400041245005800055210005700113300001500170490000700185100001900192700001800211856005300229 2009 eng d a1751-811300aTopological expansion for the Cauchy two-matrix model0 aTopological expansion for the Cauchy twomatrix model a335201, 280 v421 aBertola, Marco1 aFerrer, Prats uhttp://dx.doi.org/10.1088/1751-8113/42/33/33520100591nas a2200097 4500008004300000245004400043210004400087520030100131100002500432856003600457 2009 en_Ud 00aTwisted Covariance vs Weyl Quantisation0 aTwisted Covariance vs Weyl Quantisation3 aIn this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio \\\"why theta\\\"?1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/345101205nas a2200109 4500008004300000245008000043210006900123520082300192100002001015700002401035856003601059 2008 en_Ud 00aTopological Gauge Theories on Local Spaces and Black Hole Entropy Countings0 aTopological Gauge Theories on Local Spaces and Black Hole Entrop3 aWe study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.1 aBonelli, Giulio1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/199200725nas a2200097 4500008004300000245008100043210006900124520037600193100002200569856003600591 2008 en_Ud 00aTopological methods for an elliptic equation with exponential nonlinearities0 aTopological methods for an elliptic equation with exponential no3 aWe consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/259401148nas a2200121 4500008004300000245006300043210006200106520076200168100002000930700002200950700001800972856003600990 2008 en_Ud 00aTransition layer for the heterogeneous Allen-Cahn equation0 aTransition layer for the heterogeneous AllenCahn equation3 aWe consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$.1 aMahmoudi, Fethi1 aMalchiodi, Andrea1 aWei, Juncheng uhttp://hdl.handle.net/1963/265600781nas a2200133 4500008004100000020002200041245006700063210006700130260001300197520035900210100002300569700001900592856003600611 2008 en d a978-3-642-21718-000aTransport Rays and Applications to Hamilton–Jacobi Equations0 aTransport Rays and Applications to Hamilton–Jacobi Equations bSpringer3 aThe aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully).1 aBianchini, Stefano1 aGloyer, Matteo uhttp://hdl.handle.net/1963/546300512nas a2200121 4500008004300000245004900043210004800092520014900140100002500289700001700314700002300331856003600354 2007 en_Ud 00aTime optimal swing-up of the planar pendulum0 aTime optimal swingup of the planar pendulum3 aThis paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart.1 aBroucke, Mireille E.1 aMason, Paolo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/186700987nas a2200133 4500008004300000245005700043210005600100520056800156100002100724700002200745700002500767700002500792856003600817 2007 en_Ud 00aTime-dependent systems of generalized Young measures0 aTimedependent systems of generalized Young measures3 aIn this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna1 aMorini, Massimiliano uhttp://hdl.handle.net/1963/179500630nas a2200097 4500008004300000245003900043210003900082520035800121100001700479856003600496 2007 en_Ud 00aTwisted noncommutative equivariant0 aTwisted noncommutative equivariant3 aWe propose Weil and Cartan models for the equivariant cohomology of covariant actions on toric deformation manifolds. The construction is based on the noncommutative Weil algebra of Alekseev and Meinrenken; we show that one can implement a Drinfeld twist of their models in order to take into account the noncommutativity of the spaces we are acting on.1 aCirio, Lucio uhttp://hdl.handle.net/1963/199100778nas a2200109 4500008004300000245004900043210004800092520045100140100002300591700001800614856003600632 2006 en_Ud 00aThomae type formulae for singular Z_N curves0 aThomae type formulae for singular ZN curves3 aWe give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs. An important step of the proof is the use of the Szego kernel computed explicitly in algebraic form for non-singular 1/N-periods. The proof inherits principal points of Nakayashiki\\\'s proof [31], obtained for non-singular ZN curves.1 aEnolski, Victor Z.1 aGrava, Tamara uhttp://hdl.handle.net/1963/212502083nas a2200109 4500008004300000245007400043210006900117520171700186100001701903700001701920856003601937 2006 en_Ud 00aTime Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field0 aTime Minimal Trajectories for a Spin 12 Particle in a Magnetic f3 aIn this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| ≤ M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M → ∞ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E → 0, giving a partial proof of a conjecture formulated in a previous paper.1 aBoscain, Ugo1 aMason, Paolo uhttp://hdl.handle.net/1963/173400584nas a2200121 4500008004300000245002800043210002400071520026800095100002000363700002400383700001900407856003600426 2006 en_Ud 00aOn topological M-theory0 atopological Mtheory3 aWe construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds.1 aBonelli, Giulio1 aTanzini, Alessandro1 aZabzine, Maxim uhttp://hdl.handle.net/1963/176501554nas a2200109 4500008004300000245008800043210006900131520116300200100002101363700002401384856003601408 2006 en_Ud 00aTopological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds0 aTopological symmetry of forms N1 supersymmetry and Sduality on s3 aWe study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT\\\'s (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory.1 aBaulieu, Laurent1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/216800485nas a2200121 4500008004100000022001400041245008200055210006900137300001600206490000700222100001900229856011500248 2006 eng d a0305-447000aTwo-matrix model with semiclassical potentials and extended Whitham hierarchy0 aTwomatrix model with semiclassical potentials and extended Whith a8823–88550 v391 aBertola, Marco uhttps://www.math.sissa.it/publication/two-matrix-model-semiclassical-potentials-and-extended-whitham-hierarchy00714nas a2200109 4500008004300000245007100043210006900114520035100183100001700534700001700551856003600568 2005 en_Ud 00aTime minimal trajectories for two-level quantum systems with drift0 aTime minimal trajectories for twolevel quantum systems with drif3 aOn a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds.1 aBoscain, Ugo1 aMason, Paolo uhttp://hdl.handle.net/1963/168801372nas a2200109 4500008004300000245007100043210006800114520100700182100001701189700002001206856003601226 2005 en_Ud 00aTime Optimal Synthesis for Left-Invariant Control Systems on SO(3)0 aTime Optimal Synthesis for LeftInvariant Control Systems on SO33 aConsider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations.1 aBoscain, Ugo1 aChitour, Yacine uhttp://hdl.handle.net/1963/225801557nas a2200121 4500008004300000245011100043210006900154520110800223100002101331700002301352700002401375856003601399 2005 en_Ud 00aTopological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry0 aTopological vector symmetry topological gauge fixing of BRSTQFT 3 aThe scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincaré supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting \\\"equivariant topological field theory\\\" corresponds to the twist of super Yang-Mills theory on omega backgrounds.1 aBaulieu, Laurent1 aBossard, Guillaume1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/174101069nas a2200133 4500008004100000245003500041210003500076260001800111520069800129100002800827700002300855700002100878856003600899 2005 en d00aTraffic flow on a road network0 aTraffic flow on a road network bSISSA Library3 aThis paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights.1 aCoclite, Giuseppe Maria1 aPiccoli, Benedetto1 aGaravello, Mauro uhttp://hdl.handle.net/1963/158401375nas a2200109 4500008004300000245010700043210006900150260003000219520095800249100002201207856003601229 2004 en_Ud 00aTensor of coherences parametrization of multiqubit density operators for entanglement characterization0 aTensor of coherences parametrization of multiqubit density opera bAmerican Physical Society3 aFor multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parameterization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight on the possible origin of entanglement for such densities.1 aAltafini, Claudio uhttp://hdl.handle.net/1963/284500335nas a2200109 4500008004100000245004100041210004000082260001000122653003500132100002200167856003600189 2004 en d00aTime-dependent singular interactions0 aTimedependent singular interactions bSISSA10aRotating singular interactions1 aCorreggi, Michele uhttp://hdl.handle.net/1963/531001348nas a2200133 4500008004100000245006700041210006400108260001000172520093800182100002001120700002001140700001801160856003601178 1997 en d00aThree-Phase Solutions of the Kadomtsev - Petviashvili Equation0 aThreePhase Solutions of the Kadomtsev Petviashvili Equation bSISSA3 aThe Kadomtsev]Petviashvili KP. equation is known to admit explicit periodic\\r\\nand quasiperiodic solutions with N independent phases, for any integer\\r\\nN, based on a Riemann theta-function of N variables. For Ns1 and 2,\\r\\nthese solutions have been used successfully in physical applications. This\\r\\narticle addresses mathematical problems that arise in the computation of\\r\\ntheta-functions of three variables and with the corresponding solutions of\\r\\nthe KP equation. We identify a set of parameters and their corresponding\\r\\nranges, such that e¨ery real-valued, smooth KP solution associated with a\\r\\nRiemann theta-function of three variables corresponds to exactly one choice\\r\\nof these parameters in the proper range. Our results are embodied in a\\r\\nprogram that computes these solutions efficiently and that is available to the\\r\\nreader. We also discuss some properties of three-phase solutions.1 aDubrovin, Boris1 aFlickinger, Ron1 aSegur, Harvey uhttp://hdl.handle.net/1963/648400952nas a2200121 4500008004100000020001500041245008400056210006900140260001000209520055500219100002000774856003600794 1993 en d a030644534400aTopological conformal field theory from the point of view of integrable systems0 aTopological conformal field theory from the point of view of int bSISSA3 aRecent results on classification of massive topological conformal field theories (TCFT) in terms of monodromy data of auxiliary linear operators with rational coefficients are presented. Procedure of coupling of a TCFT to topological gravity is described (at tree-level approximation) via certain integrable hierarchies of hydrodynamic type and their tau-functions. It is explained how the calculation of the ground state metric on TCFT can be interpreted in terms of harmonic maps. Also a construction of some models via Coxeter groups is described.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647901654nas a2200121 4500008004300000245006200043210006000105260001300165520127600178100002401454700001801478856003601496 1992 en_Ud 00aTopological "observables" in semiclassical field theories0 aTopological observables in semiclassical field theories bElsevier3 aWe give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}} \rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

1 aNolasco, Margherita1 aReina, Cesare uhttp://hdl.handle.net/1963/354100341nas a2200097 4500008004100000245006500041210006000106260001800166100002400184856003500208 1985 en d00aThe two-point boundary value problem from the Cauchy problem0 atwopoint boundary value problem from the Cauchy problem bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/33200377nas a2200097 4500008004100000245009200041210006900133260001800202100002400220856003500244 1983 en d00aTowards a theory for periodic solutions to first order ordinary differential equations.0 aTowards a theory for periodic solutions to first order ordinary bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/29500357nas a2200097 4500008004100000245007200041210006900113260001800182100002400200856003500224 1982 en d00aThree uniqueness theorems for strongly non-linear elliptic problems0 aThree uniqueness theorems for strongly nonlinear elliptic proble bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/167