29/07/24  Seminario  14:30  15:30  1201 Dal Passo  Marianne Déglise  ENS Paris Saclay 
ARTS Extra
Combinatorial study of coefficients of the decomposition theorem for universal linear degenerations
We study a geometric/combinatorial characterisation of supports for linear degenerations of flag varieties in an attempt to determine the coefficients of the decomposition theorem. We show that it behaves correctly when applying the operation suspension, and obtain positive results in the PBWlocus. 
10/07/24  Seminario  16:00  17:00  1201 Dal Passo  Leonardo Sangaletti  University of Leipzig 
Operator Algebras Seminar
An L4 quantum energy inequality for the thermal sector
Energy density and its positivity properties represent a fundamental subject in classical and quantum physics. In this talk, we will investigate this topic in the thermal representation of a free massive quantum scalar field. After a brief review of the fundamental mathematical tools at the base of this work, we will construct the GNS representation of our QFT induced by a state at thermal equilibrium (KMS). Therein, we will identify the generator of the time evolution and its spatial density. The symmetry between the "particles" and "holes" makes evident the impossibility for a lower bound for the expectation value of the energy density in this representation. In order to tackle this problem, we will investigate and extend some results of modular theory and noncommutative Lp spaces. In this way, we will obtain a general result concerning the expectation value of operators affiliated to a von Neumann algebra. Finally, the proven results will be applied to our setting to derive an L4 state dependent nontrivial QEI.
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0 
09/07/24  Seminario  14:30  15:30  1201 Dal Passo  Maria Michaela Porzio  Sapienza Università di Roma  Seminario di Equazioni Differenziali
The role of the data on the regularity of the solutions to some non singular parabolic equations
In this talk we describe the influence of the initial data and the forcing terms on the regularity of the solutions to a class of evolution equations including the heat equation, linear and semilinear parabolic equations, together with the nonlinear pLaplacian equation. We focus our study mainly on the regularity (in terms of belonging to appropriate Lebesgue spaces) of the gradient of the solutions.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

05/07/24  Seminario  16:00  17:00  1201 Dal Passo  Ping Xu  U Penn State 
ARTS Midsummer Day Edition
Derived differentiable manifolds
One of the main motivations behind derived differential geometry is to deal with singularities arising from zero loci or intersections of submanifolds. Both cases can be considered as fiber products of manifolds which may not be smooth in classical differential geometry. Thus, we need to extend the category of differentiable manifolds to a larger category in which one can talk about "homotopy fiber products". In this talk, we will discuss a solution to this problem in terms of dg manifolds. The talk is mainly based on a joint work with Kai Behrend and HsuanYi Liao.

05/07/24  Seminario  14:30  15:30  1201 Dal Passo  Mathieu Stiénon  U Penn State 
ARTS Midsummer Day Edition
Formal geometry of groupoids
I will give a brief survey of the formal geometry of groupoids. 
03/07/24  Seminario  16:00  17:00  1201 Dal Passo  Vedran Sohinger  University of Warwick 
Operator Algebras and Mathematical Physics Seminar
Invariant measures as probabilistic tools in the analysis of nonlinear ODEs and PDEs
Gibbs measures for nonlinear dispersive PDEs have been used as
a fundamental tool in the study of lowregularity almost sure
wellposedness of the associated Cauchy problem following the pioneering
work of Bourgain in the 1990s. In the first part of the talk, we will
discuss the connection of Gibbs measures with the KuboMartinSchwinger
(KMS) condition. The latter is a property characterizing equilibrium
measures of the Liouville equation. In particular, we show that Gibbs
measures are the unique KMS equilibrium states for a wide class of
nonlinear Hamiltonian PDEs. Our proof is based on Malliavin calculus and
GrossSobolev spaces. This is joint work with Zied Ammari.
In the second part of the talk, we will explain a general principle that
allows us to obtain almost sure global solutions for Hamiltonian PDEs
provided that one has a stationary probability measure. In this context,
stationarity refers to a solution of the associated Liouville equation.
This more general notion replaces the invariance from before. The second
part of the talk is joint work with Zied Ammari and Shahnaz Farhat.
Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0

21/06/24  Seminario  14:30  15:30  1101 D'Antoni  Adam Doron  Haifa University 
Operator Algebras Seminar
Arveson's hyperrigidity conjecture is false
A classical result in approximation theory due to Korovkin asserts that a sequence of positive unital maps on C([0,1]) converges pointwise to the identity if they merely converge to the identity on the functions 1,x,x^2. This result was later generalized by Saskin, who showed that convergence to the identity on a generating function system implies convergence to the identity everywhere if and only if the system has full Choquet boundary.
Arveson's last open conjecture in his seminal work on noncommutative boundary theory predicts that a noncommutative analogue of Saskin's result holds. We refute Arveson's conjecture with an elementary counterexample. All notions will be explained during the talk.
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0

19/06/24  Seminario  16:00  17:00  1201 Dal Passo  Nicola Pinamonti  University of Genova 
Operator Algebras Seminar
Secular growths and their relation to Equilibrium states in perturbative Quantum Field Theories
During this talk we discuss the emergence of secular growths in the correlation functions of interacting quantum field theories when treated with perturbation methods. It is known in the literature that these effects are present if the interaction Lagrangian density changes adiabatically in a finite interval of time. If this happens, the perturbative approach cannot furnish reliable results in the evaluation of scattering amplitudes or in the evaluation of various expectation values.
We show, during this talk, that these effects can be avoided for adiabatically switchedon interactions, if the spatial support of the interaction is compact and if the background state is suitably chosen. In particular, this is the case when the background state is chosen to be at equilibrium and when thermalisation occurs at late time. The same result holds also if the background state is only invariant under time translation or if the explicit time dependence is not too strong, in a precise sense which will be discussed in the talk.
Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/homepage?authuser=0 
17/06/24  Seminario  15:00  16:00  1201 Dal Passo  Tan BuiThanh  University of Texas at Austin  Learn2Solve: A Deep Learning Framework for RealTime Solutions of Forward, Inverse, and UQ Problems
Digital models (DMs) are designed to be replicas of systems and processes. At the core of a digital model (DM) is a physical/mathematical model that captures the behavior of the real system across temporal and spatial scales. One of the key roles of DMs is enabling “what if” scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, to calibrate parameters to match the actual process and to quantify the uncertainties. In this talk, we will present various (faster than) realtime Scientific Deep Learning (SciDL) approaches for forward, inverse, and UQ problems. Both theoretical and numerical results for various problems including transport, heat, Burgers, (transonic and supersonic) Euler, and NavierStokes equations will be presented. 
12/06/24  Seminario  16:00  17:00  1201 Dal Passo  Ko Sanders  FAU ErlangenNuremberg 
Operator Algebras Seminar
On distributions of positive type and applications to QFT
When quantum fields are represented as operators on a Hilbert space, their twopoint distributions naturally give rise to distributions of positive type. A number of basic results on such distributions, especially for translation invariant twopoint distributions, have been known for a long time. E.g., the BochnerSchwartz Theorem fully characterises translation invariant distributions of positive type. In this talk I will present two apparently new results on distributions of positive type, one pertaining to pointwise products and the other to methods for cutting and pasting. Both results were motivated by physical questions and extend the toolbox of theoretical physics. I will present the results in a general mathematical context before discussing their applications to quantum energy inequalities and to separable states for a free scalar QFT. 