Pagina 31

05/10/21Seminario14:3015:301101 D'AntoniClaudio OnoratiTor Vergata
Geometry Seminar
Remarks on sheaves on hyper-Kahler manifolds

The geometry of moduli spaces of sheaves on K3 surfaces is very rich and led to very deep results in the last decades. Moreover, under certain hypotheses, these varieties are smooth projective and have a hyper-Kahler structure, providing non-trivial examples of compact hyper-Kahler manifolds. In higher dimensions the situation is much more complicated, nevertheless in the '90s Verbitsky introduced a set of sheaves on hyper-Kahler manifolds, called hyper-holomorphic, whose moduli spaces are singular hyper-Kahler (but not compact in general). Recently O'Grady proved that such sheaves belong to a larger set of sheaves for which there exists a good wall-and-chamber decomposition of the ample cone. This suggests an analogy between the study of moduli spaces of hyper-holomorphic sheaves on hyper-Kahler manifolds and the study of moduli spaces of sheaves on K3 surfaces. After having recalled the needed definitions and results, in this talk I will face the formality problem for such set of sheaves. In particular, I will extend the notion of hyper-holomorphic to complexes of locally free sheaves, and show how the associated dg Lie algebra of derived endomorphism is formal, namely quasi-isomorphic to its cohomology. As a corollary one gets a different proof of a quadraticity result of Verbitsky. This is a joint work in progress with F. Meazzini (INdAM).

This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.
28/09/21Seminario14:3015:301101 D'AntoniRick MirandaColorado State University
Geometry Seminar
Moduli spaces for rational elliptic surfaces (of index 1 and 2)

Elliptic surfaces form an important class of surfaces both from the theoretical perspective (appearing in the classification of surfaces) and the practical perspective (they are fascinating to study, individually and as a class, and are amenable to many particular computations). Elliptic surfaces that are also rational are a special sub-class. The first example is to take a general pencil of plane cubics (with 9 base points) and blow up the base points to obtain an elliptic fibration; these are so-called Jacobian surfaces, since they have a section (the final exceptional curve of the sequence of blowups). Moduli spaces for rational elliptic surfaces with a section were constructed by the speaker, and further studied by Heckman and Looijenga. In general, there may not be a section, but a similar description is possible: all rational elliptic surfaces are obtained by taking a pencil of curves of degree 3k with 9 base points, each of multiplicity k. There will always be the k-fold cubic curve through the 9 points as a member, and the resulting blowup produces a rational elliptic surface with a multiple fiber of multiplicity m (called the index of the fibration). A. Zanardini has recently computed the GIT stability of such pencils for m=2; in joint work with her we have constructed a moduli space for them via toric constructions. I will try to tell this story in this lecture.

This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.
24/09/21Seminario14:0015:001201 Dal PassoChristian GassUni GoettingenRenormalization in string-localized field theories: a microlocal analysis

String-localized quantum field theory (SL QFT) provides an alternative to gauge theoretic approaches to QFT. In the last one-and-a-half decades, many conceptual benefits of SL QFT have been discovered. However, a renormalization recipe for loop graphs with internal SL fields was not at hand until now. In this talk, I present a proof that the problem of renormalization remains a pure short distance problem in SL QFT. This happens in spite of the delocalization of SL fields and the analytic complexity of their propagators – provided that one takes care in how to set up perturbation theory in SL QFT. As a result, the improved short-distance behavior of SL fields remains a meaningful notion, which indicates that there can exist renormalizable models in SL QFT whose point-localized counterparts are non-renormalizable. The talk is based on arXiv:2107.12834.
22/09/21Seminario15:0016:001201 Dal PassoWael BahsounLoughboroughMap lattices coupled by collisions: chaos per lattice unit

We study coupled map lattices where the interaction takes place via rare but intense 'collisions' and the dynamics on each site is given by a piecewise uniformly expanding map of the interval. Using transfer operator techniques, we derive an explicit formula for 'first collision rates' per lattice unit. This is joint work with F. Sélley.
14/07/21Seminario16:0017:00Maria Stella AdamoSapienza Università di Roma
Reflection positive representations and Hankel operators in the multiplicity free case

- In streaming mode - MS Teams link in the abstract

Reflection positivity plays an important role both in mathematics and physics. It appears as the Osterwalder--Schrader positivity in Constructive QFT, and more recently, it became relevant in the context of the representation theory of Lie groups. In this talk, we will mainly discuss reflection positive representations for the symmetric semigroups (Z,N,-id_Z) and (R,R_+,-id_R) and our new perspective given by positive Hankel operators, which are nicely characterized by their Carleson measure. In this regard, we showed that positive Henkel representations produce reflection positive representations by a suitable change of scalar product on the reflection positive Hilbert space.

This is joint work with K.-H. Neeb, J. Schober.

This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.

MS Teams link
30/06/21Seminario16:0017:00Daniele GuidoUniversità di Tor Vergata
Noncommutative self-similar fractals as self-similar C*-algebras

- in streaming mode - link in the abstract

Suitably regular self-similar fractals may be defined as fixed points in the category of compact p-pointed spaces, namely in a purely topological setting. Moreover, this procedure may be quantized, producing self-similar C*-algebras that can be considered noncommutative self-similar fractals. We illustrate the mentioned procedure in the case of the commutative and noncommutative Sierpinski Gasket (SG).
After this purely topological definition, we endow the C*-algebra with a noncommutative Dirichlet form, and with a spectral triple. Both constructions parallel analogous construction for the SG. In particular, the spectral triple produces a noncommutative metric (Lip-norm) on the algebra, and allows the reconstruction of a canonical noncommutative integral and of the noncommutative Dirichlet form.

This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.

MS Teams link
Purdue University - USA
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Shifted Yangians and quantum affine algebras revisited"
- in streaming mode -
(see the instructions in the abstract)

  In the first part of the talk, I will recall some basic results about shifted Yangians (and their trigonometric versions-the shifted quantum affine algebras), which first appeared in the work of Brundan-Kleshchev relating type A Yangians and finite W-algebras and have become a subject of renewed interest over the last five years due to their close relation to quantized Coulomb branches introduced by Braverman-Finkelberg-Nakajima.
  In the second part of the talk, I will try to convince that the case of antidominant shifts (opposite to what was originally studied in the work of Brundan-Kleshchev in type A and of Kamnitzer-Webster-Weekes-Yacobi in general type) is of particular importance as the corresponding algebras admit the RTT realization (at least in the classical types).
  In particular, this provides a conceptual explanation of the coproduct homomorphisms, gives rise to the integral forms of shifted quantum affine algebras, and also yields a family of (conjecturally) integrable systems on the corresponding Coulomb branches. As another application, the GKLO-type homomorphisms used to define truncated version of the above algebras provide a wide class of rational/trigonometric Lax matrices in classical types.
  This talk is based on the joint works with Michael Finkelberg as well as Rouven Frassek and Vasily Pestun.
  N.B.: please click HERE to attend the talk in streaming
UNAM Oaxaca - Mexico
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Newton-Okounkov bodies for cluster varieties"
- in streaming mode -
(see the instructions in the abstract)

  Cluster varieties are schemes glued from algebraic tori. Just as tori themselves, they come in dual pairs and it is good to think of them as generalizing tori. Just as compactifications of tori give rise to interesting varieties, (partial) compactifications of cluster varieties include examples such as Grassmannians, partial flag varieties or configurations spaces. A few years ago Gross-Hacking-Keel-Kontsevich developed a mirror symmetry inspired program for cluster varieties. I will explain how their tools can be used to obtain valuations and Newton-Okounkov bodies for their (partial) compactifications. The rich structure of cluster varieties however can be exploited even further in this context which leads us to an intrinsic definition of a Newton-Okounkov body.
  The theory of cluster varieties interacts beautifully with representation theory and algebraic groups. I will exhibit this connection by comparing GHKK's technology with known mirror symmetry constructions such as those by Givental, Baytev-Ciocan-Fontanini-Kim-van Straten, Rietsch and Marsh-Rietsch (joint work in progress with M. Cheung, T. Magee and A. Nájera Chávez).
  N.B.: please click HERE to attend the talk in streaming
17/06/21Seminario16:0017:00Mauro ArtigianiUniversidad del Rosario (Colombia)
DinAmicI: Another Internet Seminar (DAI Seminar)
      Double rotations and their ergodic properties  
     - in  streaming  mode -  
     (see the  instructions in the abstract)  

Double rotations are the simplest subclass of interval translation mappings. A double rotation is of finite type if its attractor is an interval and of infinite type if it is a Cantor set. It is easy to see that the restriction of a double rotation of finite type to its attractor is simply a rotation. It is known due to Suzuki - Ito - Aihara and Bruin - Clark that double rotations of infinite type are defined by a subset of zero measure in the parameter set. We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization, we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic. In my talk I plan to outline this proof that is based on the recent result by Fougeron for simplicial systems. I also hope to discuss briefly some challenging open questions and further research plans related to double rotations. The talk is based on a joint work with Charles Fougeron, Pascal Hubert and Sasha Skripchenko.

Note: The zoom link to the seminar will be posted on the DinAmicI website and on Moreover, it will be also streamed live via the youtube DinAmicI channel.
16/06/21Seminario16:0017:00Nicola PinamontiUniversità di Genova
Sine-Gordon fields with non vanishing mass on Minkowski spacetime and equilibrium states.

- in streaming mode - instructions in the abstract

During this talk we shall discuss the construction of the massive Sine-Gordon field in the ultraviolet finite regime when the background is a two-dimensional Minkowski spacetime. The correlation functions of the model in the adiabatic limit will be obtained combining recently developed methods of perturbative algebraic quantum field theory with techniques developed in the realm of constructive quantum field theory over Euclidean spacetimes. More precisely, perturbation theory is used to represent interacting fields as power series in the coupling constant over the free theory. Adapting techniques like conditioning and inverse conditioning to spacetimes with Lorentzian signature, we shall see that these power series converge if the interaction Lagrangian has generic compact support. Finally, adapting the cluster expansion technique to the Lorentzian case, we shall see that the adiabatic limit of the correlation functions of the interacting equilibrium state at finite temperature is finite.
The talk is based on a joint work with D. Bahns and K. Rejzner []

This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.

MS link

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