31/03/23  Seminario  16:00  17:00  1201 Dal Passo  Elena PASCUCCI  "Sapienza" Università di Roma 
Algebra & Representation Theory Seminar (ARTS)
"Fundamental Superalgebras in PI Theory"
Fundamental superalgebras are special finitedimensional superalgebras over an algebraically closed field of characteristic zero defined in terms of certain multialternating graded polynomials. They play a key role in Kemer's Representability Theorem. In the present talk we provide new examples of fundamental superalgebras. Finally, if time allows, we shall give a characterization of fundamental superalgebras in terms of the representation theory of the hyperoctahedral group.
This is based on a joint work with Antonio Giambruno and Ernesto Spinelli. 
31/03/23  Seminario  14:30  15:30  1201 Dal Passo  Giulia IEZZI  Università di Roma "Tor Vergata" & RWTH Aachen University 
Algebra & Representation Theory Seminar (ARTS)
"A realisation of some Schubert varieties as quiver Grassmannians"
Quiver Grassmannians are projective varieties parametrising subrepresentations of quiver representations. Their geometry is an interesting object of study, due to the fact that many geometric properties can be studied via the representation theory of quivers. For instance, this method was used to study linear degenerations of flag varieties, obtaining characterizations of flatness, irreducibility and normality via rank tuples.
We give a construction for smooth quiver Grassmannians of a specific wild quiver, realising a class of Schubert varieties inside flag varieties. This allows for a definition of linear degenerations of Schubert varieties.

29/03/23  Seminario  16:00  17:00  1201 Dal Passo  KarlHermann Neeb  FAU ErlangenNürnberg 
Operator Algebras Seminar
Causal symmetric spaces and nets of operator algebras
In the theory of local observables in Algebraic Quantum Field Theory (AQFT) modular theory creates a oneparameter group of modular automorphisms from a single state and this group often has a geometric implementation. If modular groups are contained in finitedimensional Lie groups, they naturally lead to gradings of the Lie algebra and further to causal symmetric spaces. Conversely, we explain how nets of local observables (resp. of standard subspaces) on causal symmetric spaces can be constructed for all irreducible unitary representations of simple Lie groups which are either linear or locally isomorphic to SL(2,R).
This is joint work with Jan Frahm (Aarhus), Gestur Olafsson (Baton Rouge) and Vincenzo Morinelli (Rome) 
28/03/23  Seminario  14:30  15:30  1201 Dal Passo  Francesca Oronzio  Università di Roma 
Seminario di Equazioni Differenziali
ADM mass and potential theory
In this talk, we describe some monotonicity formulas holding along the regular level sets of suitable pharmonic functions in asymptotically flat Riemannian 3manifolds with a single end, with or without boundary, having nonnegative scalar curvature. Using such formulas, we obtain some geometric inequalities, including the positive mass inequality and the Riemannian Penrose inequality.

21/03/23  Seminario  16:30  17:30  1201 Dal Passo  Wael Bahsoun  Loughborough  Linear response due to singularities
It is well known that a family of tentlike maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value of the turning point. In this note we prove the following result: if we consider a tentlike family with a cusp at the turning point, we recover the linear response. This is a joint work with Stefano Galatolo. 
17/03/23  Seminario  16:00  17:00  1201 Dal Passo  Paolo SARACCO  Université Libre de Bruxelles 
Algebra & Representation Theory Seminar (ARTS)
"Glimpses from truss theory"
Trusses are like affine rings: as a ring is an abelian group with a compatible multiplication, a truss is a torsor (over an abelian group) with a compatible multiplication. Introduced by Brzeziński in 2017 to unify the classical theory of rings with the modern theory of braces, trusses unexpectedly revealed the existence of a previously uncharted territory, whose exploration is not just leading to fascinating discoveries, but it is also shedding new light on groups and rings themselves. This talk would like to be a brief walk in the world of ternary operations to meet heaps, trusses, their modules and their novel heaps of modules.

17/03/23  Seminario  14:30  15:30  1201 Dal Passo  Antonio IOPPOLO  Università de L'Aquila 
Algebra & Representation Theory Seminar (ARTS)
"A taste of polynomial identities"
A polynomial identity of an algebra A is a polynomial (in noncommuting variables) vanishing under all evaluations in A. Algebras satisfying at least one of these nontrivial relations are called PIalgebras. The first goal of this talk is to show how it is possible to characterize PIalgebras by means of numerical invariants related to their identities. Along the way we will highlight the combinatorial and analytical aspects of the theory, its connection with invariant theory, representation theory and growth problems. In the last part, we will look at some of the latest developments in this area, when it comes to algebras with additional structure. 
15/03/23  Seminario  17:00  18:00  1201 Dal Passo  Yasuyuki Kawahigashi  The University of Tokyo  $alpha$induction for biunitary connections
The tensor functor called alphainduction arises from a Qsystem in a braided unitary fusion category. In the operator algebraic language, it
gives extensions of endomorphism of N to M arising from a subfactor N subset M of finite index and finite depth giving a braided fusion category of endomorpshisms of N. We study this alphainduction for biunitary connections, which give a characterization of finitedimensional
nondegenerate commuting squares. We show that the resulting alphainduced biunitary connections are flat if we have a local Qsystem. 
15/03/23  Seminario  16:00  17:00  1201 Dal Passo  Mizuki Oikawa  The University of Tokyo  New center construction and alphainduction for equivariantly braided tensor categories
alphainduction is known to be a construction of a modular invariant full Qsystem from a chiral Qsystem of a conformal net. In this talk, I would like to introduce the equivariant version of this procedure. Indeed, we need a new construction of tensor categories, the neutral double construction, introduced by the speaker. Moreover, I would like to explain the relationship between the neutral double construction and an equivariant version of the center construction, which is also introduced by the speaker. 
10/03/23  Seminario  16:00  17:00  1201 Dal Passo  Evgeny FEIGIN  HSE (Mosca) & Weizmann Institute of Science (Israel) 
Algebra & Representation Theory Seminar (ARTS)
"Cauchy identities and representation theory"
The celebrated Cauchy identity rewrites a certain infinite product as a sum of products of Schur functions. The identity has a vast number of applications and interpretations; in particular, one can understand the infinite product as the character of polynomial functions on the space of square matrices and the products of Schur functions as characters of tensor products of irreducible gl(n) modules.
The classical Cauchy identity has (at least) three natural generalizations: a nonsymmetric version, a qversion and their mixture. The representation theory of the nonsymmetric Cauchy is governed by the Borel subalgebra, the qCauchy identity is controlled by the representations of the current algebras and the nonsymmetric qCauchy identity has to do with the modules over the Iwahori algebra. We will discuss all these identities and explain the relevant representation theory.
Based on joint works with Anton Khoroshkin, Ievgen Makedonskyi and Daniel Orr. 