| 25/06/21 | Seminario | 15:00 | 16:00 | | Oleksandr TSYMBALIUK | 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
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| 18/06/21 | Seminario | 15:00 | 16:00 | | Lara BOSSINGER | 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
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| 17/06/21 | Seminario | 16:00 | 17:00 | | Mauro Artigiani | Universidad 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 Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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| 16/06/21 | Seminario | 16:00 | 17:00 | | Nicola Pinamonti | Università 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 [arxiv.org:2103.09328]
This talk is part of the activity of the MIUR Excellence Department
Project MATH@TOV CUP E83C18000100006.
MS link
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| 16/06/21 | Seminario | 14:30 | 15:30 | | Stefano Galatolo | Pisa | Self consistent transfer operators in a weak coupling regime. Invariant measures, convergence to equilibrium, linear response and control of the statistical properties.
MS Teams link
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems subjected to a mean field coupling. We consider a large class of self consistent transfer operators and prove general statements about existence and uniqueness of invariant measures, speed of convergence to equilibrium, statistical stability and linear response in a "weak coupling" or weak nonlinearity regime. We apply the general statements to examples of different nature: coupled expanding maps, coupled systems with additive noise, systems made of different maps coupled by a mean field interaction and other examples of self consistent transfer operators not coming from coupled maps. We also consider the problem of finding the optimal coupling between maps in order to change the statistical properties of the system in a prescribed way. |
| 11/06/21 | Seminario | 15:00 | 16:00 | | Lucien HENNECART | Université Paris Saclay |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Perverse sheaves with nilpotent singular support for curves and quivers"
- in streaming mode -
(see the instructions in the abstract)
Perverse sheaves on the representation stacks of quivers are fundamental in the categorification of quantum groups. I will explain how to prove that semisimple perverse sheaves with nilpotent singular support on the stack of representations of an affine quiver form Lusztig category and how to extend this question to quivers with loops. The analogous question for curves is to determine perverse sheaves on the stack of coherent sheaves whose singular support is a union of irreducible components of the global nilpotent cone. We solve this problem for elliptic curves, for which we also show that the characteristic cycle map induces a bijection between simple Eisenstein spherical perverse sheaves and irreducible components of the global nilpotent cone. This constitutes a step towards the understanding of the degree zero part of the cohomological Hall algebra of a curve.
N.B.: please click HERE to attend the talk in streaming
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| 11/06/21 | Seminario | 14:00 | 15:00 | 1201 Dal Passo | Roberto Fringuelli | Tor Vergata | The Picard group of the universal moduli stack of principal bundles over smooth projective curves
Geometry seminar in live mode!!! Up to 15 seat available (write to codogni@mat.uniroma2.it to book your seat). At the end of the abstract the link for streaming, if you are not coming in person.
Abstract: The Wess-Zumino-Witten model is a type of two-dimensional conformal field theory, which associates to the data of a smooth (projective) complex curve C, n points in C and n irreducible representations of a fixed complex Lie algebra, a finite-dimensional vector space satisfying certain axioms. The same construction can be done for families of marked curves. In this way, we get the sheaf of conformal blocks over the moduli space of marked smooth curves. This sheaf has a geometric interpretation as the sheaf of generalized theta functions, which is the push-forward of a certain line bundle from the universal moduli stack of principal bundles (with some extra-structure) over marked smooth curves to the moduli stack of marked smooth curves. The above application to conformal field theory leads naturally to the study of the Picard group of these universal moduli stacks. In this talk, we present a complete description of the Picard group of the universal moduli stack of G-bundles over n-marked smooth k-curves of genus g, for any reductive group G over an algebraically closed field k. As a consequence, we compute the divisor class group of the associated universal moduli space of semistable G-bundles. It is a joint work with Filippo Viviani.
Link for the streaming (via Teams):
https://teams.microsoft.com/l/meetup-join/19%3a0NlJ6uoaQVwRPyZ_hsMzkr18r_fRackRhBjBZVmmcsM1%40thread.tacv2/1622714552681?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22c4733e0c-f6c1-43fc-9f2a-e36dbb12a33f%22%7d
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| 10/06/21 | Seminario | 14:00 | 15:00 | | Francesco Palmurella | ETH Zürich | The parametric approach to the Willmore flow
( MS Teams Link for the streaming )
We introduce a parametric framework for the study of Willmore gradient flows which enables to consider a general class of weak, energy-level solutions and opens the possibility to study energy quantization and finite-time singularities. In this first work we restrict to a small-energy regime and prove that, for small-energy weak immersions, the Cauchy problem in this class admits a unique solution. Joint work with T. Rivière.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 09/06/21 | Seminario | 16:00 | 17:00 | | Laszlo Zsido | Università Tor Vergata |
On the equality and inequality of weights and operator valued weights
- in streaming mode -
MS Teams link
This talk is part of the activity of the MIUR Excellence Department
Project MATH@TOV CUP E83C18000100006.
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| 04/06/21 | Seminario | 16:00 | 17:00 | | Matteo Tanzi | New York University (USA) |
DinAmicI: Another Internet Seminar (DAI Seminar)
”Random-like properties of chaotic forcing”
- in streaming mode -
(see the instructions in the abstract)
We prove that skew systems with a sufficiently expanding base have “approximate” statistical properties similar to random ergodic Markov chains. For example, they exhibit approximate exponential decay of correlations, meaning that the exponential rate is observed modulo a controlled error. The fiber maps are only assumed to be Lipschitz regular and to depend on the base in a way that guarantees diffusive behaviour on the vertical component. The assumptions do not imply an hyperbolic picture and one cannot rely on the spectral properties of the transfer operators involved. The approximate nature of the result is the inevitable price one pays for having so mild assumptions on the dynamics on the vertical component. The error in the approximation is shown to go to zero when the expansion of the base tends to infinity.
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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