## Past seminars 2011 (go back to current seminars)

When Where Who Title (Click for abstract)
Tue 20 Dec 2011 14:30 SISSA, room 134 Prof. Emilia Mezzetti (University of Trieste) Linear systems of matrices of constant rank
Abstract. After introducing the general facts on spaces of matrices of constant rank and their relations with vector bundles on projective spaces, I will give a survey on recent results in the skew-symmetric case, and some new connections with instantons.
Fri 16 Dec 2011 14:30 SISSA, room 136 Dr. Antonio Lerario (SISSA) Introduction to Real Algebraic Geometry II
Abstract.
Fri 16 Dec 2011 10:00 Santorio, room 136 Prof. A. Sitarz (University of Krakow) On modular Fredholm modules and twisted cocycl
Abstract.
Thu 15 Dec 2011 14:30 Santorio, room 136 Prof. Richard Eager (IPMU) Dimer Models and Integrable Systems
Abstract. Dimer models provide an efficient description of the 4d N=1 SUSY gauge theories on the world-volume of coincident D3-branes at Calabi-Yau singularities. The first third of this talk will be a pedagogical introduction to the correspondence of between toric geometry and dimer models. Next I will introduce Goncharov and Kenyon's construction of integrable systems associated to dimer models. These dimer models give rise to relativistic integrable systems that match those arising from 5d N=1 gauge theories studied by Nekrasov. We apply the correspondence to dimer models associated to the Yp,0 geometries, showing that they give rise to the relativistic generalization of the periodic Toda chain originally studied by Ruijsenaars.
Wed 14 Dec 2011 16:30 SISSA, room 136 M. Tommasini (SISSA) Introduction to Stacks II
Abstract.
Wed 7 Dec 2011 16:30 SISSA, room 136 M. Tommasini (SISSA) Introduction to Stacks I
Abstract.
Wed 7 Dec 2011 15:00 Santorio, room 136 Dr. Antonio Moro (SISSA) Introductory seminar series to SHOCK WAVES (III)
Abstract. We will discuss the low diffusion limit of Burgers' equation
Wed 7 Dec 2011 14:00 SISSA, room 136 Dr. Fabian Belmonte (SISSA) The magnetic Weyl quantization
Abstract.
Mon 5 Dec 2011 11:00 SISSA, room 134 Prof. Teoman Turgut (Bogazici Univ., Istanbul) Simple singular interaction on manifolds
Abstract. Delta functions on two and three dimensional manifolds are examples
of singular interactions which require renormalization at a simple level.
We will prove that for certain classes of manifolds after renormalization
the energy is bounded from below. We will discuss an analog of Sturm
comparison theorem. The ground state wave function is always positive
hence nondegenerate as in the usual potential problems.
We will comment on the decay of bound state wave functions.
We will show that one can introduce a beta-function which is negative.
If time permits we will talk about a related model, a single spin
system interacting with relativistic bosons in two dimensions.
We will prove that the energy is bounded from below.
Thu 1 Dec 2011 14:30 SISSA, room 132 Dr. Nicola Pinamonti () Quantum space-time and the horizon problem
Abstract. We shall discuss some properties of some spherically symmetric solutions of semiclassical Einstein equations coupled to a scalar quantum massless field.
If we impose the principle of gravitational stability against localization of events, we notice that there is a lower bound (of the order of Planck length) on the dimension of the region where an event can be localized. In deriving this result, we shall not use concepts like "energy" in combination with the Heisenberg principle and we shall not make any linear approximation to Einstein equations.
In the second part of the talk, this minimal length will be used in order to estimate the role of space time non-commutativity in some cosmological models possessing a Big Bang singularity. If radiation is
assumed to be in a thermal state, the arising scenario is similar to a power law inflationary universe where the horizon problem disappears.
Based on joint work with prof. Sergio Doplicher.
Wed 30 Nov 2011 16:00 SISSA, room 136 Dr. A. Lerario (SISSA) Topics in Real Algebraic Geometry I
Abstract.
Wed 30 Nov 2011 14:30 SISSA, room 136 Dr. Antonio Moro (SISSA) Introductory seminar series to SHOCK WAVES
Abstract. We will discuss shock structure, Rankine-Hugoniot condition and low diffusion limit of the Burgers equation.
Tue 29 Nov 2011 14:00 SISSA, room 134 Prof. Alexander Kuznetsov (Steklov Institute, Moscow) Instanton bundles on Fano threefolds
Abstract. I will talk about instanton bundles on Fano threefolds of
index 2. In particular, jumping lines and monadic representations will be discussed.
Thu 24 Nov 2011 15:30 SISSA, room 136 Prof. Paolo Aschieri (University of Piemonte Orientale, Vercelli, Italy) Deformation quantization of homomorphisms and connections
Abstract.
Thu 24 Nov 2011 14:00 SISSA, room 137 Prof. Pierre Martinetti () Minimal length in quantum space and integrations of the line element in Noncommutative Geometry
Abstract. We question the emergence of a minimal length in quantum spacetime,
confronting two notions that appeared at various points in the
literature:
"quantum length" as the spectrum of an operator in the Doplicher
Fredenhagen Roberts (DFR) model on the one side; Connes "spectral
distance" in
noncommutative geometry (NCG) on the other side. Although on the
Euclidean space the two notions merge into the one of geodesic
distance, they
yield distinct results in the noncommutative framework. In particular,
on the Moyal plane, the quantum length is bounded above from zero while
the spectral distance can be arbitrarily small. We show how to
reconcile the two points of view by a natural process of "spectral
triple doubling" in NCG.
This turns the quantum length into a true distance function and,
simultaneously, emphasises the "quantum mechanics flavor" of the
spectral distance.
As an example, we apply this procedure to two classes of states: the
stationary and the coherent states of the quantum harmonic oscillator.
Wed 23 Nov 2011 16:30 SISSA, room 136 A. Lo Giudice, A. Pustetto (SISSA) A compactification of the moduli space of principal Higgs bundles
Abstract.
Wed 23 Nov 2011 14:30 SISSA, room 136 Dr. A. Raimondo (SISSA) Frobenius manifold for the dispersionless Kadomtsev--Petviashvili equation II/II
Abstract.
Fri 18 Nov 2011 09:30 SISSA, room 136 Dr. Bram Mesland (Utrecht) KK-theory and Spectral Triples
Abstract.
Thu 17 Nov 2011 14:00 SISSA, room 132 Dr. Bram Mesland (Utrecht) KK-theory and Spectral Triples
Abstract.
Wed 16 Nov 2011 16:00 SISSA, room 136 G. Sanna (SISSA) Introduction to Orbifolds
Abstract.
Wed 16 Nov 2011 14:30 SISSA, room 136 Dr. Bram Mesland (Utrecht) KK-theory and Spectral Triples
Abstract.
Wed 16 Nov 2011 14:30 SISSA, room 133 Dr. A. Raimondo (SISSA) Frobenius manifold for the dispersionless Kadomtsev--Petviashvili equation I / II
Abstract.
Wed 9 Nov 2011 17:00 SISSA, room 136 A. Lo Giudice, A. Pustetto (SISSA) Introduction to Moduli of Sheaves
Abstract.
Wed 9 Nov 2011 14:30 SISSA, room 136 Prof. Yousuke Ohyama (Osaka University/Japan) Asymptotics of the Painleve equations and Hukuhara's theorem
Abstract. we discuss convergence of asypmtotic expansions of the
Painleve equations by Hukuhara's method.
Wed 9 Nov 2011 14:00 SISSA, room 005 Dr. Fabian Belmonte (SISSA) Magnetic Weyl calculus II
Abstract.
Wed 26 Oct 2011 14:00 SISSA, room 136 Dr. Fabian Belmonte (SISSA) Magnetic Weyl calculus
Abstract.
Tue 25 Oct 2011 16:00 SISSA, room 128 Giangiacomo Sanna (SISSA) Tautological and universal relations in Gromov-Witten theory
Abstract. We give a short introduction to moduli of stable curves and
maps, then we focus on a subring of the cohomology called the
tautological ring: the intersection theory in it gives rise to
relations between the coefficients of any Gromov-Witten potential.
These relations are universal in the target manifold: we present an
algorithm by Y.P.Lee that computes some (conjecturally all) such
relations.
Mon 24 Oct 2011 11:00 SISSA, room 136 Dr. Antonio Moro (SISSA) Shock waves
Abstract. Shock waves classically arise in fluid dynamics to describe phenomena in certain critical regimes where a particular physical model fails. We will discuss some general properties of shock waves as solutions to hyperbolic quasilinear PDEs within the framework of integrable systems of hydrodynamic type and their deformations. Integrable hydrodynamic type systems have been shown to possess a remarkable geometric structure (Dubrovin-Novikov) and arise also as important ingredients in the asymptotic theory of weakly dispersive soliton equations (Whitham equations), slow modulations of their algebro-geometric solutions and in the theory of Frobenius manifolds.
Fri 21 Oct 2011 11:00 SISSA, room 005 Tommaso Matteini (SISSA) Introduction to abelian varieties and to the problem of their projective embeddings
Abstract. We characterize abelian varieties among complex tori. We
discuss the problem of finding equations of projective embeddings of
abelian varieties and we show that this problem is equivalent to the
one of finding relations among theta functions. We introduce Jacobian
varieties of complex curves and we describe how Picard groups of
curves are related to them. We focus on the 1-dimensional case
(elliptic curves) and on the 2-dimensional one. In particular, we
describe a construction from the theory of integrable systems that
gives explicitely the equations of an embedding for abelian surfaces,
using the KdV hierarchy.
Thu 20 Oct 2011 15:30 SISSA, room 131 Dr. Fabian Belmonte (SISSA) Twisted crossed products and covariant families of magnetic pseudodifferential operators II
Abstract.
Wed 19 Oct 2011 16:30 SISSA, room 136 Prof. Peter Newstead (Liverpool) FOUR CONJECTURES
Abstract. This Seminar has four parts and is about four conjectures: Green's conjecture, the slope conjecture, and the conjectures of Butler and Mercat, in the framework of Brill-Noether theory for moduli of vector bundles on curves.
Wed 19 Oct 2011 14:30 SISSA, room 136 Dr. Andrea Raimondo (SISSA) Semiclassical limit for generalized KdV equations before the gradient catastrophe
Abstract.
Wed 12 Oct 2011 16:00 SISSA, room 136 Dr. Fabian Belmonte (SISSA) Twisted crossed products and covariant families of magnetic pseudodifferential operators
Abstract.
Fri 7 Oct 2011 16:30 SISSA, room 136 Prof. Peter Newstead (Liverpool) FOUR CONJECTURES
Abstract. This Seminar has four parts and is about four conjectures: Green's conjecture, the slope conjecture, and the conjectures of Butler and Mercat, in the framework of Brill-Noether theory for moduli of vector bundles on curves.
Fri 7 Oct 2011 11:00 SISSA, room 005 Prof. Carlos Simpson () Geometric structures on the moduli space of connections
Abstract. We will review several different kinds of geometric structure carried by the moduli space of connections on a smooth projective variety, including a decomposition into Lagrangian subspaces; mixed Hodge structures on the local rings at VHS; and perfect complexes of cohomology.
Wed 5 Oct 2011 14:30 SISSA, room 136 Prof. Luis Alvarez-Consul (ICMAT Madrid)
Abstract.
Tue 4 Oct 2011 16:30 SISSA, room 136 Prof. Peter Newstead (Liverpool) FOUR CONJECTURES
Abstract. This Seminar has four parts and is about four conjectures: Green's conjecture, the slope conjecture, and the conjectures of Butler and Mercat, in the framework of Brill-Noether theory for moduli of vector bundles on curves.
Fri 30 Sep 2011 11:00 SISSA, room 136 Antonio Lerario (SISSA) Cell structures on Grassmannians and the Schubert calculus
Abstract.
Thu 29 Sep 2011 11:00 SISSA, room 136 Alex Massarenti (SISSA) The Automorphisms group of $\bar M_{g,n}$
Abstract.
Tue 27 Sep 2011 16:30 SISSA, room 136 Prof. Peter Newstead (Liverpool) FOUR CONJECTURES
Abstract. This Seminar has four parts and is about four conjectures: Green's conjecture, the slope conjecture, and the conjectures of Butler and Mercat, in the framework of Brill-Noether theory for moduli of vector bundles on curves.
Thu 22 Sep 2011 14:30 SISSA, room 136 Prof. Claudio Bartocci () The bi-Hamiltonian structure of the Calogero-Moser system
Abstract. The bi-Hamiltonian structure of the rational n-particle Calogero-Moser system can be constructed by means of a double projection from a natural OmegaN-structure on the cotangent bundle of gl(n,R).
Wed 21 Sep 2011 14:30 SISSA, room 136 Prof. Rafael Herrera (CIMAT, Guanajuato) Spinorial characterization of CR-structures
Abstract. We present a spinorial way to characterize CR-structures by means of special spinor fields of twisted spin structures, which is reminiscent of Cartan's definition of pure spinor in the classical (untwisted) spin case.
Tue 20 Sep 2011 16:00 SISSA, room 136 Prof. Fabrizio Catanese () New results on uniformization by symmetric bounded domains and on varieties quotient of these
Abstract. I will report on new results and problems stemming from joint work with M. Franciosi (on the characterizations we gave of surfaces whose universal cover is a product of curves) and from joint work and work in progress with Antonio Di Scala. This work gives the characterization of varieties whose universal cover is a polydisk, respectively a bounded symmetric domain of tube type.
Tue 20 Sep 2011 14:30 SISSA, room 136 Dr. O.Fabert (Univ. Freiburg) Computing descendants from primaries in symplectic field theory
Abstract. While in Gromov-Witten theory it is well-known that the descendant
potential can be computed from the primary potential (without
descendants), in this talk I want to show that this is no longer true
for the symplectic field theory invariants. After giving hints that
the desired reconstruction result only becomes true when we work with
a (yet to be defined) non-equivariant version of SFT, in the case when
the target manifold is a symplectic mapping torus and in local SFT I
show that the only missing piece of geometrical information is the
first descendant Hamiltonian. Apart from giving an explicit
reconstruction formula, I show using explicitely computed examples in
local SFT that this information is indeed neccessary. This is joint
work with Paolo Rossi
Tue 20 Sep 2011 11:30 SISSA, room 136 Prof. Alessandro Pizzo (University of California (UC Davis)) Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction
Abstract. We show that, in a model where a non-relativistic particle is
coupled to a quantized relativistic scalar Bose field, the embedded mass
shell of the particle dissolves in the continuum when the interaction is
turned on, provided the coupling constant is sufficiently small. More
precisely, under the assumption that the fiber eigenvectors corresponding
to the putative mass shell are differentiable as functions of the total
momentum of the system, we show that a mass shell could exist only at a
strictly positive distance from the unperturbed embedded mass shell near
the boundary of the energy-momentum spectrum. (Joint work with W. De Roeck
and J. Froehlich)
Mon 19 Sep 2011 16:00 SISSA, room 136 Dr. Paolo Lorenzoni (Milano Bicocca University ) Deformations of exact and homogeneous Poisson pencils of hydrodynamic type
Abstract. In this talk we discuss some properties of deformations of Poisson pencils of
hydrodynamic type.
More specifically, we are interested in determining those structures of the fully
deformed pencils
that are inherited through the interaction between structural properties of the
dispersionless pencils
(in particular exactness or homogeneity) and suitable finiteness conditions on the
central invariants (like polynomiality).

Fri 9 Sep 2011 14:30 SISSA, room 136 Fabio Tanturri (SISSA) Orbit-cone correspondence and divisors on toric varieties
Abstract.
Fri 9 Sep 2011 11:00 SISSA, room 136 Alessandro Gentile (SISSA) Electrodynamics from noncommutative geometry
Abstract.
Thu 8 Sep 2011 15:30 SISSA, room 136 P. Coronica (SISSA) Teoria di Morse applicata ai gruppi di Lie: il teorema di Bott
Abstract.
Thu 8 Sep 2011 11:00 SISSA, room 136 G.Sanna (SISSA) Moduli of curves and invariance conjectures
Abstract. We introduce the moduli space of stable complex curves and its
orbifold structure with low genus examples. The geometrically
meaningful part of its cohomology, the tautological ring, has a
remarkable inductive structure that allows one to compute all
intersection numbers. Moreover, we describe the Y.P.Lee's algorithm to
derive relations in any semi-simple formal Gromov-Witten theory from
relations in the tautological ring.
Wed 7 Sep 2011 16:30 SISSA, room 136 Prof. Dimitri Markushevich () Holomorphically symplectic fourfolds associated to a marked Enriques surface
Abstract. To a marked Enriques surface, one can associate two hypersurfaces of dimension 4: an Eisenbud-Popescu-Walter sextic and a cubic. Each of them gives rise to a holomorphically symplectic fourfold. For the EPW sextic, this is a canonical double covering ramified in codimension 2, and for the cubic its Fano scheme parametrizing lines on it. In the talk, I will present some results on the study of these symplectic fourfolds. This is a joint work with I. Dolgachev.
Wed 31 Aug 2011 14:30 SISSA, room 136 Prof. Dimitri Markushevich () Rationality of moduli spaces of mathematical instantons
Abstract.
Mon 29 Aug 2011 14:30 SISSA, room 136 Markus Perling (Ruhr-Universitaet Bochum) Exceptional sequences and tilting bundles on rational surfaces
Abstract. We discuss exceptional sequences of sheaves and tilting sheaves on
smooth complete rational surfaces. We present structural theorems
for the case of exceptional sequences consisting of invertible sheaves
and explain how one can use these to construct tilting bundles.
Fri 22 Jul 2011 14:30 SISSA, room 136 Matteo Tommasini (SISSA) Moduli spaces of coherent systems
Abstract. I will give an informal talk on moduli spaces of coherent systems. I will mainly describe problems that arise naturally in investigating geometric properties of these moduli spaces as a real stability condition $\alpha$ varies.

This is a work in progress under the supervision of professors Barbara
Fantechi and Peter Newstead (University of Liverpool).
Wed 20 Jul 2011 14:30 SISSA, room 136 Prof. Antonella Grassi (University of Pennsylvania, Philadelphia) Tate Cycles-Anomalies
Abstract. We investigate constraints and consistencies
for 6-dimensional supersymmetric gauge theory coupled
to gravity realized as F-theory compactification on a
Calabi-Yau threefold.
Tue 19 Jul 2011 14:30 SISSA, room 136 Dr. Fabio Ferrari Ruffino () Twisted bundles with connection and D-branes gauge theory
Abstract.
Mon 18 Jul 2011 16:00 SISSA, room 136 Dr. Galina Filipuk (University of Warsaw) Orthogonal Polynomials and the Painleve' equations
Abstract.
Mon 18 Jul 2011 14:30 SISSA, room 136 Dr. Paolo Rossi () Topological Recursion in Symplectic Field Theory
Abstract.
Mon 18 Jul 2011 12:00 SISSA, room 136 Dr. Joel Ekstrand (Uppsala University) The sigma model and sheaves of vertex algebras
Abstract.
Fri 15 Jul 2011 11:30 SISSA, room 136 Luca Rizzi (SISSA) Random matrices with external source and multiple orthogonal
Abstract.
Thu 14 Jul 2011 15:30 SISSA, room 134 Riccardo Lena (SISSA) Natural Representations in Complex Geometry
Abstract.
Thu 14 Jul 2011 14:30 SISSA, room 136 Prof. Ettore Aldrovandi (Florida State University, Tallahassee) Exact sequences and fibrations of classifying stacks
Abstract.
Thu 14 Jul 2011 14:30 SISSA, room 134 Mattia Pedrini (SISSA) Representations of the Virasoro algebra
Abstract.
Wed 13 Jul 2011 11:00 SISSA, room 136 Dr. Luca Tomassini (Roma - Tor Vergata) Non-commutative space-time: some steps on curved backgrounds
Abstract.
Thu 7 Jul 2011 14:00 SISSA, room 136 Jins De Jong (SISSA) The construction of Powers-Rieffel projectors for the noncommutative 2-torus
Abstract.
Fri 1 Jul 2011 12:00 SISSA, room 136 Dr. Benoit Huard (Loughborough University) Solutions in Riemann invariants and deformations of multidimensional hydrodynamic-type systems
Abstract.
Thu 30 Jun 2011 12:00 SISSA, room 136 Dr. Marco Bertola (University of Montreal) Multi-level determinantal random point processes, Fredholm determinants and Riemann--Hilbert problems
Abstract. Joint work with M. Cafasso.
Determinantal random point processes are multi-particle statistical
models describing self-avoiding paths. The main example is self-avoiding
Brownian walkers.
Given a subset B in the configuration space, the generating function of
the number of particles in B is expressible in terms of a Fredholm
determinant of a kernel (integral operator). The study of these
determinants is related to Riemann--Hilbert problems. This connection
allows typically to relate the determinant to some transcendental
function of Painlev\'e type.
I will make a short survey using as a guide example the Airy process
introduced by Prahofer and Spohn in the study of polynuclear growth.

Thursday 30 June at 12.00 in lecture room 136 (SISSA Santorio Building,
I floor)
Wed 15 Jun 2011 16:00 SISSA, room 136 Prof. Allen Stern (Tuscaloosa, USA) Properties of Snyder space
Abstract. Although the Snyder algebra was written down over 60 years ago,
remarkably, its consequences have not yet been fully understood.
Here we examine the subalgebra generated by the spatial coordinates
and momenta and show that it has two distinct infinite dimensional
representations. Both are spanned by spherical harmonics defined
on one hemisphere of S3. They correspond the position operator having
either an integer or half-integer spectrum and yield two distinct
spatial lattices. The lattices are consistent with the continuous
symmetries of space-time. Two different approaches can be taken
to introducing particle dynamics on these lattices. In the more
conservative approach, one holds on to the traditional interpretation
of time as a real parameter associated with the evolution of the
system. However, then consistency demands that the Hamiltonian is
deformed, thereby leading to non standard energy-momentum dispersion
relations.
On the other hand, one can retain the conventional energy-momentum
corresponds to the spectra of some noncommuting operator.
The introduction of such a time operator has interesting consequences
for kinematics on the lattice.

Wed 15 Jun 2011 14:30 SISSA, room 136 Prof. Ashok K. Raina (Tata Institute, Mumbai, India) Fay's Matrix Identity for Vector Bundles on a Curve
Abstract. Among the less well known identities established by Fay
is a matrix identity which has some claim to be a
vector bundle generalisation of his better known trisecant
identity. We show how an earlier proof of the latter can
be generalised to prove his matrix identity.
Tue 14 Jun 2011 11:30 Santorio, room 136 Prof. Ken McLaughlin (Arizona State University)
Abstract.
Mon 6 Jun 2011 14:30 Santorio, room 136 Prof. Tom Claeys (Louvain-La-Neuve) Critical behaviour in random matrix theory and integrable systems
Abstract.
Mon 30 May 2011 14:30 Santorio, room 136 Dr. Kazunobu Maruyoshi (SISSA) Conformal Field Theory Techniques in Random Matrix Models
Abstract. Reference: Ivan K. Kostov, arXiv:hep-th/9907060.
Fri 27 May 2011 10:00 Riccardo Lena and Mattia Pedrini (SISSA) Reading seminar on the paper : L. G. Brown, R. G. Douglas, P. A. Fillmore, Extensions of C*-algebras and K-homology, Annals of Mathematics 105 265-324 (1977)
Abstract. In fulfullment of the requirements of the course
"Introduction to C*-Algebra",

Tue 24 May 2011 16:30 Santorio, room 136 Dr. Jins De Jong (SISSA) Remarks on the convergence of the Feynman path integral
Abstract.
Mon 16 May 2011 14:30 Santorio, room 136 Prof. Tamara Grava (SISSA) Combinatorial probability, random matrices and integrable systems
Abstract. References
Baik, J.; Deift, P.; Johansson, K. On the distribution of the length of
the longest increasing subsequence of random permutations. J. Amer. Math.
Soc. 12 (1999), no. 4, 1119 - 1178.
Mon 9 May 2011 14:30 Santorio, room 136 Prof. Tamara Grava (SISSA) Combinatorial probability, random matrices and integrable systems
Abstract. References
Baik, J.; Deift, P.; Johansson, K. On the distribution of the length of
the longest increasing subsequence of random permutations. J. Amer. Math.
Soc. 12 (1999), no. 4, 1119 - 1178.
Wed 4 May 2011 14:30 Santorio, room 136 Prof. Vasile Brinzanescu (Romanian Academy of Sciences, Bucharest) Vector bundles on non-Kaehler elliptic fibrations
Abstract. We study moduli of semi-stable vector bundles on non-Kahler elliptic complex surfaces and on non-Kahler principal elliptic bundles, which are Calabi-Yau type 3-folds. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction (joint work with R. Moraru, A. Halanay and G. Trautmann).
Thu 28 Apr 2011 16:00 Santorio, room 133 Antonio Lerario (SISSA) Lagrangian submanifolds and applications to symplectomorphisms
Abstract. We discuss Weinstein Tubular Neighborhood theorem. We will show some examples of
Lagrangian submanifolds and their link with symplectomorphisms.

The seminar is intended also for who did not attended the previous one.

Thu April 28, 2011 @ 04.00 p.m.

Mon 18 Apr 2011 15:30 Santorio, room 136 Prof. Maxim Pavlov (Taiwan) Integrable hydrodynamic chains associated with Dorfman Poisson brackets
Abstract. Three distinguish cases are extracted. Corresponding hydrodynamic chains and associated three dimensional hydrodynamic systems of the first order (or equivalently: three dimensional quasilinear equations of the second order) are presented. Integrable hierarchies of commuting hydrodynamic chains are described. they are extended to negative values of moments and times.
Thu 14 Apr 2011 16:00 Santorio, room 133 Antonio Lerario (SISSA) Homotopy methods in Symplectic Geometry
Abstract. We briefly discuss Moser argument and its implications for the problem of
equivalence of two symplectic manifolds.

(Moser relative Theorem, Darboux Theorem, Weinstein Tubular Neighborhood)
Thu 14 Apr 2011 14:30 Santorio, room 133 Dr. Stefano Nardulli (Univ. Palermo) JOINT ICTP/SISSA GEOMETRIC ANALYSIS SEMINARS 2011
Abstract.
Mon 11 Apr 2011 14:30 Santorio, room 136 Dr. Andrea Raimondo (SISSA) Kontsevich Integral and KdV equation
Abstract. References
Itzykson, C.; Zuber, J.-B. Combinatorics of the modular group. II. The
Kontsevich integrals. Internat. J. Modern Phys. A 7 (1992), no. 23, 5661-
5705.
Kontsevich, M. Intersection theory on the moduli space of curves and the
matrix Airy function. Comm. Math. Phys. 147 (1992), no. 1, 1-23.
Thu 7 Apr 2011 16:30 Santorio, room 136 Antonio Lerario (SISSA) The Cech - De Rham spectral sequence, part II
Abstract. The spectral sequence of a fiber bundle, Leray-Hirsch theorem, Sphere
bundles.
Tue 5 Apr 2011 11:30 Santorio, room 134 Dr. Andrea Raimondo (SISSA) Kontsevich Integral and KdV equation
Abstract. References
Itzykson, C.; Zuber, J.-B. Combinatorics of the modular group. II. The
Kontsevich integrals. Internat. J. Modern Phys. A 7 (1992), no. 23, 5661-
5705.
Kontsevich, M. Intersection theory on the moduli space of curves and the
matrix Airy function. Comm. Math. Phys. 147 (1992), no. 1, 1-23.
Fri 1 Apr 2011 16:30 Santorio, room 136 Antonio Lerario (SISSA) The Cech - De Rham spectral sequence
Abstract. The topics will be (up to order):
Cech De Rham complex, spectral sequence of a fiber bundle, Soboloev's
imbedding theorems, Leray-Hirsch theorem, Sphere bundles.
Wed 30 Mar 2011 09:30 Santorio, room 136 Jins de Jong (SISSA) The standard form of von Neumann algebras
Abstract. Seminar in fulfilment of the requirements for the course on C*-algebras.
Reference:
Uffe Haagerup, "The standard form of von Neumann algebras",
Math. Scand. 37, 271-285 (1975)
Mon 28 Mar 2011 14:30 Santorio, room 136 Prof. Antonio Moro (SISSA) Moments of the Riemann zeta function and unitary random matrices
Abstract. References
Keating, J. P.; Snaith, N. C. Random matrix theory and z(1/2 + it). Comm.
Math. Phys. 214 (2000), no. 1, 57 - 89.
Wed 23 Mar 2011 14:30 Santorio, room 136 Pietro Tortella (SISSA) Holomorphic Lie algebroids and moduli for their representations
Abstract. The basic ingredient to make differential geometry is the tangent bundle. In some situation one may wish to replace this by some other bundle with additional structure: to this end one introduces Lie algebroids, wich is a generalization of both the tangent bundle and Lie algebras; this is a very general tool that finds applications in foliation theory, Poisson geometry, quantization and many others fields.

In my talk I want to give a quick introduction to this subject, giving a hint of possible applications, and finally focus on the holomorphic case, where one can build moduli spaces for their representations.
Tue 22 Mar 2011 16:00 Santorio, room 136 Dr. Ian Strachan (Glasgow University, UK) Modular Frobenius Manifold
Abstract.
Mon 21 Mar 2011 14:30 Santorio, room 136 Prof. Antonio Moro (SISSA) Moments of the Riemann zeta function and unitary random matrices.
Abstract. References
Keating, J. P.; Snaith, N. C. Random matrix theory and z(1/2 + it). Comm.
Math. Phys. 214 (2000), no. 1, 57 - 89.
Tue 15 Mar 2011 16:00 Santorio, room 136 Prof. E. Ferapontov (Loughborough University, United Kingdom) On the integrability of symplectic Monge-Ampere equations
Abstract.
Mon 14 Mar 2011 14:30 Santorio, room 136 Stefano Romano (SISSA) Unitary Random Matrices. Toeplitz determinant and Ablowitz Laddik equation.
Abstract. References
Adler, M.; Van Moerbeke P. Integrals over classical Groups, Random
permutations, Toda and Toeplitz lattices. arXiv:math/9912143.
Masato Hisakado, Unitary Matrix Models and Painlev III. arXiv:hep-th/9609214.
Wed 9 Mar 2011 11:00 Santorio, room 134 Prof. Alexander Its (IUPUI (Indianapolis)) On the Riemann-Hilbert approach to the normal matrix model
Abstract. We present an alternative way to build-up the Riemann-Hilbert formalism
for the normal matrix model which was recently suggested by P. Bleher and
A. Kuijlaars. Our approach is an extension of the Lax-pair construction
of R. Teodorescu, E. Bettelheim, O. Agam, A. Zabrodin, and P. Wiegmann,
and it mimics the isomonodromy technique which was used in the early 90s
for the Riemann-Hilbert formulation of the Hermitian matrix model.
Tue 8 Mar 2011 11:00 Santorio, room 136 Prof. Elizabeth Its (IUPUI (Indianapolis)) Riemann-Hilbert Approach to Scattering Problems in Elastic Media
Abstract. We are developing Riemann-Hilbert (RH) approach to scattering problems in
elastic media. The approach is based on a version of RH method introduced
in nineties by A. Fokas for studying boundary problems for linear and
integrable nonlinear PDEs. The suitable Lax pair formulation of the
elastodynamic equation is obtained. The integral representations obtained
from this vector Lax pair are applied to Rayleigh wave propagation in
an elastic quarter space and half space. This reduces the problem to the
analysis of certain underdetermined matrix RH problem on a torus.
We showed that the problem can be in fact re-formulated as a well-posed RH
problem with a shift. Some results of the described analysis will be
discussed. Part of this work is done jointly with Alexander Its and Julius
Kaplunov.
Fri 4 Mar 2011 12:00 Santorio, room 136 Prof. D. Shepelsky (Institute for Low Temperature Physics, Kharkov, Ukraine ) Long-time asymptotics for the Camassa-Holm equation
Abstract.
Wed 2 Mar 2011 09:30 Santorio, room 136 Luca Rizzi (SISSA) Seminar/Exam: inequalities and quantum field theory
Abstract. The reading seminar on the paper
S.J. Summers, R. Werner, /Bell?s inequalities and quantum field theory. I. General setting/,J. Math. Phys. *28*, 2440 (1987) <http://jmp.aip.org/resource/1/jmapaq/v28/i10/p2440_s1>
is in fulfilment of the requirements for the course "Introduction to C*-algebras"
Mon 28 Feb 2011 14:30 Santorio, room 136 Stefano Romano (SISSA) Unitary Random Matrices. Toeplitz determinant and Ablowitz Laddik equation.
Abstract. References
Adler, M.; Van Moerbeke P. Integrals over classical Groups, Random
permutations, Toda and Toeplitz lattices. arXiv:math/9912143.
Masato Hisakado, Unitary Matrix Models and Painlev III. arXiv:hep-th/9609214.
Wed 23 Feb 2011 14:30 Santorio, room 136 Prof. Richard J. Szabo (Heriot-Watt University) Crystals, instantons and quantum geometry
Abstract. We describe the statistical mechanics of a melting crystal in three
dimensions, and its relationships with diverse topics in mathematical
physics. On the mathematics side, the model is connected to the
combinatorics of plane partitions and the enumeration of
Donaldson-Thomas invariants in algebraic geometry. On the physics side,
it is related to certain integrable hierarchies, matrix models,
Chern-Simons gauge theory, and a toy model of quantum gravity in six
dimensions. Its partition function can also be computed by enumerating
the contributions from noncommutative instantons to a six-dimensional
topological gauge theory; this yields an interpretation of the melting
crystal model as a discretization of six-dimensional spacetime at the
Planck scale. We also describe analogous relations between a melting
crystal model in two dimensions and N=4 supersymmetric Yang-Mills theory
in four dimensions.
Mon 21 Feb 2011 16:00 Santorio, room 128 Prof. Kenji Yajima (Gakushuin University, Tokyo) Resolvent estimates in amalgam spaces and asymptotic expansion for Schroedinger equations
Abstract. We study mapping properties of the resolvent of Schroedinger
operators and prove the limiting absorption principle in weighted
amalgam spaces. We apply the result to the corresponding
Schroedinger equation and obtain the asymptotic expansion
in time of solutions in remote past and far future.
Mon 21 Feb 2011 14:30 Santorio, room 136 Prof. Boris Dubrovin (SISSA) Hermitian Random Matrices. Orthogonal Polynomials. Hankel Determinant and Toda Lattice. 1/N expansion and graph enumeration.
Abstract.
Fri 18 Feb 2011 11:00 Santorio, room 137 Prof. Ryu Sasaki (Yukawa Institute, Kyoto University) Exceptional orthogonal polynomials in Quantum Mechanics
Abstract. Global solutions of Fuchsian differential equations with
more than 3 (hypergeometric) or four (Heun)
regular singularities had been virtually unkown. Here I present a
complete set of eigenfunctions of a Schroedinger
equation with $3 +\el$ ($\el=1,2,...$) regular singularities.
They are obtained as the eigenfunctions of
exactly solvable quantum mechanical systems.
Mon 14 Feb 2011 14:30 Santorio, room 136 Prof. Boris Dubrovin (SISSA) Hermitian Random Matrices. Orthogonal Polynomials. Hankel Determinant and Toda Lattice. 1/N expansion and graph enumeration.
Abstract.
Mon 7 Feb 2011 14:30 Santorio, room 136 Prof. Boris Dubrovin (SISSA) Hermitian Random Matrices. Orthogonal Polynomials. Hankel Determinant and Toda Lattice. 1/N expansion and graph enumeration.
Abstract.
Thu 27 Jan 2011 14:00 Santorio, room 136 Dr. Antonio Lerario (SISSA) Systems of quadratic inequalities
Abstract. Systems of quadratic inequalities are very flexible objects in mathematics, e.g any system of polynomial equations can be reduced to a system of quadratic equations by substitutions. Thus the set X of the
solutions of a system of quadratic inequalities can describe a very large class of semi-algebraic sets (the complexity of X is hidden in the number
of linearly independent inequalities). To study such a system we focus on the dual object: the convex hull, in
the space of all real quadratic forms on $\mathbb{R}^n$, of those quadratic forms involved in the system (n is the number of variables in the system). It turns out that the homology of X is determined by the arrangement of
this convex hull with respect to the cone of degenerate forms. This approach allows to efficiently compute homology for a very big number of
variables n as long as the number of linearly independent inequalities is
limited. Moreover, it works also for systems of integral quadratic inequalities, i.e. in the infinite dimension, beyond the semi-algebraic context.
The calculations are organized in a spectral sequence whose member $E_2$ and the differential $d_2$ have a simple clear geometric interpretation.

This is a joint work with Prof. Agrachev.
Wed 26 Jan 2011 14:30 Santorio, room 136 Dr. Ian Strachan (School of Mathematics & Statistics, University of Glasgow) Almost Duality: theory, symmetries and examples
Abstract.
Wed 19 Jan 2011 14:30 Santorio, room 136 Dr. Wu Chaozhong (SISSA) R-matrices and Hamiltonian Structures for Certain Lax Equations
Abstract.
Tue 18 Jan 2011 16:00 Santorio, room 136 Dr. Antonio Lerario (SISSA) Topology of intersections of real quadrics
Abstract. A well known result states that any projective algebraic variety is isomorphic to a set theoretic intersection of quadrics. Once a variety X in RP^n is presented as the zero locus of homogeneous quadratic polynomials, the description of its homology has a simple geometric interpretation. It can be reduced to the study of the arrangement, in the space of all quadratic forms in n+1 variables, of the quadratic forms defining X. Elementary operations on the homology of X, such as hyperplane sections or the computation of the rank of the map induced by the inclusion in RP^n, naturally fit in the previous geometric view. The aim of this seminar is to present a joint work with Prof. Agrachev in which the previous ideas are developed.
Wed 12 Jan 2011 14:30 Santorio, room 136 Dr. Caroline Kalla ()
Abstract.