## Past seminars 2009 (go back to current seminars)

When Where Who Title (Click for abstract)
Fri 18 Dec 2009 15:00 MB, room C Prof. Fabio Cipriani (Politecnico di Milano) The geometry of the Sierpinski gasket
Abstract. The purpose of the seminar is to show the construction of non trivial Fredholm modules on self-similar fractal spaces and Dirac operators on the gasket based on Kigami harmonic structures and associated Dirichlet forms.
Thu 17 Dec 2009 15:30 MB, room G Prof. Fabio Cipriani (Politecnico di Milano) Dirichlet forms and Noncommutative Geometry
Abstract. The seminar is intended to illustrate the geometrical aspects underlying the notion of energy.

Examples will include:

i) Markovian semigroups and Dirichlet forms on the Clifford algebra of a Riemannian manifold and on the algebras of observables in quantum statistical mechanics;

ii) derivations on algebras of dynamical systems, others appearing in free probability and in rigidity-deformation theory.
Wed 16 Dec 2009 15:00 MB, room C Prof. Andrea Posilicano () Schroedinger operators on graphs
Abstract.
Wed 16 Dec 2009 11:00 MB, room C A. Pustetto and A. Lo Giudice (SISSA) reading seminar on Cuntz Algebras
Abstract. (based on J. Cuntz, Commun.Math.Phys. 57, 173-185 (1977))
Mon 14 Dec 2009 14:30 MB, room C Dr. Igor Mencattini (SISSA) Seminars series: Representation theory of simple Lie algebras. On a result of Kostant about the adjoint quotients (part IV)
Abstract. no abstract available
Fri 11 Dec 2009 14:30 MB, room D Giuseppe De Nittis (SISSA) Topological quantum numbers arising from symmetries. Application to Quantum Hall Effect
Abstract. Topological quantum numbers play a prominent role in many fields of quantum physics. In particular topological quantum numbers provide a very elegant explanation for the Quantum Hall effect. In dealing with topological quantum numbers, some aspects need a deeper analysis: 1) Does there exist a general framework in which topological quantum numbers emerge? 2) Does there exist a computable procedure which enables us to derive the underlying topology associated to a quantum system? Is this topology (and the related topological invariants) unique for a given system?

Under general assumptions, a natural topological structure emerges from the existence of a symmetry group. This topology can be extracted through a procedure that generalizes the usual Bloch-Floquet transform and it is a "fingerprint" for the physical system.

This procedure shows that the physics of a Bloch electron in a very weak magnetic field (QHE in Hofstadter regime) and that of a Bloch electron in a very strong magnetic field (QHE in Harper regime) are apparently similar but intimately different. Although the algebraic structure is the same, these systems are not unitarily equivalent since they produce different Chern numbers.

In summary, the "abstract" algebraic structure does not contain all the physical information. The "concrete" Hilbert space representations provide additional structures (symmetries) which define a topological content, thus yielding a richer description than the simple algebraic structure.
Thu 10 Dec 2009 11:00 MB, room D Dr. Igor Mencattini (SISSA) Seminars series: Representation theory of simple Lie algebras. On a result of Kostant about the adjoint quotients (part III)
Abstract. no abstract available
Wed 9 Dec 2009 15:30 MB, room C Prof. () Conformal structures in noncommutative geometry
Abstract. It is well known that a compact Riemannian spin manifold $(M,g)$ can be reconstructed from its canonical spectral triple $(C^\infty(M),L^2(SM),D)$, where $SM$ denotes the spinor bundle and $D$ the Dirac operator. We show that the Riemannian metric $g$ can be reconstructed up to conformal equivalence from $(C^\infty(M),L^2(SM),sign(D))$. This clarifies and proves an old folk-wisdom in non-commutative geometry.
Wed 9 Dec 2009 14:00 MB, room C Prof. Pietro Corvaja () Upper bounds for the G.C.D. of a^n-1,b^n-1, arithmetic applications and geometric and analytic analogues
Abstract. A recent result of Bugeaud, Zannier and the speaker asserts that $GCD(a^n-1, b^n-1) \ll exp(\epsilon n)$, for fixed multiplicative independent integers $a>b>1$ and positive real $\epsilon$. Some arithmetic applications will be shown, as well as its formal relations with recent results from algebraic geometry and complex analysis. In particular, we show some estimates for the intersection between algebraic or entire curves in semi-abelian varieties with higher codimensional subvarieties.
Wed 2 Dec 2009 14:30 MB, room D Dr. Andrea Raimondo (SISSA) Introduction to the Maslov index
Abstract. no abstract available
Thu 26 Nov 2009 12:00 MB, room D Prof. Marcos Jardim (IMECC, Campinas) The ADHM variety
Abstract. The ADHM equation was introduced by Atiyah, Drinfeld, Hitchin and Manin in relation to the construction of instantons on the Euclidean 4-space. Later, it was shown by Nakajima that there exists a 1-1 correspondence between "stable" solutions and torsion-free sheaves on CP^2. We investigate the affine variety of all solutions of the ADHM equation, and relate the "unstable" solutions with perverse sheaves on CP^2.
Wed 25 Nov 2009 16:00 MB, room C Dr. Igor Mencattini (SISSA) Seminars series: Representation theory of simple Lie algebras. On a result of Kostant about the adjoint quotients (part II)
Abstract. During the seminar, I will briefly review definition and the main properties of the Weyl groups. Then I will present some results about the ring of W and G invariant polynomials defined on, respectively, h and g. Here g is a semisimple Lie algebra, h is a Cartan subalgebra of g and W and G are, respectively, the Weyl and adjoint group of g. These results will be important to get a description of the adjoint quotient.
Wed 25 Nov 2009 14:30 MB, room D Davide Masoero (SISSA) Cauchy problem for highly oscillating solutions of time-dependent Schroedinger equation
Abstract.
Wed 18 Nov 2009 16:00 MB, room C Dr. Igor Mencattini (SISSA) Seminars series: Representation theory of simple Lie algebras. On a result of Kostant about the adjoint quotients (part I)
Abstract. Let g be a finite dimensional Lie algebra and G its adjoint group. During the seminar I will overview some of the properties of the so called adjoint morphism $\chi:g\rightarrow g/G$, which was intensively studied by Kostant. The first part of the seminar will be devoted to some reminder about the structure of the simple finite dimensional Lie algebras. The final goal (to be reached in the following lectures) is to present some of the main properties of the fibers of the adjoint morphism, in particular of nilpotent cone.
Wed 18 Nov 2009 14:30 MB, room D Prof. Ivan T. Todorov (INRNE, Sofia) Trying to understand 'why the SM?'
Abstract. The quantum numbers of the basic fermions in the standard model look less queer if we consider either of the "Grand Unification chains" G:=S(U(2)xU(3)) --> SU(5) --> Spin(10), or G --> Spin(4)xSpin(6) --> Spin(10); moreover, G is just the intersection of the Georgi-Glashow SU(5) and the Pati-Salam Spin(4)xSpin(6) = SU(2)xSU(2)xSU(4) within Spin(10) (see [BH]). The GUTs (in particular, Spin(10)), however, are plagued by a plethora of Higgs fields. The noncommutative geometry approach of Chamseddine-Connes [CC], on the other hand, yields the same fermion multiplet (and the standard model action coupled to gravity) with no additional Higgs'es. We observe that the intermediate algebra of Connes, H + H + M(4, C) (where H is the quaternion algebra and M(4, C) stands for the complex 4x4 matrices) appears as an associative extension of the Pati-Salam Lie algebra su(2) + su(2) + su(4) involved in the second GUT chain above.

[BH] J. Baez, J. Huerta, 0904.1556 [hep-th];
[CC] A. Chamseddine, A. Connes, 0706.3688, 3690; A. Chamseddine, 0901.0577 [hep-th].
Tue 17 Nov 2009 14:00 MB, room D Prof. () Gromov-Witten invariants and rational curves on Grassmannians
Abstract.
Wed 11 Nov 2009 14:30 MB, room D Davide Masoero (SISSA) WKB connection formula
Abstract. no abstract available
Mon 9 Nov 2009 14:30 MB, room B Prof. Maxim Pavlov (P.N. Lebedev Physical Institute of Russian Academy of Sciences) Integrability of the Manakov-Santini hierarchy
Abstract. We introduce a new type of integrable systems: vector hydrodynamic chains, i.e. hydrodynamic chains with an arbitrary number of species of moments. In a particular case, we concentrate our attention on two types of hydrodynamic chains associated with the Manakov-Santini quasilinear system. In the talk we will describe new features of this new type of integrable systems.
Wed 4 Nov 2009 14:30 MB, room C Dr. Antonio Moro (SISSA) The method of steepest descent, part II
Abstract. no abstract available
Wed 28 Oct 2009 14:30 MB, room D Dr. Antonio Moro (SISSA) The method of steepest descent
Abstract. no abstract available
Tue 27 Oct 2009 11:00 MB, room C Antonio Lerario (SISSA) Topology of generalized loop spaces for subriemannian problems on compact lie groups
Abstract. Given a left invariant distribution U on a compact Lie group G, we consider generalized loop spaces A of admissible curves (i.e. curves whose velocities lie in U). We fix a geodesic j corresponding to a one parameter subgroup and we show that it possible to reduce the study of the local homology of A_{j(0),j(t)} at j to some combinatorial geometry of the Stiefel diagram on the Lie algebra of G.
Fri 23 Oct 2009 14:30 MB, room A Francesco Sala (SISSA) The Mehta-Ramanathan restriction theorem
Abstract. no abstract available
Wed 21 Oct 2009 14:30 MB, room D Prof. Boris Dubrovin (SISSA) Integrable systems and asymptotics
Abstract. no abstract available
Mon 12 Oct 2009 17:00 MB, room C Gharchia Abdellaoui (SISSA) Semiclassical evolution of gaussian wave packets
Abstract. no abstract available
Mon 12 Oct 2009 16:00 MB, room LM Francesco Mancarella (SISSA) Off-diagonal geometric phase for mixed states
Abstract. no abstract available
Mon 12 Oct 2009 14:30 MB, room C Prof. Peter Newstead (University of Liverpool) Brill-Noether theory for vector bundles on algebraic curves
Abstract. lecture three of three
Mon 5 Oct 2009 14:30 MB, room C Prof. Peter Newstead (University of Liverpool) Brill-Noether theory for vector bundles on algebraic curves
Abstract. lecture two of three
Tue 29 Sep 2009 14:30 MB, room D Prof. Tom Coates (Imperial College, London) Gromov-Witten invariants and modular forms
Abstract. no abstract available
Mon 28 Sep 2009 14:30 MB, room C Prof. Peter Newstead (University of Liverpool) Brill-Noether theory for vector bundles on algebraic curves
Abstract. lecture one of three
Fri 25 Sep 2009 11:00 MB, room C Dr. Maxim Zabzine (Uppsala university) Chiral de Rham complex and non linear sigma model
Abstract. no abstract available
Fri 18 Sep 2009 12:00 MB, room C Pietro Giavedoni (SISSA) no title available
Abstract. no abstract available
Thu 17 Sep 2009 12:00 MB, room C Prof. Hanfeng Li (University of Buffalo) Hilbert C*-modules admitting no frames
Abstract. It is a consequence of Kasparov's stabilization theorem that every countably generated Hilbert C*-module over a unital C*-algebra has frames. I will show thatthis fails in general for arbitrary Hilbert C*-modules.
Thu 23 Jul 2009 11:30 MB, room C Gharchia Abdellaoui (SISSA) Lie Groups and Riemannian Homogenious Spaces
Abstract. no abstract available
Tue 21 Jul 2009 15:45 MB, room LM Stefano Romano (SISSA) Yang-Baxter equation and integrable systems: an introduction
Abstract. seminar/exam for the Ph.D. course "Integrable Systems and Lie Algebras"
Tue 21 Jul 2009 15:00 MB, room LM Emanuele Parodi (SISSA) (Pseudo)Differential operators and systems of KdV type
Abstract. seminar/exam for the Ph.D. course "Integrable Systems and Lie Algebras"
Thu 16 Jul 2009 15:30 MB, room C Gharchia Abdellaoui (SISSA) The Narasimhan-Seshadri theorem
Abstract. exam for the course "Special metrics on vector bundles"
Thu 16 Jul 2009 14:30 MB, room C Stefano Maggiolo (SISSA) An introduction to Donaldson's polynomial invariants
Abstract. exam for the course "Special metrics on vector bundles"
Wed 15 Jul 2009 12:00 MB, room C Dr. Simon Brain (SISSA) Moduli Spaces of Noncommutative Instantons: Gauging Away Noncommutative Parameters
Abstract. I will show how to construct families of instantons on the theta-deformed four-sphere. Each of these families is in general parameterised by a noncommutativ\e space. I will discuss what it means for families to be gauge-equivalent and show how the noncommutativity can always be gauged away' to obtain a classica\l parameter space.
Fri 10 Jul 2009 14:30 MB, room C Prof. D. Petz (University of Budapest) Markov triplets in the CCR context
Abstract. no abstract available
Tue 7 Jul 2009 14:00 ICTP seminar room Prof. Ermanno Lancocelli () Levi curvatures and related problems
Abstract. The Levi curvatures of a real hypersurfaces of C^{n+1} are related to the Levi form the way the usual Mean or Gauss curvatures are related to the real Hessi\an form. They were implicitly introduced by Bedford and Gaveau in 1978, and more explicitly, in the case n=1, by Tomassini in 1988. Later on, Montanari and\ Lanconelli extended these notions to any dimension, following the lines of the works by Caffarelli, Nirenberg and Spruck on the real Monge-Ampere equation\s. Montanari and Lanconelli showed that, for hypersurface graphs on real functions, the Levi curvatures can be expressed in terms of second order fully non\linear PDO's with an underlying sub-Riemannian structure. The properties of these structures allowed one to obtain: 1) A strong comparison principle for hy\persurfaces having the same Levi curvatures; 2)Isoperimetric inequalities; 3) Alexandrov-type sphere theorems; 4) Existence theorems of Lipschitz-continuous\ viscosity solutions to the prescribed Levi-curvature problems; 5) (only for n=1) Smoothness of the Lipschitz-continuous viscosity solutions. The results in\ 3) and 5) only give partial answers to problems which are still largely open.
Mon 22 Jun 2009 14:30 MB, room C Antonio Lerario (SISSA) First steps in GAGA
Abstract.
Thu 18 Jun 2009 15:00 MB, room C Stefano Romano (SISSA) Geodesic flow and Dirac operator
Abstract. no abstract available
Thu 18 Jun 2009 14:00 MB, room C Pietro Tortella (SISSA) Generalized laplacian operators and heat kernels
Abstract. no abstract available
Tue 16 Jun 2009 11:00 MB, room C Prof. Peter Michor (Universitat Wien) Curvature on diffeomorphism groups and nonlinear Grassmannians alias differentiable Chow varieties alias shape spaces
Abstract. For a Riemannian manifold M suitable Sobolev metrics on the space of vector fields induce right invariant weak Riemannian metrics on the group Diff(M) of al\l diffeomorphisms on $M$. This induces metrics on all spaces Emb(K,M) where K is a fixed compact manifold. Diff(M) as a subset of Emb(M,M) is also of this k\ind. As is the quotient Emb(K,M)/Diff(K). We study geodesic equations and curvature on all these spaces, in two different ways: With Arnold's curvature form\ula on Diff(M) and O'Neill's formula, or directly with Mario's curvature formula', which is a new covariant way to compute curvature. This is joint work wi\th David Mumford and Mario Micheli.
Mon 15 Jun 2009 10:00 MB, room C Stefano Maggiolo (SISSA) Mathai-Quillen formalism for Gromov-Witten invariants
Abstract. no abstract available
Thu 11 Jun 2009 12:00 MB, room C Flavia Poma (SISSA) Supersymmetry, Morse theory and equivariant cohomology
Abstract. no abstract available
Wed 10 Jun 2009 12:00 MB, room C Dr. Max Lein () An overview on the recent developments on the quantization of magnetic systems on $\R^d$: applications to mathematical physics
Tue 9 Jun 2009 12:00 MB, room B Dr. Max Lein () An overview on the recent developments on the quantization of magnetic systems on $\R^d$: the algebraic aspects
Mon 8 Jun 2009 16:30 MB, room C Dr. Max Lein () An overview on the recent developments on the quantization of magnetic systems on $\R^d$: magnetic Weyl calculus
Fri 5 Jun 2009 14:30 MB, room C Rayhanealsadat Karbalaii Ghomi (SISSA) Quantum Walk on Star Graphs
Abstract. no abstract available
Thu 21 May 2009 16:00 MB, room D Prof. Madaleine Sirugue (University of Marseille - Luminy) Random Cameo-type graphs with independent edges: beyond being models of real world, they are also very interesting mathematical objects
Abstract. no abstract available
Thu 21 May 2009 14:30 MB, room D Flavia Poma (SISSA) Moduli space of stable bundles on algebraic curves
Abstract. no abstract available
Wed 20 May 2009 14:30 MB, room D Dr. (Universidad de Salamanca) Semistable principal Higgs bundles
Abstract. no abstract available
Wed 20 May 2009 11:30 MB, room D Dr. Alessia Cattabriga () Algebraic representations of links
Abstract. A link in a 3-dimensional manifold is a 1-dimensional submanifold homeomorphic to the disjoint union of a finite number of circles. We describe how, using t\\\he notion of (g,b)-decompositions, it is possible to represent links via the elements of the mapping class group of punctured surfaces. Moreover, we anal\y\z\e how this representation can be utilized to calculate some link invariants.
Thu 7 May 2009 15:00 MB, room D Prof. Jeffrey Rauch (University of Michigan) Geometric optics II
Abstract. no abstract available
Thu 7 May 2009 14:00 MB, room D Prof. Kurusch E. Fard () The pre-Lie relation, rooted trees and the Magnus expansion
Abstract. W. Magnus' classical paper on the exponential solution of differential equations for a linear operator received much attention since its appearance in 1954,\ both in applied mathematics as well as physics. In this talk we review recent work on the classical Magnus expansion, unveiling a new structure by using th\e language of pre-Lie algebras as well as Hopf algebras of rooted trees. The pre-Lie relation implies a reduction in the number of terms in the Magnus expan\sion. This observation has to be seen in the light of the computation of commutators in particular numerical integration schemes, which is a major expense o\f many algorithms. Hence it appears to make sense to look for ways to reduce the number of commutators. Motivations as well as applications, ranging from nu\merical methods to the process of renormalisation in perturbative quantum field theory, naturally appear.
Wed 6 May 2009 14:30 MB, room C Prof. Jeffrey Rauch (University of Michigan) Geometric optics I
Abstract. no abstract available
Tue 5 May 2009 16:00 MB, room B Prof. Jeffrey Rauch (University of Michigan) Parametric Resoniance for the wave equation
Abstract. no abstract available
Tue 5 May 2009 15:00 MB, room C Prof. Kurusch E. Fard () The combinatorics of Bogoliubov's recursion in perturbative renormalisation
Abstract. In this talk we describe various combinatorial aspects of perturbative renormalisation using the language of connected graded Hopf algebras. The analog of B\ogoliubov's preparation map on the Lie algebra of Feynman graphs is identified with the Magnus expansion.
Tue 5 May 2009 14:00 MB, room C Prof. Ugo Bruzzo (SISSA) ADHM data for instantons on S4 and framed bundles on P2
Abstract. no abstract available
Thu 30 Apr 2009 10:00 MB, room C Dr. Stefano Liberati (SISSA, Astrophysics sector) Quantum gravity and special relativity: high energy astrophysics tests
Abstract. In this seminar I will review some ideas about the nature of spacetime symmetries at the Planck scale with particular attention to deviations from Lorentz\ invariance. After such a review we shall discuss many of the observational tests which high energy astrophysics provides nowadays for testing Lorentz inv\ariance.
Wed 29 Apr 2009 15:00 MB, room C Dr. Gherardo Piacitelli (SISSA) Models of quantum space-time 3
Abstract. part 3
Wed 29 Apr 2009 11:00 MB, room LM Annibale Magni (SISSA) Perelman's functionals for the Ricci flow
Abstract. no abstract available
Tue 28 Apr 2009 14:30 MB, room C Prof. Ugo Bruzzo (SISSA) ADHM data for instantons on S4 and framed bundles on P2
Abstract. no abstract available
Tue 28 Apr 2009 10:00 MB, room C Dr. Gherardo Piacitelli (SISSA) Models of quantum space-time 2
Abstract. part 2
Fri 24 Apr 2009 10:00 MB, room C Dr. Gherardo Piacitelli (SISSA) Models of quantum space-time 1
Abstract.
Wed 22 Apr 2009 15:00 MB, room C Dr. Gherardo Piacitelli (SISSA) Models of quantum space-time 0. A reminder on Weyl quantisation and C*algebras
Abstract. In this seminar, preparatory for the next seminaries and intended for a broader audience than mathematical physicists, we will recall the ideas underlying W\eyl quantisation and the resulting symbolic calculus for finitely many degrees of freedom. Then we will introduce C*-algebras and their representations as a\ convenient language for Quantum Physics; the connection with topology will be shortly highlighted.
Wed 22 Apr 2009 13:30 MB, room C Richard Sanders (Radboud Universiteit, Nijmegen) The Yang-Mills theory on the noncommutative two dimensional torus
Abstract. In differential geometry, the Yang-Mills problem is to determine which connections associated to the associated vector bundle of a principal bundle minimize\s the so-called Yang-Mills action. Their relevance lies in the fact that these minimal solutions (also dubbed instantons) are the leading order terms in the\ Feynmann path-integral and are closely related to phenomena like tunneling. In the noncommutative geometry setting, however, we will depart from the viewpo\int that we need a principal bundle and tackle the problem directly for any given vector bundle. This approach is highly succesfull for the noncommutative t\wo dimensional torus, the deformation of the regular one. We are able to explicitly calculate both the set of minimal connections and the moduli space, the \set of minimal connections factored out by the gauge group. This seminar is the exam for the course "Geometric methods of Yang-Mills theory" by Prof. Reina.\ In a certain sense it forms part 2 of the seminar "Projective modules on the two dimensional noncommutative torus" given on Tuesday, although we will quick\ly review the results obtained therein. In order to enjoy the seminar as much as possible, a background in differential geometry and operator algebras is we\lcomed.
Tue 21 Apr 2009 13:00 MB, room C Richard Sanders (Radboud Universiteit, Nijmegen) Projective modules on the two-dimensional noncommutative torus
Abstract. The noncommutative torus is a continuous deformation of the classical manifold. In a sense it is the simplest example of a noncommutative "manifold" and ser\ves as an excellent toy model for the techniques of noncommutative (Riemannian spin) geometry. The noncommutative torus admits an analogy of vector bundles:\ projective modules. In this talk we will explicitly find and classify all projective modules by using various techniques of functional analysis and operato\r algebras. This talk is the final exam for the course "Introduction to Noncommutative Riemannian Spin Geometry" by Prof. Dabrowski and is in a sense the in\troduction to the seminar "Yang-Mills theory on the noncommutative torus" given on Wednesday 22nd. An elementary background in operator algebras is suggeste\d to appreciate the seminar to its fullest extent.
Wed 8 Apr 2009 15:00 MB, room C Dr. Hua-Liang Chang (SISSA) An introduction to mixed Hodge structure
Abstract. We will give a naive guide to mixed hodge structure theory following notes of Alan H. Durfee (Proceedings of Symposia in Pure Math Volume 40 Part 1 page 313\). Mixed hodge structure is hodge structure for varieties that are not compact or smooth. It was constructed by Deligne and studied in 80-90's by Griffiths,\ Schmidt,... and others. In this talk I will present the definition of MHS and three examples in the notes.
Tue 7 Apr 2009 14:00 ICTP seminar room Prof. Tristan Riviere (ETH, Zurich, Switzerland) Conservation laws in conformal geometric analysis
Abstract. no abstract available
Thu 2 Apr 2009 14:00 MB, room D Prof. Michael Skeide () Bimodules over B(H) vs Bimodules over L^\infty --- or essentially commutative bimodules vs the most noncommutative bimodules that exist
Abstract. B(H), the algebra of all bounded operators on a Hilbert space H, is often considered the most noncommutative object. However, when we consider Hilbert bimod\ules (more precisely, von Neumann bimodules) over B(H), they are all trivial in the sense that they have an orthnormal bimodule basis. In other words, they \appear as tensor products of B(H) with a another Hilbert space. They are also centered in the sense that they are generated by their central elements. On th\e contrary, Hilbert or von Neumann bimodules over commutative algebras are centered, if and only if left and right action coincide. Although in commutative \algebra it is sometimes a comon habit to consider modules over a commutative ring as bimodules (with left action equal to right action), in practise, such a\ behaviour happens almost never in practical application. For instance, such natural objects as Brownian motion or Ornstein-Uhlenbeck processes give natural\ly rise to bimodules over commutative algebras that do not have a single nonzero element that would commute with the algebra. Bimodules over commutative alg\ebras are, therefore, among the most noncommutative objects one can imagine: Classical probability in terms of Hilbert modules reveals to be true quantum pr\obability.
Wed 1 Apr 2009 14:30 MB, room D Prof. Nicola Ciccoli () Geometric quantization of Poisson spheres
Abstract. Since the beginning of the 90's Karasev, Weinstein and Zakrzewski independently proposed a procedure to understand deformation quantization through geometr\ic quantization. Recently new results on how to build the symplectic groupoid integrating a Poisson homogeneous space and the paper "A groupoid approach to \quantization" by E. Hawkins renewed interest in this program. In this talk we will describe the procedure on the toy model of Podles' Poisson spheres. This \will give us the opportunity to talk about some features of quantization as a functor.
Thu 26 Mar 2009 14:30 MB, room C Dr. Rongmin Lu (University of Adelaide) The Gamma Genera and a Regularization of an Equivariant Euler Class
Abstract. no abstract available
Tue 24 Mar 2009 14:30 MB, room C Dr. Simon Brain (SISSA) Noncommutative istantons and twistor transform (part 2)
Abstract. see part one
Thu 19 Mar 2009 15:00 MB, room D Dr. Taras Skrypnyk (SISSA) Generalized Gaudin systems
Abstract. no abstract available
Wed 18 Mar 2009 14:00 MB, room C Giuseppe De Nittis (SISSA) Quantum representations and topological effects
Abstract. review of the following articles by G. Morchio and F. Strocchi, arXiv:0901.0870\, arXiv:0805.2870, arXiv:0707.3357
Tue 17 Mar 2009 14:30 MB, room C Dr. Simon Brain (SISSA) Noncommutative Instantons and Twistor Transform
Abstract. series in Topics of Mathematical Physics - original article: Noncommutative Instantons and Twistor Transform'', A.Kapustin, A.Kuznetsov and D.Orlov CMP, 2\20, pag 385-432, (2001)
Mon 16 Mar 2009 14:00 MB, room C Emanuele Costa (SISSA) The Dirac recipe of quantization: classical and quantum mechanics on manifolds
Abstract. review of the following articles by G. Morchio and F. Strocchi, arXiv:0901.0870, arXiv:0805.2870, arXiv:0707.3357
Mon 16 Mar 2009 11:00 MB, room D Prof. Lothar Goettsche (ICTP) Introduction to modular forms (part 3)
Abstract. no abstract available
Thu 12 Mar 2009 14:00 MB, room D Prof. Lothar Goettsche (ICTP) Introduction to modular forms (part 2)
Abstract. no abstract available
Mon 9 Mar 2009 14:00 MB, room C Prof. Lothar Goettsche (ICTP) Introduction to modular forms (part 1)
Abstract. no abstract available
Mon 9 Mar 2009 09:30 MB, room C Giuseppe De Nittis (SISSA) Topologically non-equivalent realizations of the non-commutative rational torus, part 2
Abstract. In this talk I will briefly describe two faithful, but not unitarily equivalent\, representations of the (abstract) C*-algebra of the non-commutative torus \(NC\T). When the deformation parameter is rational (M\N) each of these representati\ons is related (essentially in a unique way) to a rank N vector vector b\undle o\ver a two dimensional torus. The non unitary equivalence occurs in a different\ topology of these vector bundles.
Thu 5 Mar 2009 14:30 MB, room C Giuseppe De Nittis (SISSA) Topologically non-equivalent realizations of the non-commutative rational torus
Abstract. In this talk I will briefly describe two faithful, but not unitarily equivalent, representations of the (abstract) C*-algebra of the non-commutative torus (\NCT). When the deformation parameter is rational (M\N) each of these representations is related (essentially in a unique way) to a rank N vector vector bund\le over a two dimensional torus. The non unitary equivalence occurs in a different topology of these vector bundles.
Wed 4 Mar 2009 14:00 MB, room C Rayhanealsadat Karbalaii Ghomi (SISSA) Quantum random walk in one dimension
Abstract. no abstract available
Tue 3 Mar 2009 11:00 MB, room C Matteo Tommasini (SISSA) Elliptic curves: classification and group law
Abstract. Elliptic curves are degree 3 smooth curves in P2 with a marked point. In this talk I will briefly describe how to classify them; then I will explain how we \can induce on such curves an additive group law such that the marked point is the zero of such group. This can be done in two different ways: the first one \is purely geometrical (i.e: we just intersect lines and curves), while the second one uses the fact that any elliptic curve is homeomorphic to a torus using\ a function called Weierstrass-P-function. Now on a torus there is a very simple additive law (induced by the additive law on the complex plane), then we ca\n also define a group law on an elliptic curve using the previous homeomorphism and it turns out that the two descriptions are equivalent.
Wed 11 Feb 2009 11:00 MB, room C Dr. Alexander Pavlov () Multipliers of C*-algebras and Hilbert C*-modules
Abstract. no abstract available
Mon 9 Feb 2009 14:00 MB, room C Stefano Romano (SISSA) Analysis of the singularities for the Ricci flow (series)
Abstract. Existence, uniqueness and regularity estimates for the Ricci flow
Wed 4 Feb 2009 11:00 MB, room C Dr. Fabio Vlacci () Some results (on the zero sets) of regular functions of hypercomplex variable
Abstract. The aim of this seminar is to give a survey of a series of recent developments in the theory of functions of a hypercomplex variable. The central idea und\erlying these developments consists in requiring a function to be holomorphic on suitable slices of the space on which the function itself is defined. Spec\ifically, we apply this approach to functions defined on the space H of quaternions, on the space O} of octonions, and (if time remains...) on the Clifford \algebra Cl(0,3) of type (0,3). The properties of these functions resemble (most of) those of holomorphic functions, and yet the different nature of the alg\ebras onwhich we work introduces new and exciting phenomena. We will particularly focus our attention to the sets of zeroes of these functions and provide a\ (universal) proof for a version of the Fundamental Theorem of Algebra.
Mon 2 Feb 2009 14:00 MB, room C Pietro Tortella (SISSA) Analysis of the singularities for the Ricci flow (series)
Abstract. The talk will be mainly an exposition of the theory of the Gromow-Hausdorff topology in the class of smooth manifolds.
Thu 29 Jan 2009 14:00 MB, room C Dr. Hua-Liang Chang (SISSA) On genus one Gromov-Witten invariant of Quintic Calabi Yau
Abstract. The genus one Gromov Witten invariant is predicted by mirror symmetry and computed by A.Zinger with symplectic methods. In a joint work with J.Li, we provid\\e an algebraic proof of the computation. I will give an introduction to the work and outline the structure of the proof.
Wed 21 Jan 2009 14:00 MB, room C Flavia Poma (SISSA)
Abstract. no abstract available
Mon 19 Jan 2009 14:00 MB, room C Davide Barilari (SISSA) Analysis of the singularities for the Ricci flow (series)
Abstract. Introduction to the Gromow-Hausdorff topology
Fri 16 Jan 2009 14:30 MB, room C Dr. Donatella Iacono (SISSA) Unobstructed deformations and Tian-Todorov Theorem
Abstract. In this seminar we will introduce the notions of obstructions, T^1-lifting and the Tian-Todorov theorem.
Thu 15 Jan 2009 14:30 MB, room C Pietro Giavedoni (SISSA) Random normal matrices and polynomial curves (part 3)
Abstract. no abstract available
Tue 13 Jan 2009 14:30 MB, room C Prof. Dimitri Markushevich (Lille) Lagrangian fibrations on Hilbert powers of K3 surfaces via twisted Fourier-Mukai transform
Abstract. no abstract available
Tue 13 Jan 2009 11:00 MB, room C Prof. Rainer Verch (University of Leipzig) Dirac Field on Moyal-Minkowski Spacetime and Non-Commutative Potential Scattering
Abstract. no abstract available