## Notiziario Scientifico

**Notiziario dei seminari di carattere matematico**

a cura del Dipartimento di Matematica

*Guido Castelnuovo*, Sapienza Università di Roma

Settimana dal 26-09-2022 al 02-10-2022

**Lunedì 26 settembre 2022**

Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma

seminario

Apoorva Khare (Indian Institute of Science)
*Higher order Verma modules, and a positive formula for all highest weight modules*

We study weights of highest weight modules \(V\) over a Kac-Moody algebra \(\mathfrak{g}\) (one may assume this to be \(\mathfrak{sl}_n\) throughout the talk, without sacrificing novelty). We will begin with several positive weight-formulas for arbitrary non-integrable simple modules, and mention the equivalence of several "first order" data that helps prove these formulas. We then discuss the notion of "higher order holes" in the weights, and use these to present two positive weight-formulas for arbitrary modules \(V\). One of these is in terms of "higher order Verma modules", and we will end with BGG resolutions and Weyl-Kac type character formulas, for these modules in certain cases. (Joint with G.V.K. Teja, and with Gurbir Dhillon.)

**Martedì 27 settembre 2022**

Ore 10:00, 1B1, Dipartimento SBAI, Sapienza Università di Roma

PhD Course

Masahiro Yamamoto (The University of Tokyo - INdAM Visiting Professor)
*Inverse problems and time-fractional partial differential equations 4*

We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems. The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications. For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).

Per informazioni, rivolgersi a: * francesco.petitta@uniroma1.it*

**Martedì 27 settembre 2022**

aula Marconi CNR, Roma

Convegno
*ROUND MEANFIELD crowd-opinion-cells (meanfield between France and Italy)*

IRL LYSM "Ypatia Laboratory of Mathematical Sciences"

Programma:

- 9:30
*caffè di benvenuto* - 10:30 Pierre Degond,
*Mean-field limit of systems of topologically interacting particles* - 11:30 Emiliano Cristiani,
*A-round mean-field games in pedestrian dynamics* - 14:30 David Poyato,
*Mean field limit of non-exchangeable multi-agent systems* - 16:00 Marta Menci and Roberto Natalini,
*Mean-Field limit for hybrid models with chemotaxis: theory and numerics*

**Mercoledì 28 settembre 2022**

aula Marconi CNR, Roma

Convegno
*ROUND MEANFIELD crowd-opinion-cells (meanfield between France and Italy)*

IRL LYSM "Ypatia Laboratory of Mathematical Sciences"

Programma:

- 9:30 Giacomo Borghi and Lorenzo Pareschi,
*On stochastic particle systems in global optimization* - 11:00 Thierry Paul and Emmanuel Trelat,
*Considerations on micro/macroscopic scale equations* - 12:20 Marco Di Francesco,
*The "follow-the-leader" approximation of one-dimensional nonlinear transport equations*

**Mercoledì 28 settembre 2022**

Ore 10:00, 1B1, Dipartimento SBAI, Sapienza Università di Roma

PhD Course

Masahiro Yamamoto (The University of Tokyo - INdAM Visiting Professor)
* Inverse problems and time-fractional partial differential equations 5*

We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems. The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications. For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).

Per informazioni, rivolgersi a: * francesco.petitta@uniroma1.it*

**Mercoledì 28 settembre 2022**

Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma

seminario di Algebra e Geometria

Hironori Shiga (Chiba University)
*K3 hypergeometric modular forms*

In 1977 at the Cortona Conference on several complex variables the speaker proposed to make studies on “the K3 modular function”. That is the explicit expression of the inverse of the period map for a family of K3 surfaces. In this talk, we give a short summary of our study on this direction for 45 years. A recent result is based on the studies by Prof. Salvati-Manni and others. You can see the outline of the talk by two papers by A. Nagano and H. Shiga on Transformation Groups (2022) and Math. Nachrichten (2022).

Per informazioni, rivolgersi a: * diverio@mat.uniroma1.it*

**Mercoledì 28 settembre 2022**

Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"

Seminario di Equazioni Differenziali

Jean Dolbeaut ( Université Paris Dauphine - PSL)
*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

Per informazioni, rivolgersi a: * sorrentino@mat.uniroma2.it*

**Giovedì 29 settembre 2022**

aula Marconi CNR, Roma

Convegno
*ROUND MEANFIELD crowd-opinion-cells (meanfield between France and Italy)*

IRL LYSM "Ypatia Laboratory of Mathematical Sciences"

Programma:

- 9:30 Nathalie Ayi and Nastassia Pouradier Duteil,
*Continuum limits of collective dynamics with time-varying weights* - 11:30 Stefano Rossi,
*Mean-field limit for particle systems with topological interactions* - 14:30 Benoît Bonnet-Weill,
*Some results related to consensus formation in graphon dynamics* - 16:00 Mario Pulvirenti,
*Propagation of chaos for a stochastic system modelling epidemics via a coupling approach* - 17:00
*Fin*

**Giovedì 29 settembre 2022**

Accademia Nazionale dei Lincei, Palazzo Corsini, Via della Lungara 10, Roma

Conferenza
*Partial Differential Equations and related Function Spaces*

Programma:

- 9:00
*Welcome address* - 9:10 Denis BONHEURE (Université Libre de Bruxelles):
*Classification of radial blow-up at the first critical exponent for the Lin-Ni-Takagi equation in a ball* - 10:00 Mathias SCHAEFFNER (Technische Universität Dortmund):
*Regularity for nonuniformly elliptic equations and applications in homogenization* - 10:50
*Intervallo* - 11:10 Angela ALBERICO (Istituto per le Applicazioni del Calcolo “M.Picone”, CNR, sede di Napoli):
*Fractional Orlicz-Sobolev Embeddings* - 12:00 Xavier Ros OTON (Universitat de Barcelona):
*The singular set in the Stefan problem* - 14:30 Jean DOLBEAULT (CEREMADE, Université Paris Dauphine, Paris):
*Stability estimates in critical functional inequalities* - 15:20 Cristiana DE FILIPPIS (Università di Parma):
*Schauder estimates for any taste* - 16:10
*Intervallo* - 16:30 Cristina TROMBETTI (Università di Napoli “Federico II”):
*A symmetry result in a free boundary problem* - 17:20 Giulio CIRAOLO (Università di Milano):
*Classification results for critical p-Laplace equations*

**Giovedì 29 settembre 2022**

Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre

Seminario di Geometria

Luca Schaffler (Roma Tre)
*Unimodal singularities and boundary divisors in the KSBA moduli of a class of Horikawa surfaces*

Smooth minimal surfaces of general type with \(K^2=1\), \(p_g=2\), and \(q=0\) constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space \(\mathbf{M}\) of their canonical models admits a modular compactification \(\overline{\mathbf{M}}\) via the minimal model program. We describe eight new irreducible boundary divisors in such compactification parametrizing reducible stable surfaces. Additionally, we study the relation with the GIT compactification of \(\mathbf{M}\) and the Hodge theory of the degenerate surfaces that the eight divisors parametrize. This is joint work with Patricio Gallardo, Gregory Pearlstein, and Zheng Zhang.

Per informazioni, rivolgersi a: * amos.turchet@uniroma3.it*

**Venerdì 30 settembre 2022**

Accademia Nazionale dei Lincei, Palazzo Corsini, Via della Lungara 10, Roma

Conferenza
*Partial Differential Equations and related Function Spaces*

Programma:

- 9:00 Enno LENZMANN (Universität Basel):
*On uniqueness for the prescribed Q-curvature problem in one dimension* - 9:50 Tobias KOENIG (Institut de Mathématiques de Jussieu, Paris):
*Multibubble blow-up analysis for the Brezis-Nirenberg problem in three dimensions* - 10:40
*Intervallo* - 11:10 Iwona CHLEBICKA (University of Warsaw):
*Absence of Lavrentiev's phenomenon in anisotropic spaces* - 12:00 Petru MIRONESCU (Université Lyon 1):
*Sobolev maps to manifolds*

**Venerdì 30 settembre 2022**

Ore 14:30, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"

Algebra and Representation Theory Seminar

Daniele Valeri (Sapienza Università di Roma)
*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 W-algebras W(g , f ), where g is a simple Lie algebra and f a nilpotent element, admit an integrable hierarchy of bi-Hamiltonian PDEs. This integrable hierarchy generalizes the Drinfeld-Sokolov hierarchy which is obtained when f is the sum of negative simple root vectors.

Per informazioni, rivolgersi a: * lanini@mat.uniroma2.it*

**Venerdì 30 settembre 2022**

Ore 16:00, Aula "Roberta Dal Passo", Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"

Algebra and Representation Theory Seminar

Apoorva Khare (Indian Institute of Science)
*Higher-order theory for highest weight modules: positive weight-formulas, and resolutions and characters for higher order Verma modules*

We introduce higher order Verma modules over a Kac-Moody algebra g (one may assume this to be sln throughout the talk, without sacrificing novelty). Using these, we present positive formulas (without cancellations) for the weights of arbitrary highest weight g-modules V. The key ingredient is that of "higher order holes" in the weights, which we introduce and explain.

Per informazioni, rivolgersi a: * lanini@mat.uniroma2.it*

Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente
mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana
interessata. Le comunicazioni pervenute in ritardo saranno ignorate.
Per informazioni, rivolgersi all'indirizzo di posta elettronica
*seminari@mat.uniroma1.it*.

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