Seminari/Colloquia
Pagina 8
Date  Type  Start  End  Room  Speaker  From  Title 

27/02/24  Seminario  16:00  17:00  1201 Dal Passo  Dario Darji  University of Louisville (US)  Applications of Local Entropy Theory
Local entropy theory is a culmination of deep results in dynamics, ergodic theory and combinatorics. Given a dynamical system with positive entropy, it gives, in some sense, the location of where the entropy resides. It is a powerful tool that can be applied in a variety of settings. In this talk, we will show how the speaker (with his coauthors) has been able to apply local entropy theory to settle some problems in continuum theory, and in dynamics of maps on the space of finite measures.

27/02/24  Seminario  14:30  16:00  1101 D'Antoni  Sam Molcho  ETH  Equivariant localization in the absence of a group action
Consider the moduli space of stable, nmarked curves M and the tautological subring R^*(M) of its Chow ring. The standard calculus for R^*(M) is based on the ''strata algebra" SA(M), which is constructed via the inductive structure of the boundary of M and the excess intersection formula, and in which calculations are expressed in terms of ''graph sums". In this talk I will discuss a new calculus for R^*(M), based on the introduction of a new ring L^*(M), built out of tropical geometry, and in which several standard calculations simplify significantly. I will explain how the comparison between SA and L is analogous to the comparison between equivariant cohomology and equivariant cohomology of the fixed locus in GKM theory.
Finally, I will sketch how this idea can be used to give explicit formulas for the BrillNoether cycles  informally, the cycles on M parametrizing curves on which a line bundle of the form omega^k(sum a_ix_i) has at least r+1 linearly independent sections.
This is a joint work with M. Abreu and N. Pagani.

21/02/24  Seminario  17:15  18:15  1201 Dal Passo  Alexander Stottmeister  University of Hannover  Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras
We discuss the embezzlement of entanglement and its relation to the
classification of the latter, as well as its application to relativistic
quantum field theory. Embezzlement (of entanglement), introduced by van
Dam and Hayden, denotes the task of producing any entangled state to
arbitrary precision from a shared entangled resource state, the
embezzling state, using local operations without communication while
perturbing the resource arbitrarily little. We show that Connes'
classification of type III von Neumann algebras can be given a
quantitative operational interpretation in terms of embezzlement. In
particular, this quantification implies that all type III factors, apart
from some type III_0 factors, host embezzling states. In contrast,
semifinite factors (type I or II) cannot host embezzling states.
Specifically, type III_1 factors are characterized as 'universal
embezzlers', meaning every normal state is embezzling. The latter
observation provides a simple explanation as to why relativistic quantum
field theories maximally violate Bell inequalities.
To understand the connection between embezzlement of entanglement and
the classification of von Neumann algebras, we use a technique
introduced by Haagerup and Størmer that associates to each normal state
on a von Neumann algebra a state on the flow of weights. Our results
then follow by quantifying the invariance of states on the flow of
weights on the restriction of the dual modular flow.
If time permits, we will also discuss the connection between embezzling
states and embezzling families, as used by van Dam and Hayden.
This is joint work with Lauritz van Luijk, Reinhard F. Werner, and Henrik Wilming. 
21/02/24  Seminario  16:00  17:00  1201 Dal Passo  Wojciech Dybalski  Adam Mickiewicz University  The Balaban variational problem in the nonlinear sigma model
The minimization of the action of a QFT with a constraint dictated
by the block averaging procedure is an important part of
the Balaban's approach to renormalization. It is particularly
interesting for QFTs with nontrivial target spaces, such as
gauge theories or nonlinear sigma models on a lattice. We analyse this
step for the O(4) nonlinear sigma model in two dimensions and
demonstrate in this case how various ingredients of the Balaban approach
play together. First, using variational calculus on Lie groups, the
equation for the minimum is derived. Then this nonlinear equation is
solved by the Banach fixed point theorem. This step requires a detailed
control of lattice Green functions and their integral kernels via random
walk expansions.

16/02/24  Seminario  16:00  17:00  1201 Dal Passo  "Cointeracting bialgebras and applications to graphs"
Pairs of cointeracting bialgebras appear recently in the literature of combinatorial Hopf algebras, with examples based on formal series, on trees (Calaque, EbrahimiFard, Manchon and Bruned, Hairer, Zambotti), graphs (Manchon), posets... These objects have one product (a way to combine two elements in a single one) and two coproducts (the first one reflecting a way to decompose a single element into two parts, maybe into several ways, the second one reflecting a way to contract parts of an element in order to obtain a new one). All these structures are related by convenient compatibilities.
We will give several results obtained on pairs of cointeracting bialgebras: actions on the group of characters, antipode, polynomial invariants... and we will give applications to a Hopf algebra of graphs, including the Fortuin and Kasteleyn's random cluster model, a variation of the Tutte polynomial.  
16/02/24  Seminario  14:30  15:30  1201 Dal Passo  Pieri Rules Over Grassmannians
The classical Pieri rule is a multiplication formula for Schubert class and Chern classes of the tautological bundle. Combinatorially, it is given by adding a chain of boxes on partitions. In this talk, we will discuss its generalization to equivariant Motivic Chern classes and its dual basis Segre motivic classes. Our formula is in terms of ribbon Schubert operators, which is roughly speaking adding ribbons on partitions. As an application, we have found a little surprising relation between motivic Chern classes and Segre motivic classes, extending the relation between ideal sheaves and structure sheaves over Grassmannians.
 
14/02/24  Seminario  16:00  17:00  1201 Dal Passo  Ricardo Correa da Silva  FAU ErlangenNürnberg  Crossing Symmetry and Endomorphisms of Standard Subspaces
This seminar aims to introduce the "crossing map", a transformation of operators in Hilbert spaces defined in terms of modular theory and inspired by "crossing symmetry" from elementary particle physics, and discuss the strong connection between crossingsymmetric twists and endomorphisms of standard subspaces. Crossing symmetry has many interesting connections, including Ttwisted ArakiWoods algebras, qSystems, and algebraic Fourier transforms.

13/02/24  Seminario  14:30  16:00  1101 D'Antoni  Thibault Poiret  University of St. Andrews  Universal Neron models of curves and Jacobians via logarithms
Given a dense open immersion U > S, some smooth and proper families X_U > U do not extend to smooth proper families over S. More often (but still not always), there is a "best smooth extension", the Neron model.
I will talk about how to construct Neron models for families of smooth curves and their Jacobians. Neron models are not compatible with base change, so there are no "moduli spaces of Neron models", but we will see that they relate to some logarithmic moduli functors, and that their base change behaviour can be understood tropically (in terms of combinatorics of dual graphs).Given a dense open immersion U > S, some smooth and proper families X_U > U do not extend to smooth proper families over S. More often (but still not always), there is a "best smooth extension", the Neron model.
I will talk about how to construct Neron models for families of smooth curves and their Jacobians. Neron models are not compatible with base change, so there are no "moduli spaces of Neron models", but we will see that they relate to some logarithmic moduli functors, and that their base change behaviour can be understood tropically (in terms of combinatorics of dual graphs).

06/02/24  Seminario  16:00  17:00  1201 Dal Passo  Margherita Nolasco  Università degli Studi dell'Aquila  Microcanonical phase transitions for the vortex system
We consider the Microcanonical Variational Principle for the vortex system in a bounded domain. In particular, we are interested in the thermodynamic properties of the system in domains of second kind, i.e. for which the equivalence of ensembles does not hold. For connected domains close to the union of disconnected disks (dumbbell domains), we show that the system may exhibit firstorder phase transitions, while the entropy is convex for large energy (joint work with Dario Benedetto and Emanuele Caglioti).
Note: This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV. 
06/02/24  Seminario  14:30  16:00  1101 D'Antoni  Roberto Vacca  Università di Roma Tor Vergata  Some examples of Ulrich sheaves
In this talk we will introduce Ulrich sheaves on projective algebraic varieties.
The corresponding notion for modules over rings originated from the work of Ulrich, but only after a paper by Eisenbud and Schreyer its geometric side received many attention due to the connection with determinantal and Pfaffian representations of (Chow forms of) varieties.
The main questions are existence of such sheaves and, if so, their minimal rank.
Positive answer to the first question is known for curves, surfaces (up to change of polarization), Veronese varieties, Segre varieties and complete intersections. Outside those examples, very few is known in dimension at least 3; therefore we will focus on Fano 3folds.

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