We consider an n×n linear system of ODEs with an irregular singularity of Poincar\'e rank 1 at z=∞, holomorphically depending on parameter t within a polydisc in Cn centred at t=0. The eigenvalues of the leading matrix at z=∞ coalesce along a locus Δ contained in the polydisc, passing through t=0. Namely, z=∞ is a resonant irregular singularity for t∈Δ. We analyse the case when the leading matrix remains diagonalisable at Δ. We discuss the existence of fundamental matrix solutions, their asymptotics, Stokes phenomenon and monodromy data as t varies in the polydisc, and their limits for t tending to points of Δ. When the deformation is isomonodromic away from Δ, it is well known that a fundamental matrix solution has singularities at Δ. When the system also has a Fuchsian singularity at z=0, we show under minimal vanishing conditions on the residue matrix at z=0 that isomonodromic deformations can be extended to the whole polydisc, including Δ, in such a way that the fundamental matrix solutions and the constant monodromy data are well defined in the whole polydisc. These data can be computed just by considering the system at fixed t=0. Conversely, if the t-dependent system is isomonodromic in a small domain contained in the polydisc not intersecting Δ, if the entries of the Stokes matrices with indices corresponding to coalescing eigenvalues vanish, then we show that Δ is not a branching locus for the fundamental matrix solutions. The importance of these results for the analytic theory of Frobenius Manifolds is explained. An application to Painlev\'e equations is discussed.

%B Duke Math. J. %I Duke University Press %V 168 %P 967–1108 %8 04 %G eng %U https://doi.org/10.1215/00127094-2018-0059 %R 10.1215/00127094-2018-0059 %0 Journal Article %J ASTRONOMY & ASTROPHYSICS %D 2018 %T Iterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments %A Puglisi, Giuseppe %A Poletti, Davide %A Fabbian, Giulio %A Baccigalupi, Carlo %A Luca Heltai %A Stompor, Radek %B ASTRONOMY & ASTROPHYSICS %V 618 %P 1–14 %G eng %U https://arxiv.org/abs/1801.08937 %R 10.1051/0004-6361/201832710 %0 Journal Article %J ArXiv e-prints %D 2017 %T The injectivity radius of Lie manifolds %A Paolo Antonini %A G. De Philippis %A Nicola Gigli %K (58J40) %K 53C21 %K Mathematics - Differential Geometry %XWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

%B ArXiv e-prints %G eng %U https://arxiv.org/pdf/1707.07595.pdf %0 Journal Article %J Ergodic Theory and Dynamical Systems %D 2017 %T Integrability of dominated decompositions on three-dimensional manifolds %A Stefano Luzzatto %A Sina Türeli %A Khadim Mbacke War %X

We investigate the integrability of two-dimensional invariant distributions (tangent sub-bundles) which arise naturally in the context of dynamical systems on 3-manifolds. In particular, we prove unique integrability of dynamically dominated and volume-dominated Lipschitz continuous invariant decompositions as well as distributions with some other regularity conditions.

Inspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid, is the quotient of a finite dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an "Almeida-Molino" integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a "de Rham" integrable lift for any given transitive Abelian Lie algebroid.

%B ArXiv e-prints %G eng %U https://arxiv.org/pdf/1707.04855.pdf %0 Thesis %D 2016 %T Instanton counting on compact manifolds %A Massimiliano Ronzani %K Supersymmetry %X In this thesis we analyze supersymmetric gauge theories on compact manifolds and their relation with representation theory of infinite Lie algebras associated to conformal field theories, and with the computation of geometric invariants and superconformal indices. The thesis contains the work done by the candidate during the doctorate programme at SISSA under the supervision of A. Tanzini and G. Bonelli. • in Chapter 2, we consider N = 2 supersymmetric gauge theories on four manifolds admitting an isometry. Generalized Killing spinor equations are derived from the consistency of supersymmetry algebrae and solved in the case of four manifolds admitting a U(1) isometry. This is used to explicitly compute the supersymmetric path integral on S2 × S2 via equivariant localization. The building blocks of the resulting partition function are shown to contain the three point functions and the conformal blocks of Liouville Gravity. • in Chapter 3, we provide a contour integral formula for the exact partition function of N = 2 supersymmetric U(N) gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the contour integral for U(2) N = 2∗ theory on P2 for all instanton numbers. In the zero mass case, corresponding to the N = 4 supersymmetric gauge theory, we obtain the generating function of the Euler characteristics of instanton moduli spaces in terms of mock-modular forms. In the decoupling limit of infinite mass we find that the generating function of local and surface observables computes equivariant Donaldson invariants, thus proving in this case a long-standing conjecture by N. Nekrasov. In the case of vanishing first Chern class the resulting equivariant Donaldson polynomials are new. • in Chapter 4, we explore N = (1, 0) superconformal six-dimensional theories arising from M5 branes probing a transverse Ak singularity. Upon circle compactification to five dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional in- stanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show which relations among vertex correlators of qW algebrae are implied by the S-duality of the pq-web. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35219 %1 35521 %2 Mathematics %4 1 %# MAT/07 %$ Submitted by mronzani@sissa.it (mronzani@sissa.it) on 2016-09-16T15:39:32Z No. of bitstreams: 1 Tesi.pdf: 1068628 bytes, checksum: abe8948669f9ea6ac56f6026c511b4ab (MD5) %0 Journal Article %J Dynamical Systems %D 2016 %T Integrability of C1 invariant splittings %A Stefano Luzzatto %A Sina Türeli %A Khadim Mbacke War %XWe derive some new conditions for integrability of dynamically defined C1 invariant splittings, formulated in terms of the singular values of the iterates of the derivative of the diffeomorphism which defines the splitting.

%B Dynamical Systems %I Taylor & Francis %V 31 %P 79-88 %G eng %U https://doi.org/10.1080/14689367.2015.1057480 %R 10.1080/14689367.2015.1057480 %0 Thesis %D 2016 %T Integrability of continuous bundles and applications to dynamical systems %A Khadim Mbacke War %X In this dissertation we study the problem of integrability of bundles with low regularities. %I SISSA %G en %1 35529 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by kmwar@sissa.it (kmwar@sissa.it) on 2016-09-28T12:10:43Z No. of bitstreams: 1 Thesis-Khadim.pdf: 510947 bytes, checksum: 66daf50c9c84de98301953af3433621e (MD5) %0 Report %D 2016 %T Isogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes %A Filippo Salmoiraghi %A Francesco Ballarin %A Luca Heltai %A Gianluigi Rozza %X In this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model. %I Springer, AMOS Advanced Modelling and Simulation in Engineering Sciences %G en %U http://urania.sissa.it/xmlui/handle/1963/35199 %1 35493 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by Gianluigi Rozza (grozza@sissa.it) on 2016-06-20T23:55:25Z No. of bitstreams: 1 MAIN_IGA_FFD_ROM.pdf: 1631282 bytes, checksum: b050e472f11943b95d8307915a50b6da (MD5) %0 Thesis %D 2015 %T Integrability of Continuous Tangent Sub-bundles %A Sina Türeli %K Dynamical Systems, Global Analysis, Frobenius Theorem, Integrability %X In this thesis, the main aim is to study the integrability properties of continuous tangent sub-bundles, especially those that arise in the study of dynamical systems. After the introduction and examples part we start by studying integrability of such sub-bundles under different regularity and dynamical assumptions. Then we formulate a continuous version of the classical Frobenius theorem and state some applications to such bundles, to ODE and PDE. Finally we close of by stating some ongoing work related to interactions between integrability, sub-Riemannian geometry and contact geometry. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34630 %1 34833 %2 Mathematics %# MAT/05 %$ Submitted by stureli@sissa.it (stureli@sissa.it) on 2015-10-13T01:32:04Z No. of bitstreams: 1 thesis-sina-tureli-2015.pdf: 526450 bytes, checksum: 9ff71f05dd4ee459ef37ff150ebb272e (MD5) %0 Thesis %D 2015 %T Interaction functionals, Glimm approximations and Lagrangian structure of BV solutions for Hyperbolic Systems of Conservations Laws %A Stefano Modena %K Hyperbolic conservation laws %X This thesis is a contribution to the mathematical theory of Hyperbolic Conservation Laws. Three are the main results which we collect in this work. The first and the second result (denoted in the thesis by Theorem A and Theorem B respectively) deal with the following problem. The most comprehensive result about existence, uniqueness and stability of the solution to the Cauchy problem \begin{equation}\tag{$\mathcal C$} \label{E:abstract} \begin{cases} u_t + F(u)_x = 0, \\u(0, x) = \bar u(x), \end{cases} \end{equation} where $F: \R^N \to \R^N$ is strictly hyperbolic, $u = u(t,x) \in \R^N$, $t \geq 0$, $x \in \R$, $\TV(\bar u) \ll 1$, can be found in [Bianchini, Bressan 2005], where the well-posedness of \eqref{E:abstract} is proved by means of vanishing viscosity approximations. After the paper [Bianchini, Bressan 2005], however, it seemed worthwhile to develop a \emph{purely hyperbolic} theory (based, as in the genuinely nonlinear case, on Glimm or wavefront tracking approximations, and not on vanishing viscosity parabolic approximations) to prove existence, uniqueness and stability results. The reason of this interest can be mainly found in the fact that hyperbolic approximate solutions are much easier to study and to visualize than parabolic ones. Theorems A and B in this thesis are a contribution to this line of research. In particular, Theorem A proves an estimate on the change of the speed of the wavefronts present in a Glimm approximate solution when two of them interact; Theorem B proves the convergence of the Glimm approximate solutions to the weak admissible solution of \eqref{E:abstract} and provides also an estimate on the rate of convergence. Both theorems are proved in the most general setting when no assumption on $F$ is made except the strict hyperbolicity. The third result of the thesis, denoted by Theorem C, deals with the Lagrangian structure of the solution to \eqref{E:abstract}. The notion of Lagrangian flow is a well-established concept in the theory of the transport equation and in the study of some particular system of conservation laws, like the Euler equation. However, as far as we know, the general system of conservations laws \eqref{E:abstract} has never been studied from a Lagrangian point of view. This is exactly the subject of Theorem C, where a Lagrangian representation for the solution to the system \eqref{E:abstract} is explicitly constructed. The main reasons which led us to look for a Lagrangian representation of the solution of \eqref{E:abstract} are two: on one side, this Lagrangian representation provides the continuous counterpart in the exact solution of \eqref{E:abstract} to the well established theory of wavefront approximations; on the other side, it can lead to a deeper understanding of the behavior of the solutions in the general setting, when the characteristic field are not genuinely nonlinear or linearly degenerate. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/34542 %1 34739 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by smodena@sissa.it (smodena@sissa.it) on 2015-09-22T13:24:32Z No. of bitstreams: 1 Modena_tesi_2015_09_22.pdf: 1531188 bytes, checksum: 814a6709a4fcbf8b10bc95a9e3d155c7 (MD5) %0 Journal Article %J Comptes Rendus Mathematique %D 2014 %T An improvement on geometrical parameterizations by transfinite maps %A Jäggli, C. %A Laura Iapichino %A Gianluigi Rozza %X We present a method to generate a non-affine transfinite map from a given reference domain to a family of deformed domains. The map is a generalization of the Gordon-Hall transfinite interpolation approach. It is defined globally over the reference domain. Once we have computed some functions over the reference domain, the map can be generated by knowing the parametric expressions of the boundaries of the deformed domain. Being able to define a suitable map from a reference domain to a desired deformation is useful for the management of parameterized geometries. %B Comptes Rendus Mathematique %V 352 %P 263–268 %G eng %R 10.1016/j.crma.2013.12.017 %0 Journal Article %D 2014 %T Infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy %A Chaozhong Wu %A Dafeng Zuo %X Following the approach of Carlet et al. (2011) [9], we construct a class of infinite-dimensional Frobenius manifolds underlying the Toda lattice hierarchy, which are defined on the space of pairs of meromorphic functions with possibly higher-order poles at the origin and at infinity. We also show a connection between these infinite-dimensional Frobenius manifolds and the finite-dimensional Frobenius manifolds on the orbit space of extended affine Weyl groups of type A defined by Dubrovin and Zhang. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35026 %1 35264 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-17T10:32:31Z No. of bitstreams: 1 preprint2014.pdf: 358025 bytes, checksum: ef718fc5b61dfb8c0e0bd874196cfd13 (MD5) %R 10.1016/j.aim.2014.01.013 %0 Report %D 2014 %T Integrability of Dirac reduced bi-Hamiltonian equations %A Alberto De Sole %A Victor G. Kac %A Daniele Valeri %X First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE's, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies. %I SISSA %G en %U http://hdl.handle.net/1963/7247 %1 7286 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Daniele Valeri (dvaleri@sissa.it) on 2014-01-24T09:47:51Z No. of bitstreams: 1 1401.6006v1.pdf: 249123 bytes, checksum: 3b83fabf790160e10ecb05aa89251970 (MD5) %0 Report %D 2014 %T An irreducible symplectic orbifold of dimension 6 with a Lagrangian Prym fibration %A Tommaso Matteini %K Irreducible symplectic variety, Lagrangian fibration, Prym variety, automorphism of symplectic varieties %X A new example of an irreducible symplectic variety of dimension 6, with only finite quotient singularities, is described as a relative compactified Prymian of a family of genus 4 curves with involution. It is associated to a K3 surface which is a double cover of a cubic surface. It has a natural Lagrangian fibration in abelian 3-folds with polarization type (1,1,2). It does not admit any symplectic resolution. %G en %1 7360 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Tommaso Matteini (tommatte@sissa.it) on 2014-04-07T21:56:09Z No. of bitstreams: 1 1403.5523v1.pdf: 263523 bytes, checksum: 3476aafd392b9871807ce18a89b857f4 (MD5) %0 Journal Article %D 2014 %T On an isomonodromy deformation equation without the Painlevé property %A Boris Dubrovin %A Andrey Kapaev %X We show that the fourth order nonlinear ODE which controls the pole dynamics in the general solution of equation $P_I^2$ compatible with the KdV equation exhibits two remarkable properties: 1) it governs the isomonodromy deformations of a $2\times2$ matrix linear ODE with polynomial coefficients, and 2) it does not possesses the Painlev\'e property. We also study the properties of the Riemann--Hilbert problem associated to this ODE and find its large $t$ asymptotic solution for the physically interesting initial data. %I Maik Nauka-Interperiodica Publishing %G en %U http://hdl.handle.net/1963/6466 %1 6410 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:29:56Z No. of bitstreams: 1 1301.7211v2.pdf: 415681 bytes, checksum: f606a3b5df4b201ae37a9d6fa1b79016 (MD5) %R 10.1134/S1061920814010026 %0 Journal Article %J Communications in Mathematical Physics 322, nr.2 (2013): 415-452 %D 2013 %T An improved geometric inequality via vanishing moments, with applications to singular Liouville equations %A Mauro Bardelloni %A Andrea Malchiodi %B Communications in Mathematical Physics 322, nr.2 (2013): 415-452 %I SISSA %G en %U http://hdl.handle.net/1963/6561 %1 6486 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrea Malchiodi (malchiod@sissa.it) on 2013-03-14T10:23:46Z No. of bitstreams: 2 1206.0225v2.pdf: 376591 bytes, checksum: 84aab361b9f74c6f00164ed271fe2cfd (MD5) 1206.0225v2.pdf: 376591 bytes, checksum: 84aab361b9f74c6f00164ed271fe2cfd (MD5) %R 10.1007/s00220-013-1731-0 %0 Journal Article %J Proc. Amer. Math. Soc. %D 2013 %T Inversion formulae for the $\romancosh$-weighted Hilbert transform %A Marco Bertola %A Katsevich, A. %A Alexander Tovbis %B Proc. Amer. Math. Soc. %V 141 %P 2703–2718 %G eng %U http://dx.doi.org/10.1090/S0002-9939-2013-11642-4 %R 10.1090/S0002-9939-2013-11642-4 %0 Report %D 2012 %T Introduction to Riemannian and sub-Riemannian geometry %A Andrei A. Agrachev %A Davide Barilari %A Ugo Boscain %I SISSA %G en %U http://hdl.handle.net/1963/5877 %1 5747 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-05-30T13:23:26Z\r\nNo. of bitstreams: 1\r\n09M_2012_Barilari.pdf: 1146702 bytes, checksum: 28492a78df0fdf2435dd0606fdfc78f5 (MD5) %0 Journal Article %J Matematische Annalen 349 (2011) 75-115 %D 2011 %T Infinite-dimensional Frobenius manifolds for 2 + 1 integrable systems %A Guido Carlet %A Boris Dubrovin %A Luca Philippe Mertens %X We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/infinity respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold. %B Matematische Annalen 349 (2011) 75-115 %I Springer %G en_US %U http://hdl.handle.net/1963/3584 %1 716 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-03-09T09:29:31Z\\r\\nNo. of bitstreams: 1\\r\\n0902.1245.pdf: 343930 bytes, checksum: 421342a05bb8986c1bf542d6446f5792 (MD5) %R 10.1007/s00208-010-0509-3 %0 Journal Article %J Nonlinear Analysis: Theory, Methods & Applications %D 2011 %T Infinitely many positive solutions for a Schrödinger–Poisson system %A Pietro d’Avenia %A Alessio Pomponio %A Giusi Vaira %K Non-autonomous Schrödinger–Poisson system %K Perturbation method %XWe are interested in the existence of infinitely many positive solutions of the Schrödinger–Poisson system −Δu+u+V(|x|)ϕu=|u|p−1u,x∈R3,−Δϕ=V(|x|)u2,x∈R3, where V(|x|) is a positive bounded function, 1<p<5 and V(r

%B Nonlinear Analysis: Theory, Methods & Applications %V 74 %P 5705 - 5721 %G eng %U http://www.sciencedirect.com/science/article/pii/S0362546X11003518 %R https://doi.org/10.1016/j.na.2011.05.057 %0 Report %D 2011 %T Instantons on ALE spaces and Super Liouville Conformal Field Theories %A Giulio Bonelli %A Kazunobu Maruyoshi %A Alessandro Tanzini %X We provide evidence that the conformal blocks of N=1 super Liouville\\r\\nconformal field theory are described in terms of the SU(2) Nekrasov partition\\r\\nfunction on the ALE space O_{P^1}(-2). %I SISSA %G en %U http://hdl.handle.net/1963/4262 %1 3987 %2 Physics %3 Elementary Particle Theory %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-26T14:31:56Z\\nNo. of bitstreams: 1\\n1106.2505v1.pdf: 137191 bytes, checksum: 721cf25d724b7aca87a3429a0119e201 (MD5) %0 Journal Article %J Journal of Convex Analysis 18 (2011) 1141-1170 %D 2011 %T An Integro-Extremization Approach for Non Coercive and Evolution Hamilton-Jacobi Equations %A Sandro Zagatti %X We devote the \\\\textit{integro-extremization} method to the study of the Dirichlet problem for homogeneous Hamilton-Jacobi equations \\\\begin{displaymath} \\\\begin{cases} F(Du)=0 & \\\\quad \\\\textrm{in} \\\\quad\\\\O\\\\cr u(x)=\\\\varphi(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in \\\\partial \\\\O, \\\\end{cases} \\\\end{displaymath} with a particular interest for non coercive hamiltonians $F$, and to the Cauchy-Dirichlet problem for the corresponding homogeneous time-dependent equations \\\\begin{displaymath} \\\\begin{cases} \\\\frac{\\\\partial u}{\\\\partial t}+ F(\\\\nabla u)=0 & \\\\quad \\\\textrm{in} \\\\quad ]0,T[\\\\times \\\\O\\\\cr u(0,x)=\\\\eta(x) & \\\\quad \\\\textrm{for} \\\\quad x\\\\in\\\\O \\\\cr u(t,x)=\\\\psi(x) & \\\\quad \\\\textrm{for} \\\\quad (t,x)\\\\in[0,T]\\\\times \\\\partial \\\\O. \\\\end{cases} \\\\end{displaymath} We prove existence and some qualitative results for viscosity and almost everywhere solutions, under suitably convexity conditions on the hamiltonian $F$, on the domain $\\\\O$ and on the boundary datum, without any growth assumptions on $F$. %B Journal of Convex Analysis 18 (2011) 1141-1170 %I Heldermann Verlag %G en %U http://hdl.handle.net/1963/5538 %1 5375 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-02-23T14:37:59Z\\nNo. of bitstreams: 0 %0 Journal Article %J Journal of Differential Equations 250 (2011) 1788-1827 %D 2011 %T Invariant manifolds for a singular ordinary differential equation %A Stefano Bianchini %A Laura Spinolo %B Journal of Differential Equations 250 (2011) 1788-1827 %I Elsevier %G en_US %U http://hdl.handle.net/1963/2554 %1 1565 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-15T10:35:53Z\\r\\nNo. of bitstreams: 1\\r\\nSissa0408M.pdf: 296248 bytes, checksum: 7563bf5d03a78a0e2c2c606a9b609827 (MD5) %R 10.1016/j.jde.2010.11.010 %0 Thesis %D 2011 %T Invariants, volumes and heat kernels in sub-Riemannian geometry %A Davide Barilari %K Sub-Riemannian geometry %X Sub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]). %I SISSA %G en %U http://hdl.handle.net/1963/6124 %1 6005 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-08-08T07:49:33Z\\nNo. of bitstreams: 1\\nPhD_Thesis_Barilari.pdf: 924464 bytes, checksum: dd34c4627062993f1d72d4c7eff914e6 (MD5) %0 Journal Article %J Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978 %D 2010 %T Invariant Lagrange submanifolds of dissipative systems %A Andrei A. Agrachev %X We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) =\\r\\n0, q \\\\in M, on a compact manifold M . %B Russian Mathematical Surveys. Volume 65, Issue 5, 2010, Pages: 977-978 %I SISSA %G en %U http://hdl.handle.net/1963/6457 %1 6403 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Andrei Agrachev (agrachev@sissa.it) on 2013-02-05T14:35:25Z\\nNo. of bitstreams: 1\\n0912.2248v2.pdf: 74166 bytes, checksum: 6c6c803e56c96e455631b40eb7ef91b5 (MD5) %R 10.1070/RM2010v065n05ABEH004707 %0 Journal Article %J Physica D 238 (2009) 55-66 %D 2009 %T Initial value problem of the Whitham equations for the Camassa-Holm equation %A Tamara Grava %A Virgil U. Pierce %A Fei-Ran Tian %X We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp. %B Physica D 238 (2009) 55-66 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3429 %1 906 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-01-13T13:01:16Z\\nNo. of bitstreams: 1\\n0805.2558v1.pdf: 498872 bytes, checksum: 4d721f99d6ae9840be2332f3cc6a4118 (MD5) %R 10.1016/j.physd.2008.08.016 %0 Journal Article %J J. Funct. Anal. 256 (2009) 2621-2655 %D 2009 %T The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups %A Andrei A. Agrachev %A Ugo Boscain %A Jean-Paul Gauthier %A Francesco Rossi %X We present an invariant definition of the hypoelliptic Laplacian on sub-Riemannian structures with constant growth vector, using the Popp\\\'s volume form introduced by Montgomery. This definition generalizes the one of the Laplace-Beltrami operator in Riemannian geometry. In the case of left-invariant problems on unimodular Lie groups we prove that it coincides with the usual sum of squares.\\nWe then extend a method (first used by Hulanicki on the Heisenberg group) to compute explicitly the kernel of the hypoelliptic heat equation on any unimodular Lie group of type I. The main tool is the noncommutative Fourier transform. We then study some relevant cases: SU(2), SO(3), SL(2) (with the metrics inherited by the Killing form), and the group SE(2) of rototranslations of the plane.\\nOur study is motivated by some recent results about the cut and conjugate loci on these sub-Riemannian manifolds. The perspective is to understand how singularities of the sub-Riemannian distance reflect on the kernel of the corresponding hypoelliptic heat equation. %B J. Funct. Anal. 256 (2009) 2621-2655 %G en_US %U http://hdl.handle.net/1963/2669 %1 1428 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-06-11T11:38:01Z\\nNo. of bitstreams: 1\\n0806.0734v1.pdf: 494960 bytes, checksum: 640ace795ac663f09426814440b15432 (MD5) %R 10.1016/j.jfa.2009.01.006 %0 Journal Article %J PLoS Comput Biol 2009;5(7): e1000420 %D 2009 %T Investigating the Conformational Stability of Prion Strains through a Kinetic Replication Model %A Mattia Zampieri %A Giuseppe Legname %A Claudio Altafini %X Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrPSc structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils\\\' mean length) and is coherent with all experimental observations concerning strain-specific behavior. %B PLoS Comput Biol 2009;5(7): e1000420 %I PLoS %G en_US %U http://hdl.handle.net/1963/3989 %1 413 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-08-11T10:35:47Z\\nNo. of bitstreams: 1\\njournal.pcbi.1000420.pdf: 468491 bytes, checksum: fda67b47ac16d98d11bc4ac879c17ec0 (MD5) %R 10.1371/journal.pcbi.1000420 %0 Report %D 2008 %T Instanton counting on Hirzebruch surfaces %A Ugo Bruzzo %A Rubik Poghossian %A Alessandro Tanzini %X We perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa. %G en_US %U http://hdl.handle.net/1963/2852 %1 1848 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-05T18:06:43Z\\nNo. of bitstreams: 1\\n0809.0155v1.pdf: 212427 bytes, checksum: f5060bd4e1da6a5215a488041ef018ff (MD5) %0 Journal Article %J SIAM J. Control Optim. 47 (2008) 1851-1878 %D 2008 %T Invariant Carnot-Caratheodory metrics on S3, SO(3), SL(2) and Lens Spaces %A Ugo Boscain %A Francesco Rossi %X In this paper we study the invariant Carnot-Caratheodory metrics on SU(2) \\\' S3,\\nSO(3) and SL(2) induced by their Cartan decomposition. Beside computing explicitly geodesics and conjugate loci, we compute the cut loci (globally) and we give the expression of the Carnot-Caratheodory distance as the inverse of an elementary function. We then prove that the metric\\ngiven on SU(2) projects on the so called Lens Spaces L(p; q). Also for Lens Spaces, we compute\\nthe cut loci (globally). %B SIAM J. Control Optim. 47 (2008) 1851-1878 %G en_US %U http://hdl.handle.net/1963/2144 %1 2099 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-09-27T08:46:25Z\\nNo. of bitstreams: 1\\nBoscain-Rossi-2007.pdf: 587872 bytes, checksum: 6b4998700cd692ddbd99e14289405bdf (MD5) %R 10.1137/070703727 %0 Report %D 2008 %T Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems %A Stefano Bianchini %A Laura Spinolo %G en_US %U http://hdl.handle.net/1963/3400 %1 932 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-12-15T12:03:08Z\\nNo. of bitstreams: 1\\nBianchini_Spinolo.pdf: 146920 bytes, checksum: 27283c16ae26e782e9f0d17c1fbb29d4 (MD5) %0 Journal Article %J Comm. Math. Phys. 279 (2008) 77-116 %D 2008 %T The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere %A Francesco D'Andrea %A Ludwik Dabrowski %A Giovanni Landi %X Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the quantum Euclidean 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one of the spin structure of the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an `instanton\\\' projection. A real structure which satisfies all required properties modulo a suitable ideal of `infinitesimals\\\' is also introduced. %B Comm. Math. Phys. 279 (2008) 77-116 %G en_US %U http://hdl.handle.net/1963/2567 %1 1553 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-01-18T11:00:40Z\\nNo. of bitstreams: 1\\n0611100v1.pdf: 351975 bytes, checksum: 8dd0f817683bd7782e5110ca6b585b91 (MD5) %R 10.1007/s00220-008-0420-x %0 Report %D 2006 %T Infinite Horizon Noncooperative Differential Games %A Alberto Bressan %A Fabio Simone Priuli %X For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value\\nfunctions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability. %B J. Differential Equations 227 (2006) 230-257 %G en_US %U http://hdl.handle.net/1963/1720 %1 2431 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-24T09:08:57Z\\nNo. of bitstreams: 1\\nmath.AP0505212.pdf: 267217 bytes, checksum: 4c2f5eb11250fa9b31d9b46983c201e0 (MD5) %R 10.1016/j.jde.2006.01.005 %0 Journal Article %J Comm. Pure Appl. Math. 59 (2006) 1604-1638 %D 2006 %T An instability of the Godunov scheme %A Alberto Bressan %A Helge Kristian Jenssen %A Paolo Baiti %X We construct a solution to a $2\\\\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \\\\cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is close to rational, inducing a resonance with the grid. Differently from the Glimm scheme or the vanishing viscosity method, for systems of conservation laws our counterexample indicates that no a priori BV bounds or $L^1$ stability estimates can in general be valid for finite difference schemes. %B Comm. Pure Appl. Math. 59 (2006) 1604-1638 %G en_US %U http://hdl.handle.net/1963/2183 %1 2061 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-05T07:52:50Z\\nNo. of bitstreams: 1\\n0502125v1.pdf: 337578 bytes, checksum: 41193faac363c00e9f80d6c05c0b098c (MD5) %R 10.1002/cpa.20141 %0 Journal Article %J Comm. Math. Phys. 257 (2005) 169-192 %D 2005 %T Ionization for Three Dimensional Time-dependent Point Interactions %A Michele Correggi %A Gianfausto Dell'Antonio %A Rodolfo Figari %A Andrea Mantile %X We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states. %B Comm. Math. Phys. 257 (2005) 169-192 %G en_US %U http://hdl.handle.net/1963/2297 %1 1719 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-25T08:14:45Z\\nNo. of bitstreams: 1\\n0402011v2.pdf: 306766 bytes, checksum: 7efb2bcceb4c2699d662ae1af9e7dd76 (MD5) %R 10.1007/s00220-005-1293-x %0 Journal Article %J IMRP Int. Math. Res. Pap. %D 2005 %T Isomonodromic deformation of resonant rational connections %A Marco Bertola %A Mo, M. Y. %B IMRP Int. Math. Res. Pap. %P 565–635 %G eng %0 Journal Article %D 2003 %T An ill posed Cauchy problem for a hyperbolic system in two space dimensions %A Alberto Bressan %X The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global existence of solutions to the Cauchy problem remains a challenging open question. In this note we construct a conterexample showing that, even for a simple class of hyperbolic systems, in two space dimensions the Cauchy problem can be ill posed. %I Università di Padova %G en_US %U http://hdl.handle.net/1963/2913 %1 1787 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-11T13:18:40Z\\nNo. of bitstreams: 1\\nmath.AP0302227.pdf: 126071 bytes, checksum: 3536c415c6e375bb55591a913ced63c2 (MD5) %0 Journal Article %J J.Math.Anal.Appl. 284 (2003) no.1, 49 %D 2003 %T An interior estimate for a nonlinear parabolic equation %A Giuseppe Maria Coclite %B J.Math.Anal.Appl. 284 (2003) no.1, 49 %I SISSA Library %G en %U http://hdl.handle.net/1963/1622 %1 2496 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:27Z (GMT). No. of bitstreams: 1\\nmath.AP0207193.pdf: 123937 bytes, checksum: e3147ae778a391681315f33680cefa66 (MD5)\\n Previous issue date: 2002 %R 10.1016/S0022-247X(03)00157-4 %0 Journal Article %J Differential Geom. Appl. 16 (2002) 277-284 %D 2002 %T Instanton algebras and quantum 4-spheres %A Ludwik Dabrowski %A Giovanni Landi %X We study some generalized instanton algebras which are required to describe `instantonic complex rank 2 bundles\\\'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural requirements on the instantons. They turn out to be quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IC$, and the instantons are described by self-adjoint idempotents e. We shall also clarify some issues related to the vanishing of the first Chern-Connes class $ch_1(e)$ and on the use of the second Chern-Connes class $ch_2(e)$ as a volume form. %B Differential Geom. Appl. 16 (2002) 277-284 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3134 %1 1199 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-17T09:39:17Z\\nNo. of bitstreams: 1\\n0101177v2.pdf: 131163 bytes, checksum: 6756bdd801d3c677c7a70ee74fefd158 (MD5) %R 10.1016/S0926-2245(02)00066-9 %0 Journal Article %J Comm. Math. Phys. 221 (2001) 161-168 %D 2001 %T Instantons on the Quantum 4-Spheres S^4_q %A Ludwik Dabrowski %A Giovanni Landi %A Tetsuya Masuda %X We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $ch_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $ch_2(e)$ does not vanish as well and the couple $(ch_1(e), ch_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology. %B Comm. Math. Phys. 221 (2001) 161-168 %I Springer %G en_US %U http://hdl.handle.net/1963/3135 %1 1198 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-17T09:47:38Z\\nNo. of bitstreams: 1\\n0012103v2.pdf: 128667 bytes, checksum: 86c8b564b4eb5008fad8371fcfd5f265 (MD5) %R 10.1007/PL00005572 %0 Journal Article %J Mathematical Physics, Analysis and Geometry 4: 245–291, 2001 %D 2001 %T Inverse Problem and Monodromy Data for Three-Dimensional Frobenius Manifolds %A Davide Guzzetti %K Frobenius Manifolds, Painleve Equations, Isomonodromy deformations %X We study the inverse problem for semi-simple Frobenius manifolds of dimension 3 and we\r\nexplicitly compute a parametric form of the solutions of theWDVV equations in terms of Painlevé VI\r\ntranscendents. We show that the solutions are labeled by a set of monodromy data. We use our parametric\r\nform to explicitly construct polynomial and algebraic solutions and to derive the generating\r\nfunction of Gromov–Witten invariants of the quantum cohomology of the two-dimensional projective\r\nspace. The procedure is a relevant application of the theory of isomonodromic deformations. %B Mathematical Physics, Analysis and Geometry 4: 245–291, 2001 %I RIMS, Kyoto University %G en %1 6479 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Davide Guzzetti (guzzetti@sissa.it) on 2013-03-13T10:02:25Z\nNo. of bitstreams: 1\n04-InvFrob01.pdf: 305277 bytes, checksum: 9371356f1496f5c30346ccf145b00fb8 (MD5) %R 10.1023/A:1012933622521 %0 Journal Article %D 2000 %T Inverse problem for Semisimple Frobenius Manifolds Monodromy Data and the Painlevé VI Equation %A Davide Guzzetti %I SISSA Library %G en %U http://hdl.handle.net/1963/1557 %1 2561 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T13:04:06Z (GMT). No. of bitstreams: 1\\nmath.CV0010235.pdf: 1221345 bytes, checksum: 94b8360ca765cb56f658af63d2bf4f93 (MD5)\\n Previous issue date: 2000 %0 Journal Article %J ESAIM: COCV 3 (1998) 381-405 %D 1998 %T Infinite time regular synthesis %A Benedetto Piccoli %X In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function. %B ESAIM: COCV 3 (1998) 381-405 %I EDP Sciences %G en_US %U http://hdl.handle.net/1963/3517 %1 747 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-18T10:02:14Z\\nNo. of bitstreams: 1\\ncocv-Vol3.18.pdf: 313695 bytes, checksum: 34061a9e90f00985dc33afbf45ab584c (MD5) %R 10.1051/cocv:1998117 %0 Journal Article %J Duke Mathematical Journal. Volume: 76, Issue: 2, Pages: 645-668 %D 1994 %T Integrable functional equations and algebraic geometry %A Boris Dubrovin %A A.S. Fokas %A P.M. Santini %B Duke Mathematical Journal. Volume: 76, Issue: 2, Pages: 645-668 %I SISSA %G en %U http://hdl.handle.net/1963/6482 %1 6428 %2 Mathematics %4 1 %# MAT/03 GEOMETRIA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:25:35Z\\nNo. of bitstreams: 1\\ndubrovin_fokas_santini_1994.pdf: 19581899 bytes, checksum: 25c6a7352fa60a95d891bf8ae238f20c (MD5) %R 10.1215/S0012-7094-94-07623-0 %0 Book Section %B Integrable systems : the Verdier memorial conference : actes du colloque international de Luminy / Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach editors. - Boston [etc.] : Birkhauser, c1993. - p. 313-359 %D 1993 %T Integrable systems and classification of 2D topological field theories %A Boris Dubrovin %X In this paper we consider from the point of view of differential geometry and of the\\r\\ntheory of integrable systems the so-called WDVV equations as defining relations of 2-\\r\\ndimensional topological field theory. A complete classification of massive topological conformal\\r\\nfield theories (TCFT) is obtained in terms of monodromy data of an auxillary\\r\\nlinear operator with rational coefficients. Procedure of coupling of a TCFT to topological\\r\\ngravity is described (at tree level) via certain integrable bihamiltonian hierarchies of\\r\\nhydrodynamic type and their τ -functions. A possible role of bihamiltonian formalism in\\r\\ncalculation of high genus corrections is discussed. As a biproduct of this discussion new\\r\\nexamples of infinite dimensional Virasoro-type Lie algebras and their nonlinear analogues\\r\\nare constructed. As an algebro-geometrical applications it is shown that WDVV is just the\\r\\nuniversal system of integrable differential equations (high order analogue of the Painlev´e-\\r\\nVI) specifying periods of Abelian differentials on Riemann surfaces as functions on moduli\\r\\nof these surfaces. %B Integrable systems : the Verdier memorial conference : actes du colloque international de Luminy / Olivier Babelon, Pierre Cartier, Yvette Kosmann-Schwarzbach editors. - Boston [etc.] : Birkhauser, c1993. - p. 313-359 %I SISSA %@ 0817636536 %G en %U http://hdl.handle.net/1963/6478 %1 6432 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:43:16Z\\nNo. of bitstreams: 1\\ndubrovin_1993_verdier.pdf: 341620 bytes, checksum: 7aeca49fd73426f29caffc6712ae6b94 (MD5) %0 Journal Article %J Nuclear Physics B. Volume 379, Issue 3, 1992, pages : 627-689 %D 1992 %T Integrable systems in topological field theory %A Boris Dubrovin %X Integrability of the system of PDE for dependence on coupling parameters of the (tree-level) primary partition function in massive topological field theories, being imposed by the associativity of the perturbed primary chiral algebra, is proved. In the conformal case it is shown that all the topological field theories are classified as solutions of a universal high-order Painlevé-type equation. Another integrable hierarchy (of systems of hydrodynamic type) is shown to describe coupling to gravity of the matter sector of any topological field theory. Different multicritical models with the given structure of primary correlators are identified with particular self-similar solutions of the hierarchy. The partition function of any of the models is calculated as the corresponding tau-function of the hierarchy. %B Nuclear Physics B. Volume 379, Issue 3, 1992, pages : 627-689 %I SISSA %G en %U http://hdl.handle.net/1963/6477 %1 6433 %2 Mathematics %4 1 %# MAT/07 FISICA MATEMATICA %$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-11T15:45:42Z\\nNo. of bitstreams: 1\\ndubrovin_1992_npb.pdf: 2696879 bytes, checksum: 163a16f37434f88134edaeaa900f7d1e (MD5) %0 Journal Article %J Ricerche Mat. 36 (1987), no. 2, 197-214 %D 1987 %T Integral representation of some convex local functionals. %A Gianni Dal Maso %A Gabriella Paderni %B Ricerche Mat. 36 (1987), no. 2, 197-214 %I SISSA Library %G en %U http://hdl.handle.net/1963/497 %1 3407 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:33:38Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1987