Dipartimento di Matematica -UTV-

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 Abstract 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 co-authors) 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 Abstract Consider the moduli space of stable, n-marked 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 Brill-Noether 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	Operator Algebras Seminar Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras Abstract 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	Operator Algebras Seminar The Balaban variational problem in the non-linear sigma model Abstract 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 non-trivial target spaces, such as gauge theories or non-linear sigma models on a lattice. We analyse this step for the O(4) non-linear 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 non-linear 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	Loic FOISSY	LMPA-ULCO Calais	Algebra & Representation Theory Seminar (ARTS) "Cointeracting bialgebras and applications to graphs" Abstract Pairs of cointeracting bialgebras appear recently in the literature of combinatorial Hopf algebras, with examples based on formal series, on trees (Calaque, Ebrahimi-Fard, 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	Rui XIONG	University of Ottawa	Algebra & Representation Theory Seminar (ARTS) Pieri Rules Over Grassmannians Abstract 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 Erlangen-Nürnberg	Operator Algebras Seminar Crossing Symmetry and Endomorphisms of Standard Subspaces Abstract 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 crossing-symmetric twists and endomorphisms of standard subspaces. Crossing symmetry has many interesting connections, including T-twisted Araki-Woods algebras, q-Systems, 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 Abstract 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	Seminario di Equazioni Differenziali Microcanonical phase transitions for the vortex system Abstract 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 first-order 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 Abstract 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 3-folds.