11/10/22  Seminario  16:00  17:00  1201 Dal Passo  Gaetano Siciliano  University of Sao Paulo (IMEUSP, Brazil)  Seminario di Equazioni Differenziali
Critical points under the energy constraint
In the talk we discuss the existence of critical points for a family of
abstract and smooth functionals on Banach spaces under the energy constraint.
By means of the LjusternickSchnirelmann theory and the fibering method of Pohozaev
we show, under suitable assumptions, multiplicity results.
The abstract framework is then applied to some partial differential equations depending
on a parameter for which we obtain multiple solutions as well as some bifurcation results.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 
05/10/22  Seminario  16:00  17:00  1201 Dal Passo  Detlev Buchholz  University of Goettingen  Proper condensates and long range order
The usual characterization of BoseEinstein condensates is based on spectral properties of oneparticle density matrices. (OnsagerPenrose criterion). The analysis of their specific properties, such as the occurrence of longrange order between particles and peaks in momentum space densities requires, however, the transition to the thermodynamic limit, where the oneparticle density matrices are no longer defined. In the present talk, we will explain a new criterion of "proper condensation" that allows us to establish the properties of bosonic systems occupying fixed bounded regions. Instead of going to the idealization of an infinite volume, one goes to the limit of arbitrarily large densities in the given region. The resulting concepts of regular and singular wave functions can then be used to study the properties of realistic finite bosonic systems, the occurrence of condensates, and their largedistance behavior, with a precise control of accuracy. 
04/10/22  Seminario  16:00  17:00  1201 Dal Passo  Lei Zhang  University of Florida (US)  Seminario di Equazioni Differenziali
Nonsimple Blowup solutions of singular Liouville equations
The singular Liouville equation is a class of second order elliptic partial differential equations defined in two dimensional spaces:
$$Delta u+ H(x)e^{u}=4pi gamma delta_0 $$
where $H$ is a positive function, $gamma>1$ is a constant and $delta_0$ stands for a singular source placed at the origin. This deceptively simply looking equation has a rich background in geometry, topology and Physics. In particular it interprets the Nirenberg problem in conformal geometry and is the reduction of Toda systems in Lie Algebra, Algebraic Geometry and Gauge Theory. Even if we only focus on the analytical aspects of this equation, it has wonderful and surprising features that attract generations of top mathematicians. The structure of solutions is particular intriguing when $gamma$ is a positive integer. In this talk I will report recent joint works with D’Aprile and Wei that give answers to some important issues of this equation. I will report the most recent results and consequences that our results may lead to.
Note:
1) This seminar will be held in presence, although the speaker will be connected remotely via MS Teams. The MS Teams link might be provided upon request to the organizers.
2) This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006.

30/09/22  Seminario  16:00  17:00  1201 Dal Passo  Apoorva KHARE  Indian Institute of Science 
Algebra & Representation Theory Seminar (ARTS)
"Higherorder theory for highest weight modules: positive weightformulas,
resolutions and characters for higher order Verma modules"
We introduce higher order Verma modules over a KacMoody algebra g (one may assume this to be sl_{n} throughout the talk, without sacrificing novelty). Using these, we present positive formulas  without cancellations  for the weights of arbitrary highest weight gmodules V. The key ingredient is that of "higher order holes" in the weights, which we introduce and explain. 
30/09/22  Seminario  14:30  15:30  1201 Dal Passo  Daniele VALERI  “Sapienza” Università di Roma 
Algebra & Representation Theory Seminar (ARTS)
"Integrable triples in simple Lie algebras"
We define integrable triples in simple Lie algebras and classify them, up to equivalence. The classification is used to show that all (but few exceptions) classical affine Walgebras W(g,f ), where g is a simple Lie algebra and f a nilpotent element, admit an integrable hierarchy of biHamiltonian PDEs. This integrable hierarchy generalizes the DrinfeldSokolov hierarchy which is obtained when f is the sum of negative simple root vectors. 
28/09/22  Seminario  16:00  17:00  1201 Dal Passo  Jean Dolbeaut  Université Paris Dauphine  PSL  Seminario di Equazioni Differenziali Stability estimates in some classical functional inequalities
In some classical functional inequalities, optimal functions and optimal constants are known. The next question is to understand which distance to the set of the optimal functions is controlled by the deficit, that is, the difference of the two sides of the inequality written with the optimal constant. In 1991, an answer was given by Bianchi and Egnell in the case of a Sobolev inequality on the Euclidean space, using compactness methods. A major issue with the method is that the new constant is so far unknown. The purpose of this lecture is to review some examples of related functional inequalities in which one can at least give an estimate of the stability constant.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006

21/09/22  Seminario  16:15  17:45  1201 Dal Passo  Fausto Di Biase  Università  On the differentiation of integrals in measure spaces along filters
In 1936, R. de Possel observed that, in the general setting of a measure space with no metric structure, certain phenomena, relative to the differentiation of integrals, which are familiar in the Euclidean setting precisely because of the presence of a metric, are devoid of actual meaning.
In this work, in collaboration with Steven G. Krantz, we show that, in order to clarify these difficulties,it is useful to adopt the language of filters, which has been introduced by H. Cartan just a year after De Possel's contribution. 
21/09/22  Seminario  15:00  16:00  1201 Dal Passo  KarlHenning Rehren  University of Göttingen  LV formalism in perturbative AQFT
pAQFT defines nets of local algebras by a limiting construction with
relative Smatrices. The latter can be constructed perturbatively from an interaction
Lagrangian. In many instances, the construction can be improved by adding a total
derivative to the interaction Lagrangian (which would have no effect in classical
field theory).
The LV formalism controls whether and how this modification affects the
(relative) Smatrices and provides a tool to identify the local observables of the
model. 
07/07/22  Seminario  14:30  15:30  1101 D'Antoni  Tommaso de Fernex  University of Utah (USA)  ALGEBRAIC GEOMETRY SEMINAR
Local geometry of spaces of arcs
The arc space of a variety is an infinite dimensional scheme whose geometric structure captures, in a way that is not yet fully understood, certain features of the singularities of the variety. Focusing on its local rings and invariants of these rings such as embedding dimension and codimension, we explore the local structure of arc spaces. Our main tools rely on a formula for the sheaf of differentials on arc spaces and some recent finiteness results on the fibers of the map induced at the level of arc spaces from an arbitrary morphism of schemes over a field. The talk is based on joint work with Christopher Chiu and Roi Docampo.

30/06/22  Seminario  15:00  16:30  1201 Dal Passo  H. Bostelmann and D. Cadamuro  H.B University of York, D.C. University of Leipzig 
Joint seminar
Fermionic integrable models and graded Borchers triples
The operatoralgebraic construction of 1+1dimensional integrable quantum field theories has received substantial attention over the past decade. These models are characterized by their asymptotic particle spectrum and their twoparticle scattering matrix; so far, those particles have been bosonic. By contrast, we consider the case of asymptotic fermions. Abstractly, they arise from a grading of the underlying operator algebraic structures (Borchers triples); more concretely, one replaces the generating quantum fields fulfilling wedgelocal commutation relations with a variant fulfilling anticommutation relations. Many of the technical methods required can be carried over from the bosonic case; most importantly, existing results on the technically hard part of the construction (i.e., establishing the modular nuclearity condition) do not require modification. Thus we are lead to a new family of rigorously constructed quantum field theories which are physically distinct from the bosonic case (with a different net of local algebras). HaagRuelle scattering theory confirms that they indeed describe fermions. Also, their local operators fulfill a modified version of the form factor axioms, consistent with the physics literature. 