## Past seminars 2012 (go back to current seminars)

When Where Who Title (Click for abstract)
Wed 19 Dec 2012 14:30 SISSA, room 136 Mattia Cafasso (Univ. Angers) From string equations to integrable kernels
Abstract. Given two differential operators L and M, of order p and q respectively, consider the so-called string equation [L,M] = 1. This equation has been introduced in the nineties, by Douglas, in the context of minimal (p,q) models coupled to gravity. Since then it has been an important object of interest in the field of integrable systems, mainly because it gives interesting (and simple) relations between solitonic equations and the theory of isomonodromic deformations. In this talk I will consider some applications to the theory of integrable kernels (Airy and Pearcey kernels, and further generalisations) arising in the study of random models (random matrices and non--intersecting Brownian motions). The results I will show have been obtained in collaboration with M. Adler and P. van Moerbeke.
Thu 13 Dec 2012 13:30 SISSA, room 134 Jacopo Scalise (SISSA) The Stone-Cech compactification and the algebra of multipliers
Abstract.
Wed 12 Dec 2012 14:30 SISSA, room 136 Prof. P. Hajac (SISSA) The K-Theory of the Triple-Toeplitz deformation of Projective Planes
Abstract.
Tue 11 Dec 2012 16:00 SISSA, room 136 Mattia Pedrini (SISSA) Lefschetz Decompositions and statement of Homological Projective Duality
Abstract.
Tue 11 Dec 2012 11:00 Santorio, room 005 Dr. Jacopo Stoppa () Some applications of the tropical vertex group
Abstract. The tropical vertex group of Kontsevich and Soibelman is
generated by formal symplectomorphisms of the 2-dimensional algebraic
torus. It plays a role in many problems in algebraic geometry and
mathematical physics. The group itself can be understood in very
different ways. There are approaches involving the enumeration of
holomorphic curves, respectively the topology of moduli spaces of
representations. This leads to nice correspondences. After explaining
this, I will discuss joint work with M. Reineke and T. Weist in which
we determine the dual of a remarkable formula of Manschot, Pioline and
Sen for quiver representations: it is a degeneration formula in
Gromov-Witten theory. The refined tropical counts of Block and
Goettsche emerge naturally when attempting to "quantize" this picture.
One then gets another interpretation of the MPS formula as the
statement that two "quantizations" are compatible (joint with S. A.
Filippini).
Mon 10 Dec 2012 16:00 SISSA, room 136 Prof. P. Hajac (SISSA) An Introduction to the K-Theory of the Triple-Toeplitz deformation of Projective Planes
Abstract.
Mon 10 Dec 2012 14:00 SISSA, room 134 Dr. Marzieh Forough (SISSA) Continuous-trace C*-algebras II
Abstract.
Thu 6 Dec 2012 14:00 SISSA, room 134 Roland Abuaf (Institut Fourier, Grenoble) Categorical crepant resolution of singularities
Abstract. Let X be an algebraic complex variety with Gorenstein
singularities. A crepant resolution of X is often considered to be
a minimal resolution of singularities of X. Unfortunately, varieties
having a crepant resolution of singularities are very rare.
Thus it seems interesting to look for minimal resolutions among the
"non-commutative" ones.
In a recent work, Kuznetsov defines the notion of <categorical crepant
resolution of singularities> and
proves that low rank Pfaffians admit such categorical crepant
resolution of singularities.
In this talk, I will define the notion of wonderful resolution of
singularities. These resolutions are the ones encountered
in the theory of wonderful compactifications of linear semi-simple groups.
I will prove that a Gorenstein rational singularity with a wonderful
resolution admits a categorical crepant resolution of singularities.
As a consequence of this result, I will show that all determinantal
varieties (square, as well as symmetric and Pfaffians)
admit categorical crepant resolution of singularities.
Finally, I will discuss the possibility to find a categorical crepant
resolution even if the singularity does not admit a wonderful
resolution.
Thu 6 Dec 2012 11:00 SISSA, room 138 Prof. Barbara Fantechi (SISSA) The cotangent complex
Abstract. For any morphism of schemes one can define a cotangent
complex in nonpositive degree whose zeroeth cohomology is the
cotangent sheaf;
the right exact sequence of cotangent sheaves becomes a distinguished
triangle of cotangent complexes.
In this talk we sketch the definition of the cotangent complex,
describe its properties and use in deformation theory
and view it as part of the "hidden smoothness" philosophy.
Wed 5 Dec 2012 14:30 SISSA, room 136 Di Yang (Tsinghua University, Beijing, China) Semisimple Frobenius manifolds, Vertex algebras and W-Constraints
Abstract. This is a joint work with Youjin Zhang and Si-Qi Liu. The goal is to construct linear constraints for Givental's total descendant potential associated with any semisimple Frobenius manifold (FM). In this talk, we first associate a Heisenberg vertex algebra as well as its twisted-logarithmic representations with the Gauss-Manin system of any semisimple FM satisfying the condition that the constant Gram matrix is non-degenerate. Then we define the W-algebra and prove that under the natural twisted-logarithmic map it gives linear constraints to the corresponding total descendant potential, where certain localization techniques introduced by Givental are emloyed. In the case of the ADE singularities, our construction of the W-constraints agrees with Bakalov and Milanov's recent results. Our study is still in progress.
Tue 4 Dec 2012 16:00 SISSA, room 136 Alessio Lo Giudice (SISSA) Vanishing Theorems and Base point freeness
Abstract.
Mon 3 Dec 2012 16:00 SISSA, room 136 Dr. Marzieh Forough (SISSA) TBA
Abstract.
Wed 28 Nov 2012 14:30 SISSA, room 136 Dr. Scipio Cuccagna () The Hamiltonian structure of the nonlinear Schr\"odinger equation and the nonlinear Fermi golden rule
Abstract.
Wed 28 Nov 2012 10:00 SISSA, room 133 Flaviana Iurlano (SISSA) Fracture models as Gamma-limits of damage models
Abstract.
Tue 27 Nov 2012 16:00 SISSA, room 136 Fabio Tanturri (SISSA) Semiorthogonal decompositions and a full exceptional collection on P^n
Abstract. In this talk I will define a semiorthogonal decomposition of
a triangulated category, then I will show a very important example of
a full exceptional collection on the derived category of bounded
complexes of coherent sheaves on P^n.
Mon 26 Nov 2012 16:00 SISSA, room 136 Dr. Marzieh Forough (SISSA) Morita Equivalence
Abstract.
Fri 23 Nov 2012 16:00 SISSA, room 136 Alice Rizzardo (SISSA) Derived Functors and the Derived Category of Coherent Sheaves
Abstract. Under some mild hypotheses, an additive functor between two
abelian categories induces a functor between the corresponding derived
categories: this is called a derived functor. We will go through the
construction of derived functors, then see some specific examples in
the derived category of coherent sheaves.
Mon 19 Nov 2012 16:00 SISSA, room 134 Dr. Christian Scimiterna () TBA
Abstract.
Fri 16 Nov 2012 09:30 SISSA, room 136 Alex Massarenti (SISSA) Singularities of the Log Minimal Model Program
Abstract.
Wed 14 Nov 2012 14:30 SISSA, room 136 Dr. Andrea Raimondo (SISSA) A deformation of the method of characteristics and the Cauchy problem for Hamiltonian PDEs in the small dispersion limit
Abstract.
Mon 12 Nov 2012 16:00 SISSA, room 136 Dr. Simon Brain () Gauge Theory from Spectral Triples in Noncommutative Geometry
Abstract.
Mon 12 Nov 2012 09:30 SISSA, room 136 Dr. Antonio Moro (Univ. Milano Bicocca) Resolution of singularity in Thermodynamic phase transitions - Part II
Abstract.
Wed 7 Nov 2012 14:30 SISSA, room 005 Dr. Alexander Tovbis (Univ. of Central Florida) Universality of transitions at the point of gradient catastrophe for focusing Nonlinear Schr\
Abstract.
Wed 7 Nov 2012 14:30 SISSA, room 134 Francesca Arici (SISSA) Introduction to the Dixmier-Douady Invariant III
Abstract. In this final seminar we will give an answer to the following
question: are there spaces on which all continuous fields of C*-algebras
are trivial? The answer is contained in a degree three integer
cohomology class of the base space, which goes under the name of
We will present the Dixmier-Douady classification result for continuous
fields of C*-algebras and show how this specializes in the case of
continuous trace C*-algebras.
Tue 6 Nov 2012 16:00 SISSA, room 136 Piero Coronica (SISSA) Logarithmic Category
Abstract. In this talk we introduce the Logarithmic Category in which
objects are pairs (X,D) where X is a compactification of an open
variety and D is the boundary divisor.
In particular we discuss the log birational geometry in dimension 2,
showing how the Minimal Model Program for surfaces can be modified to
one in the logarithmic category.
Mon 5 Nov 2012 16:00 SISSA, room 136 Francesca Arici (SISSA) Introduction to the Dixmier Douady Invariant II
Abstract.
Tue 30 Oct 2012 16:00 SISSA, room 136 Giangiacomo Sanna (SISSA) Introduction to Derived Categories
Abstract. A free resolution of a sheaf and the sheaf itself carry in
some sense the same amount of information, but the first one is often
better behaved than the other. We will make this idea more formal by
introducing the derived category of an abelian category.
Tue 30 Oct 2012 14:00 SISSA, room 005 Prof. Claudio Procesi () Quasi-periodic orbits: the case of the NLS
Abstract.
Mon 29 Oct 2012 16:00 SISSA, room 136 Francesca Arici (SISSA) Introduction to the Dixmier Douady Invariant I
Abstract. The Dixmier Douady invariant appears in various areas of mathematics and plays an important role in the classification of algebra bundles and of continuous trace C*-algebras. In this first seminar I will mainly follow the bundle theoretic point of view and will focus on the classification of bundles with fiber the algebra of compact operators on a Hilbert space.
Mon 29 Oct 2012 14:30 SISSA, room 136 Prof. William Ugalde GOMEZ (Univ. Costa Rica/ICTP) Conformal invariants from the noncommutative residue
Abstract. We will review the deduction of a pair of conformal invariants on any
even dimensional, compact, conformal manifold without boundary, obtained
by the noncommutative residue of a pseudodifferential operator of order
-2 acting on square integrable sections of middle dimension forms on the
manifold.
These invariants relate to the so called critical GJMS-operators and the
results generalise to even dimension work of Connes
for dimension 4 in ''Quantized calculus and applications'' (1994).
Wed 24 Oct 2012 14:30 SISSA, room 136 Dr. Sina Tureli (SISSA) Introduction to Morse Homology
Abstract.
Tue 23 Oct 2012 16:00 SISSA, room 136 Tommaso Matteini (SISSA) Birational Geometry of Surfaces
Abstract. In this talk we introduce the general problem of birational
classification of complex projective varieties in the case of surfaces.
After describing the classical classification by Italians, we present
Mori's approach to the subject, which leads to generalizations in
higher dimension.
In particular we analyze the cone theorem and the contraction theorem
in many examples.
Mon 22 Oct 2012 16:00 SISSA, room 136 Fabian Belmonte (SISSA) Rieffel Deformation
Abstract.
Mon 22 Oct 2012 14:30 SISSA, room 136 Dr. Antonio Moro (University of Milano Bicocca) Resolution of singularity in thermodynamic phase transitions
Abstract. We show that, under a general assumption on the form of the entropy function, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable
via the method of characteristics, it provides the equation of state for the gas and the shock wave catastrophe set identifies the phase transition.

We then will focus on the van der Waals model as a specific example. Apparently, van der Waals'
approximation fails in the vicinity of the critical point so that the model cannot reproduce the jump
observed in the pressure-volume diagram. Based on the above macroscopic formalism, we propose a simple "effective" generalization of the van der Waals model such that, near the critical point, the balance equations reduce asymptotically to the viscous Burgers
equation that provides a local analytical description of critical isotherms.

Wed 17 Oct 2012 14:30 SISSA, room 136 Dr. Joel Ekstrand (SISSA) Vertex algebras and Poisson vertex algebras
Abstract.
Tue 16 Oct 2012 16:00 SISSA, room 136 Ada Boralevi (SISSA) Triangulated Categories
Abstract.
Mon 15 Oct 2012 16:00 SISSA, room 136 Fabian Belmonte (SISSA) Introuduction to Quantisation
Abstract.
Thu 11 Oct 2012 11:00 SISSA, room 132 Sina Tureli (SISSA) Superlocalisation formulae
Abstract.
Wed 10 Oct 2012 14:30 SISSA, room 136 Dr. Chaozhong Wu (SISSA) A Grassmannian approach to the KP hierarchies
Abstract.
Tue 9 Oct 2012 16:00 SISSA, room 136 Alex Massarenti (SISSA) Rationality, Unirationality and Rational Connection
Abstract. An algebraic variety X is rational if there is a birational map X--->P^n, unirational if there exists a dominant and generically finite rational map P^n--->X, and rationally connected if two general points of X are joined by a rational curve. We will study the main relations between these classes of varieties.
Fri 5 Oct 2012 14:30 SISSA, room 136 Prof. D. Gurevich (Valenciennes University) Elements of Braided Geometry
Abstract. I plan to introduce certain objects of Braided Geometry (Reflection Equation algebras, braided Lie algebras, braided varieties, braided Cayley-Hamilton identity, braided Weyl algebras), describe their properties, and exhibit some open problems.
Wed 3 Oct 2012 14:30 SISSA, room 136 Dr. Andrey Kapaev (SISSA) On a Painleve' equation without the Painleve' property
Abstract.
Fri 28 Sep 2012 14:00 SISSA, room 133 Alessio Lo Giudice (SISSA) Semistability of quadric bundles
Abstract.
Fri 14 Sep 2012 11:00 SISSA, room 136 Giangiacomo Sanna (SISSA) Local cohomology and Fulton-Hansen Theorem
Abstract. The problem of finding the minimal number of equations required to locally cut out a subvariety and the problem of determining whether the intersection of two varieties is connected can be solved (sometimes) using local cohomology. We shall define and use it in two examples.
Thu 13 Sep 2012 11:00 SISSA, room 136 Tommaso Matteini (SISSA) Ruled surfaces
Abstract.
Fri 27 Jul 2012 11:00 SISSA, room 136 Dr. Davide Masoero (University of Lisbon) Painleve I, Coverings of the Sphere and Belyi Functions
Abstract. The theory of poles of solutions of P-I is equivalent to the Nevanlinna problem of constructing a meromorphic function ramified over five points - counting multiplicities - and without critical points. We construct such meromorphic functions as limit of rational ones. In the case of the tritronquee solution these rational functions are Belyi functions.
Wed 25 Jul 2012 14:30 SISSA, room 136 Prof. Gaetan Borot (University of Geneva) Asymptotics of wave functions and application to knot theory
Abstract.
Mon 23 Jul 2012 11:00 SISSA, room 136 Prof. Piotr M. Hajac (IMPAN, Warsaw) Free actions of compact quantum groups on unital C*-algebras
Abstract. Let F be a field, G a finite group, and Map(G,F) the Hopf algebra
of all set-theoretic maps from G to F. If E is a finite field extension
of F and G is its Galois group, the extension is Galois if and only if
the canonical map resulting from viewing E as a Map(G,F)-comodule
is an isomorphism. Similarly, a finite covering space is regular
if and only if the analogous canonical map is an isomorphism.
In this talk, we extend this point of view to actions of compact quantum
groups on unital C*-algebras. We prove that such an action is free
if and only if the canonical map (obtained using the underlying Hopf
algebra of the compact quantum group) is an isomorphism. In particular,
we are able to express the freeness of a compact Hausdorff group action
on a compact Hausdorff space in algebraic terms.
(Joint work with P. F. Baum and K. De Commer.)
Fri 20 Jul 2012 11:30 SISSA, room 136 Marco Matassa (SISSA) (Co)homological tools in noncommutative geometry
Abstract. In this seminar I will give a brief introduction to some
(co)homological tools used in noncommutative geometry.
Starting with Hochschild and cyclic cohomology I will introduce
the Connes-Chern characters and the Connes index formula.
I am going to briefly present the recent developments
of twisted cyclic cohomology and modular Fredholm modules
and compute their pairing for the Podle&#347; sphere.

References:
- M. Khalkhali, "Basic Noncommutative Geometry"
- A. Rennie, A. Sitarz, M. Yamashita, "Twisted cyclic
cohomology and modular Fredholm modules"
Thu 19 Jul 2012 11:30 SISSA, room 136 Domenico Monaco (SISSA) Zeta function for the noncommutative 2-torus
Abstract. In these two seminars, we exhibit the proof
of the Gauss-Bonnet theorem using techniques
from index theory.
The same techniques are then generalized to deduce
an analogous result for the noncommutative 2-torus,
explaining some computations from a series
of articles by A. Connes and collaborators.

References:

A. Connes, P. Tretkoff, "The Gauss-Bonnet theorem for the
noncomuutative two torus", arXiv:0910.0188v1 [math.QA]

A. Connes, H. Moscovici, "Modular curvature for noncomuutative
two-tori", arXiv:1110.3500v1 [math.QA]

P.B. Gilkey, "Invariance theory, the heat equation, and the
Atiyah-Singer index theorem", CRC Press, 2nd edition (1995).
Thu 19 Jul 2012 10:30 SISSA, room 136 Francesca Arici (SISSA) Heat kernel proof of the Gauss-Bonnet theorem
Abstract. In these two seminars, we exhibit the proof
of the Gauss-Bonnet theorem using techniques
from index theory.
The same techniques are then generalized to deduce
an analogous result for the noncommutative 2-torus,
explaining some computations from a series
of articles by A. Connes and collaborators.

References:

A. Connes, P. Tretkoff, "The Gauss-Bonnet theorem for the
noncomuutative two torus", arXiv:0910.0188v1 [math.QA]

A. Connes, H. Moscovici, "Modular curvature for noncomuutative
two-tori", arXiv:1110.3500v1 [math.QA]

P.B. Gilkey, "Invariance theory, the heat equation, and the
Atiyah-Singer index theorem", CRC Press, 2nd edition (1995).
Thu 12 Jul 2012 18:00 SISSA, room 136 Roberta Lanciani (SISSA) The Riemann-Hurwitz theorem
Abstract.
Wed 11 Jul 2012 14:00 SISSA, room 136 Prof. E. Ferapontov (Loughborough University) Hamiltonian systems of hydrodynamic type in 2+1 dimensions
Abstract.
Tue 3 Jul 2012 11:00 SISSA, room 136 Prof. Elmar Wagner (Univ Morelia, Mexico) Pullback constructions of quantum principal bundles
Abstract. It will be shown how to construct non-trivial quantum principal
bundles by gluing trivial pieces via a pullback construction.
The example of the standard quantum Hopf fibration will be
discussed in detail. We will also indicate how
this construction simplifies index computations.
Thu 28 Jun 2012 14:30 SISSA, room 136 Luca Benzo () Linear systems containing the general curve of genus g
Abstract. Let $\bar M_g$ and $\bar M_g,n$ be respectively the (coarse) moduli space of stable and $n$-pointed stable complex curves of genus $g.$ It is a well-known fact that for $g\geq 3$ the uniruledness of $\bar M_g$ is equivalent to the existence of a surface $S$ which is not irrational ruled carrying a positive-dimensional linear system containing the general curve of genus $g.$
It will be shown how to use linear systems of this kind to construct rational curves on some $\bar M_g,n$ passing through the general point, hence proving their uniruledness. The argument uses Brill-Noether theory and characteristic linear series.
In the end the existence of linear systems containing the general curve of genus $g$ on complete intersection surfaces will be discussed.
Thu 28 Jun 2012 12:00 SISSA, room 136 Andrea Seppi (SISSA) Extensions and Ext groups
Abstract.
Wed 27 Jun 2012 14:30 SISSA, room 136 Dr. Jonathan Skowera () Bialynicki-Birula decomposition of Deligne-Mumford stacks
Abstract. An action of the multiplicative group $G_m$ can be used to decompose Deligne-Mumford stacks of stable maps, thereby facilitating the computation of cohomology through the well-known Bialynicki-Birula decomposition. In particular, this process expresses the cohomology of the stack in terms of the cohomology of fixed point loci.
As one would hope, this property applies more broadly to any smooth, proper Deligne-Mumford stack over an algebraically closed field of characteristic zero, and by an argument with motives, to any geometric cohomology theory over $Q$. The only technical assumption is that the coarse moduli space of the stack be a scheme.
Wed 27 Jun 2012 11:00 SISSA, room 136 Prof. Raoul Santachiara (LPTMS, Orsay, Paris) Conformal blocks of W-algebrae, instantons and Calogero-Sutherland model
Abstract.
Tue 26 Jun 2012 14:30 SISSA, room 136 Prof. Mauro Spera (Universita` di Verona) The Riemann zeta function as an equivariant Dirac index
Abstract. In this talk an interpretation of Riemann's zeta function is presented
in terms of an R-equivariant $L^2$-index of a Dirac-Ramond type operator, akin to the one on (mean zero) loops in flat space constructed in S.Wurzbacher, JFA (2003). We build on the formal similarity between Euler's partitio numerorum function (the $S^1$-equivariant $L^2$-index of the loop space Dirac-Ramond operator) and Riemann's zeta function. Also, a Lefschetz-Atiyah-Bott interpretation of the result is given.
Generalisations to Lapidus' fractal membranes are also discussed.
A fermionic Bost-Connes type statistical mechanical model is presented as well, exhibiting a "phase transition" at (inverse) temperature $\beta = 1$, which also holds for some "well-behaved" $g$-prime systems in the sense of Hilberdink-Lapidus.
Tue 19 Jun 2012 15:30 SISSA, room 136 Marzieh Forough (SISSA) Perturbations of self-adjoint regular Fredholm operators on Hilbert C*-modules
Abstract. In this talk, I discuss the stability of Fredholm property of
self-adjoint regular operators acting on Hilbert C*-modules under some
certain perturbations. I investigate the cases in which the perturbing
compact operators, small relatively bounded regular operator, and
relatively compact regular operators. I also consider the
perturbations of self-adjoint regular operators in terms of gap metric.
Then I employ these results to construct some continuous pathes of
self-adjoint regular Fredholm operators with respect to the gap
topology.
Also, a charecterization of finitely generated Hilbert C*-modules over
unital C*-algebras is obtained
Fri 8 Jun 2012 14:30 SISSA, room 004 Prof. M.S. Narasimhan (T.I.F.R. (Mumbai) and Indian Institute of Science (Bangalore)) Stability and its ramifications
Abstract. The lecture will be concerned with the interaction between algebraic
geometry and other fields of mathematics and physics.The main theme
will be the notion of "stability" which arose in moduli problems in
algebraic geometry and its relationship with topics in partial
differential equations,number theory and physics."
Fri 8 Jun 2012 10:00 SISSA, room 136 Domenico Monaco (SISSA) Twisted N=2 supersymmetry and Donaldson invariants
Abstract.
Thu 7 Jun 2012 11:00 SISSA, room 136 Emanuele Parodi (SISSA) Integrable Hamiltonian perturbations of nonlinear wave systems
Abstract. The study of dispersive evolutionary PDEs systems can be addressed following the perturbative approach introduced by Prof. Dubrovin and his collaborators. Focusing on the two-components systems, I will consider the subclass, important in many applications, of Hamiltonian perturbations of nonlinear wave systems. The classification of the integrable ones within the second order in the small parameter is described by two arbitrary functions of one variable. I will analyze the problem of extending that classification to the third order.
Wed 6 Jun 2012 16:30 SISSA, room 136 Prof. Antonella Grassi (University of Pennsylvania) Geometry and F-theory in physics, an introduction
Abstract.
Wed 6 Jun 2012 15:00 SISSA, room 136 Prof. Julius L. Shaneson (University of Pennsylvania) Counting lattice points in polytopes
Abstract.
Thu 31 May 2012 09:30 SISSA, room 136 Fabian Belmonte (SISSA) Crossed Products of C*-Algebras
Abstract. Many C*-algebras appearing in Operator Algebras, Strict Deformation
Quantization, Noncommutative Geometry and other fields might be
obtained by aplying one of the following procedures:
-Rieffel Deformation
-Crossed Products
The purpose of this talk is to expose the relation between those
procedures obtained in the article by P. Kasprzak: "Rieffel
Deformation via Crossed Products, J. Funct. Anal. 257, 1288-1332, 2009".
Supplementary references:
M. A. Rieffel: Deformation Quantization for Actions of R^d, Memoirs of
the AMS, 506, 1993.
D. Williams: Crossed Products of C*-Algebras, Mathematical Surveys and
Monographs, 134, American Mathematical Society, 2007.
Wed 30 May 2012 16:00 SISSA, room 136 Dr. Antonio Lerario (Purdue University) Expected topology of random real algebraic varieties
Abstract. We will discuss the expected values of metric and topological properties
of real algebraic varieties whose defining equations are random polynomials.
Wed 30 May 2012 14:30 SISSA, room 136 Matteo Casati (SISSA) On deformation of Poisson Manifolds of Hydrodynamic type
Abstract.
Tue 29 May 2012 16:00 SISSA, room 136 Piero Coronica, Benjamin Kipkirui Kikwai and Pavel Silveira Diaz (SISSA) Donaldson-Thomas Invariants III
Abstract.
Fri 25 May 2012 11:00 SISSA, room 136 Giacomo Dossena (SISSA) Spinors & diffeomorphisms
Abstract.
Thu 24 May 2012 11:30 SISSA, room 136 Matteo Casati (SISSA) Reduction of Poisson manifolds: a Marsden-Ratiu independent earlier attempt
Abstract.
Wed 23 May 2012 14:30 SISSA, room 136 Matteo Tommasini (SISSA) The Hodge-Deligne polynomials of some moduli spaces of coherent systems
Abstract.
Tue 22 May 2012 16:00 SISSA, room 136 Piero Coronica, Benjamin Kipkirui Kikwai and Pavel Silveira Diaz (SISSA) Donaldson-Thomas Invariants II
Abstract.
Tue 22 May 2012 11:00 SISSA, room 136 Marzieh Forough (SISSA) Hilbert C*-modules II
Abstract. In this talk, I first describe the Hilbert C*-module structure
on finitely generated projective modules over unital C*-algebras.
Then I give a brief review of bounded adjointable Fredholm operators
on standard Hilbert C*-modules.
Finally, I discuss the noncommutative version of Atiyah-Janich Theorem.
Fri 18 May 2012 17:00 SISSA, room 136 Celeste Damiani (SISSA) Cohomology of projective spaces
Abstract.
Wed 16 May 2012 14:30 SISSA, room 136 Dario Merzi (SISSA) Marsden-Ratiu reduction for Poisson Manifolds
Abstract.
Tue 15 May 2012 16:00 SISSA, room 136 Piero Coronica, Benjamin Kipkirui Kikwai and Pavel Silveira Diaz (SISSA) Donaldson-Thomas Invariants I
Abstract.
Wed 9 May 2012 14:30 SISSA, room 134 Prof. Leticia Brambila Paz (CIMAT, Guanajuato) On the Hilbert scheme of the moduli space of stable bundles
Abstract. Studying the geometry of projective varieties frequently involves
understanding its subvarieties. Roughly speaking, the Hilbert schemes
and the Chow schemes are schemes that parametrise
subvarieties of a projective variety. In this talk I will describe some subvarieties
of the moduli space of stable vector bundles over a curve and the Hilbert scheme associated to this subvarieties.
Wed 9 May 2012 14:30 SISSA, room 136 Stefano Romano (SISSA) 4-dimensional Frobenius manifolds and Painleve' VI
Abstract.
Tue 8 May 2012 16:00 SISSA, room 136 Mattia Pedrini (SISSA) Vasserot-Schiffman's proof of AGT Conjecture II
Abstract.
Mon 7 May 2012 16:00 SISSA, room 136 Dr. Ada Boralevi (SISSA) Homogeneus vector bundles, P-modules and quiver representations II
Abstract.
Fri 4 May 2012 15:30 SISSA, room 136 Mattia Pedrini (SISSA) Vasserot-Schiffman's proof of AGT Conjecture I
Abstract.
Fri 4 May 2012 11:00 SISSA, room 136 Benjamin Kikwai (SISSA) Smooth Morphisms
Abstract.
Wed 2 May 2012 14:30 SISSA, room 134 Prof. Dimitri Markushevich () Bubble tree compactification
Abstract.
Wed 2 May 2012 11:00 SISSA, room 134 Dario Merzi (SISSA) t t* equations and classification of N=(2,2) superconformal field theories
Abstract.
Fri 27 Apr 2012 15:30 SISSA, room 136 Tommaso Matteini (SISSA) Introduction to Hyperkahler Geometry
Abstract.
Thu 26 Apr 2012 15:30 SISSA, room 134 Pavel Silveira Diaz (SISSA) Riemann-Roch theorem
Abstract.
Thu 26 Apr 2012 14:30 SISSA, room 134 Francesca Arici (SISSA) Differentials on schemes
Abstract.
Thu 26 Apr 2012 09:30 SISSA, room 136 Marzieh Forough (SISSA) HILBERT C*-MODULES
Abstract. In this talk, I first review some basic facts of Hilbert C*-modules.
Then I discuss some important classes of operators on Hilbert
C*-modules such as bounded adjointable operators, compact operators
and unbounded regular operators.
(Suggested ref: E. C. Lance "Hilbert C*-modules").
Tue 24 Apr 2012 16:00 SISSA, room 136 Dr. Ada Boralevi (SISSA) Homogeneous vector bundles, P-modules and quiver representations
Abstract. A quiver is a directed graph. Quivers come from combinatorics, and
homogeneous vector bundles from algebraic geometry. In 1990 Bondal and
Kapranov established an equivalence of categories that links together
algebraic geometry, representation theory, and combinatorics. To any
homogeneous vector bundle on a rational homogeneous variety they
associate a finite dimensional representation of a given quiver (with
relations).

I will describe this equivalence in detail, and explain how it is an
excellent tool for computing cohomology of homogeneous bundles, which
leads to a generalization of the well-known Borel-Weil-Bott Theorem.
The talk will be as basic as possible: no previous knowledge of quiver
representations is required.

If time permits, I will then explain a conjectural link of the quiver
representations category with the Bernstein-Gelfand-Gelfand category
O, which could potentially lead to an infinite dimensional version of
the above mentioned equivalence. If people are interested, this could
constitute the subject of a second talk.
Tue 24 Apr 2012 14:30 SISSA, room 136 Marco Matassa (SISSA) The DFR Model as a Rieffel deformation (reading seminar)
Abstract. Based on
"On the operator algebra for the space-time uncertainty relations",
by M.A.Rieffel

http://arxiv.org/abs/funct-an/9701011
Wed 14 Mar 2012 14:30 SISSA, room 136 Prof. M. Pavlov (Lebedev Physical Institute, Moscow) Oriented Associativity Equations, semi-Hamiltonian Hydrodynamic Type Systems and Conjugate Curvilinear Coordinate Nets
Abstract. The Oriented Associativity Equations (OAE) are most natural
generalization of the WDVV associativity equations from the flat Egorov
to the symmetry consistent case. We introduce a basic set of
hydrodynamic type systems connected with OAE. We establish a link from
OAE to the symmetry consistent curvilinear conjugate coordinate nets
(SCCCCN), and the back-link from SCCCCN to OAE.

Tue 13 Mar 2012 10:00 SISSA, room 134 Matteo Casati (SISSA) The AKSZ formalism and topological sigma models
Abstract. In partial fulfillment of the exam for the course on Topological Field Theories.
Wed 7 Mar 2012 14:30 SISSA, room 136 Prof. B. Dubrovin (SISSA) Dressing transformations and the Givental symplectic space
Abstract.
Wed 29 Feb 2012 17:00 SISSA, room 136 Mattia Pedrini (SISSA) Alday-Gaiotto-Tachikawa relations
Abstract.
Wed 29 Feb 2012 16:00 SISSA, room 136 Dr. Francesco Sala Alday-Gaiotto-Tachikawa relations
Abstract.
Wed 29 Feb 2012 14:30 SISSA, room 136 Stefano Romano (SISSA) A polynomiality result for the Dubrovin-Zhang hierarchies
Abstract. Following the works of Buryak, Posthuma and Shadrin
(http://arxiv.org/abs/1009.5351, http://arxiv.org/abs/1104.2722), I will
discuss the construction of the full hierarchy associated to the genus
expansion of a semisimple Frobenius manifold in the framework of the
Givental group quantized action. The goal is to present the authors'
result that the hierachy obtained is indeed polynomial, as initially
conjectured by Dubrovin and Zhang.
Tue 28 Feb 2012 14:30 SISSA, room 136 Dr. Pietro Tortella Introduction to non-abelian Hodge theory
Abstract. We give an introduction to some aspects of nonabelian Hodge theory.
For X a smooth projective variety over the complex numbers, we will
construct the correspondence between flat connections and Higgs
bundles over it.
We will then study the moduli spaces of t-connections for t a complex
number, and see that these realize the twistor space of the
hyperkahler structure of the moduli space of Higgs bundles, and
compactify M_DR.
Fri 24 Feb 2012 10:30 SISSA, room 136 Dr. Francesco Sala Introduction to Donaldson-Thomas invariants II
Abstract.
Thu 23 Feb 2012 14:30 SISSA, room 136 Dr. Simone Marchesi () Jumping pairs in Steiner bundles
Abstract. In this talk we will present Steiner and Schwarzenberger
bundles on the Grassmannians and show the theory that relates them. In
the first part we will define the two families of bundles mentioned
before and study their properties. We will introduce then the concept
of jumping pair for a Steiner bundle and we will study the dimension
of the jumping locus of the bundle. Finally, we will give a complete
classification of Steiner bundles on the Grassmannian whose jumping
locus has maximal dimension and will describe them as
Schwarzenberger bundles.

U. Bruzzo
Wed 22 Feb 2012 15:30 Santorio, room 134 Prof. Piotr M. Hajac (IMPAN / Warsaw University) STABLE TRIVIALITY CRITERION FOR ASSOCIATED NONCOMMUTATIVE LINE BUNDLES
Abstract.
Wed 22 Feb 2012 14:30 SISSA, room 136 Dr. Wu Chaozhong (SISSA) One-loop deformation of principal hierarchies
Abstract.
Tue 21 Feb 2012 16:00 SISSA, room 136 Dr. Francesco Sala Introduction to Donaldson-Thomas invariants I
Abstract.
Tue 21 Feb 2012 14:30 SISSA, room 136 Prof. Francesco Zucconi () Two ray links and the rationality of some moduli spaces
Abstract. In this talk I will show how the birational geometry of the del Pezzo -3-fold and of other Fanos 3-folds can be used to describe some moduli spaces of curves.
Wed 15 Feb 2012 14:30 SISSA, room 136 Stefano Romano (SISSA) Topological recursion and genus expansion
Abstract. this is meant to be part 2 of my previous seminar and to give a very brief introduction to Givental's approach to the genus expansion of a semi-simple Frobenius manifold
Mon 13 Feb 2012 14:30 SISSA, room 136 Dario Merzi (SISSA) -vertex model: asymptotic behavior in the ferroelectric phase via RH problem
Abstract.
Wed 8 Feb 2012 14:30 SISSA, room 136 Prof. Youjin Zhang (Tsinghua University) On the genus two free energies for semi-simple Frobenius manifolds
Abstract.
Tue 7 Feb 2012 16:00 SISSA, room 136 Matteo Tommasini (SISSA) Introduction to algebraic stack III (Deligne-Mumford stacks)
Abstract.
Tue 31 Jan 2012 16:00 SISSA, room 136 Dr. Ada Boralevi (University of Trieste) Moduli spaces of orthogonal bundles
Abstract.
Fri 27 Jan 2012 16:00 SISSA, room 136 Prof. Igor Mencattini () Cluster Algebras
Abstract. I will give a brief and elementary introduction to the theory of Cluster Algebras introduced by Fomin and Zelevinsky. In the first part, after giving basic definitions and explained some examples I will discuss, in some details, the case of the so called Cluster algebras of finite type. In the second part I will make some connections between Cluster algebras and Poisson geometry.
Thu 26 Jan 2012 16:30 SISSA, room 136 Domenico Monaco (SISSA) Deformation quantization of algebraic varieties
Abstract.
Thu 26 Jan 2012 14:30 SISSA, room 137 Prof. Igor Mencattini () Cluster Algebras
Abstract. I will give a brief and elementary introduction to the theory of Cluster Algebras introduced by Fomin and Zelevinsky. In the first part, after giving basic definitions and explained some examples I will discuss, in some details, the case of the so called Cluster algebras of finite type. In the second part I will make some connections between Cluster algebras and Poisson geometry.
Wed 25 Jan 2012 16:00 SISSA, room 136 Francesca Arici (SISSA) Deformation Quantization of Poisson Manifolds
Abstract.
Wed 25 Jan 2012 14:30 SISSA, room 136 Stefano Romano (SISSA) From Frobenius manifolds to integrable hierarchies: the Dubrovin-Zhang reconstruction procedure
Abstract.
Thu 19 Jan 2012 14:30 SISSA, room 137 Dr. Oliver Serman () Singularities of moduli spaces of principal bundles on curves
Abstract. Moduli spaces of principal bundles on curves carry a very rich geometry. In this talk I will focus on the singularities of these varieties. I will show how local factoriality of GIT quotients can be used to give a description of their singular locus, and then compute the fundamental group of the smooth locus of these moduli spaces.
Wed 18 Jan 2012 14:30 SISSA, room 136 Emanuele Parodi (SISSA) Hamiltonian structure of evolutionary PDEs: Poisson brackets of hydrodynamic type and deformations
Abstract.
Thu 12 Jan 2012 14:30 SISSA, room 136 Prof. Federica Pezzotti () Mean field models and semiclassical approximation
Abstract.
Wed 11 Jan 2012 16:00 SISSA, room 136 Prof. Ugo Bruzzo (SISSA) Hypersurfaces in toric varieties
Abstract.
Wed 11 Jan 2012 14:30 SISSA, room 136 Emanuele Parodi (SISSA) Poisson brackets and Jacobi brackets in finite dimension
Abstract.