## Bollettino settimanale

### Settimana 04/12/2023 - 07/12/2023

__Seminari__

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Università degli Studi di Roma Tor Vergata

Dipartimento di Matematica

Geometry Seminar

**Date:** 05th december 2023

**Schedule:** 14:30 - Rome Time

**Where:** Conference Room 1101 "C. D'Antoni"

**Title:** "Stability conditions for varieties "

**Speaker**: Ruadhaí Dervan University of Glasgow

**Abstract**:
Stability conditions in algebraic geometry are used to construct moduli spaces. Experience from the theory of vector bundles (and coherent sheaves)
suggests it is useful to have many stability conditions, so that one can geometrically understand the birational behaviour of resulting moduli spaces by
varying the stability condition. Motivated by this, I will describe a mostly conjectural analogous story for projective varieties with an ample line bundle. Here the classical notion of stability is K-stability, which aims to construct higher dimensional analogues of the moduli space of stable curves, and the main point will be to introduce variants of K-stability defined using extra topological choices. The main results will link these new stability conditions with differential geometry,
through the solvability of certain geometric PDEs, and I will try to explain how these links come about and what the general picture should be.

**Note**: the seminar are part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the Prin 2022 Moduli Spaces and Birational Geometry.

**Organizing Committee:**

Giulio Codogni (mail to contact)

Guido Maria Lido (mail to contact)

**Further Info: ** Click here for Geometry Page

**Streaming Link (MS Teams): ** This seminar will be held: mix mode in person and streaming

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Università degli Studi di Roma Tor Vergata

Dipartimento di Matematica

Differential Equations Seminar

**Date:** 5th December 2023

**Schedule:** 16:00 - Rome Time

**Where:** Conference Room 1201 "R. Dal Passo"

**Title:** " The capillary Minkowski problem "

**Speaker**: Liangjun WengUniversità degli Studi di Roma Tor Vergata

**Abstract**:
The classical Minkowski problem asks for necessary and sufficient conditions on a non-negative
Borel measure on the unit sphere to be the surface area measure of a convex body. In a smooth setting,
it reduces to the study of a Monge-Ampere equation on the unit sphere. This problem has been completely
solved through the seminal works of Nirenberg, Pogorelov, Cheng-Yau, etc. In this talk, a new Minkowski-type problem will be introduced.
The problem asks for the existence of a convex hypersurface with prescribed Gauss-Kronecker curvature and capillary boundary supported on an obstacle, which can be deduced as
a Monge-Ampere equation with a Robin (or Neumann) boundary value condition on the spherical cap.
Then obtain a necessary and sufficient condition for solving this problem.

**Note**: the seminar are part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

**Organizing Committee:**

Alfonso Sorrentino (mail to contact)

Riccardo Molle (mail to contact)

**Further Info: ** Click here for Differential Equations Semina Page

**Streaming Link (MS Teams): ** This seminar will be held in person

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Università degli Studi Roma Tor Vergata

Dipartimento di Matematica

Operator Algebras Seminar

**Date:** 6th December 2023

**Schedule:** 16:00 - Rome Time

**Where:** Conference Room 1201 "R. Dal Passo"

**Title:** " Exact measurement schemes for local observables and the preparation of physical local product states "

**Speaker**: Christopher J. Fewster (University of York)

**Abstract**:
For a long time, quantum field theory (QFT) lacked a clear and consistent measurement framework,
a gap that was described as "a major scandal in the foundations of quantum physics" [1].
I will review the recent framework put forward by Verch and myself [2],
which is consistent with relativity in flat and curved spacetimes and has resolved the long-standing problem of "impossible measurements" put forward by Sorkin [3].
The central idea in this framework is that the "system" QFT of interest is measured by coupling it to a "probe" QFT, in which the system, probe, and their coupled variant,
all obey axioms of AQFT in curved spacetime. It has been shown that every local observable of the free scalar field has an asymptotic measurement scheme, i.e.,
can be measured to arbitrary accuracy by a sequence of probes and couplings [4]. I will describe new results that (a) show that there are exact measurement schemes
for all local observables in a class of free theories, (b) provide a protocol for the construction of Hadamard local product states in curved spacetime.
The latter is complementary to a recent existence result of Sanders [5].

*[1] Earman, J., and Valente, G. Relativistic Causality in Algebraic Quantum Field Theory, International Studies in the Philosophy of Science, 28:1, 1-48, (2014)
[2] Fewster, C.J., Verch, R. Quantum Fields and Local Measurements. Commun. Math. Phys. 378, 851–889 (2020).
[3] Bostelmann, H., Fewster, C.J., and Ruep, M.H. Impossible measurements require impossible apparatus Phys. Rev. D 103, 025017 (2021)
[4] Fewster, C.J., Jubb, I. & Ruep, M.H. Asymptotic Measurement Schemes for Every Observable of a Quantum Field Theory. Ann. Henri Poincaré 24, 1137–1184 (2023).
[5] Sanders, K. On separable states in relativistic quantum field theory, J. Phys. A: Math. Theor. 56 505201 (2023)
*

**Note**: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

**Organizing Committee:**

Vincenzo Morinelli (mail to contact)

Roberto Longo (mail to contact)

Daniele Guido (mail to contact)

Giuseppe Ruzzi (mail to contact)

**Further Info: ** Click here for Operator Algebras Page

**Streaming Link (MS Teams): ** This seminar will be held in person

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Università degli Studi Roma Tor Vergata

Dipartimento di Matematica

Rome Centre on Mathematics for Modelling and Data ScienceS

**Date:** 7th December 2023

**Schedule:** 15:00 - Rome Time

**Where:** Conference Room 1201 "R. Dal Passo"

**Title:** " Mixing of the Averaging process on graphs "

**Speaker**: Matteo Quattropani (La Sapienza)

**Abstract**:
The Averaging process (a.k.a. repeated averages) is a mass redistribution model over the vertex set of a graph. Given a graph G,
the process starts with a non-negative mass associated to each vertex. The edges of G are equipped with Poissonian clocks:
when an edge rings, the masses at the two extremes of the edge are equally redistributed on these two vertices.
Clearly, as time grows to infinity, the state of the system will converge (in some sense) to a flat configuration in which all
the vertices have the same mass. This very simple process has been introduced to the probabilistic community by Aldous and Lanoue in 2012.
However, up to few years ago, there was no graph for which sharp quantitative results on the time needed to reach equilibrium were available.
Indeed, the analysis of this process requires different tools compared to the classical Markov chain framework, and even in the case of seemingly
straightforward geometries—such as the complete graph or the 1-d torus—it can be handled only by means of non trivial probabilistic and functional
analytic techniques. During the talk, I’ll try to give a broad overview of the problem and of its difficulties, and I'll present the few examples
that have been completely settled.

Based on joint work with P. Caputo (Università Roma Tre) and F. Sau (Università di Trieste)

**Organizing Committee:**

Domenico Marinucci (mail to contact)

Michele Salvi (mail to contact)

Stefano Vigogna (mail to contact)

**Further Info: ** Click here for Operator Algebras Page

**Streaming Link (MS Teams): ** Click Here for streaming - This seminar will be held in mix mode: in person and streaming

__Eventi__

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Università degli Studi di Roma "Tor Vergata"

Dipartimento di Matematica

**Corso di Dottorato**

Nonlinear analysis for nonlocal elliptic problems (Advanced topics in Analysis)

**Period:** Period: 23-11-13 - 23.12.07

**Schedule:**

Period | Time |
---|---|

23.11.13 | h: 11:00 / 13:00 Mercuri |

23.11.15 | h: 09:00 / 11:00 Molle |

23.11.17 | h: 15:00 / 17:00 Molle |

23.11.20 | h: 14:00 / 16:00 Molle |

23.11.22 | h: 09:00 / 11:00 Molle |

23.11.24 | h: 15:00 / 17:00 Molle |

23.11.27 | h: 14:00 / 16:00 Mercuri |

23.11.30 | h: 15:00 / 17:00 Mercuri |

23.12.04 | h: 14:00 / 16:00 Mercuri |

23.12.07 | h: 15:00 / 17:00 Mercuri |

**Where:** see the info on Further Info

**Organizing Committee:** Riccardo Molle (Contatto E-Mail)

**Speaker:** Carlo Mercuri Dipartimento di Scienze Fisiche, Informatiche e Matematiche - Università di Modena e Reggio Emilia

**Title:** Nonlinear analysis for nonlocal elliptic problems (Advanced topics in Analysis)

**Abstract: **

This course introduces the language, concepts, and methods for nonlinear PDEs in unbounded domains.
We will review classical approaches mainly based on the direct method of the Calculus of
Variations, to study some classes of nonlinear elliptic PDEs on R^N. We will mainly consider two
`toy problems': the Choquard equation, and the nonlinear Schrödinger-Poisson-Slater equation. Although these
equations share some features, such as non-linearity and nonlocality, they require a separate analysis.
Emphasis will be given to these equations' variational formulation, functional setting, and relevant
compactness properties.
Known results and suggestions for new research projects in this area will be discussed.
The first part of the course will be devoted to some basic concepts of the variational approach to
nonlinear analysis, based on extending Calculus to infinite dimensional Banach spaces. Some
elementary tools in critical point theory will be introduced, such as the Lagrange multipliers rule and
the Mountain Pass Theorem. These can help identify nontrivial solutions to PDEs characterized by
'energy levels'. Some exercises will be discussed as a preparation for the second part of the course.
Students who already know these tools can skip this part and attend directly the second part of the
course.

**Further Info:** Click here

**Streaming Link (MS Teams):** in presence