Bollettino settimanale


Pagina d'informazione di seminari ed eventi scientifici che avranno luogo settimanalmente per lo più in area romana. Per la pubblicazione rivolgersi a Giorgio Chiarati che ne cura la gestione. Per consultare la pagina di tutti i seminari di Dipartimento Click here.

 

Settimana 16/05/2022 - 20/05/2022

 


 

Seminari

European Mathematical Society (E.M.S.)
Women in Math Committee (WiM)

 


EMS/WiM DAY within the initiative of "May 12th" in memory of Maryam Mirzakhani

Date: Friday May 20, 2022

The Women in Math Committee (WiM) of the European Mathematical Society is organising an event called "EMS/WiM Day" within the initiative of "May 12th", a celebration of women in Mathematics in memory of Maryam Mirzakhani. The event consists of scientific talks (at the level of a Colloquium talk) of two distinguished speakers, which will take place online on Friday, 20 May 2022 with the following

Schedule:
14:45 CEST Welcome
15:00 CEST Tara Brendle (Glasgow University, UK)
16:00 CEST Tere M. Seara (UPC, Barcelona, Spain)
Any interested person may attend at: Zoom Link
Passcode: 216273 (more details at the end of this message)

Title: "The titles and abstracts of the talks are given below."
Organizing EMS Committee: Shiri Artstein, Alessandra Celletti, Maria del Mar Gonzalez, Mikaela Iacobelli, Stanislava Kanas, Marjeta Kramar Fijavz, Isabel Labouriau, Pablo Mira, Jiri Rakosnik, Elena Resmerita, Anne Taormina.


Speaker: Tara Brendle (Glasgow University, UK)
Title: "Symmetries of manifolds"

Abstract: Riemann introduced manifolds in the mid-19th century as a mechanism for understanding n-dimensional space. Landmark achievements in mathematics since then include the classification of 2-manifolds in the early 20th century as well as the more recent (though more complicated) classification of 3-manifolds completed by Perelman. However, the story does not end with classification: there is a rich theory of symmetries of manifolds, encoded in their mapping class groups. In this talk we will explore some aspects of mapping class groups in dimensions 2 and 3, with a focus on illustrative examples.


Speaker: Tere M. Seara (UPC, Barcelona, Spain)
Title: "Arnold diffusion: an overview and recent results "

Abstract: In this talk I will talk about the phenomenon known as Arnold diffusion. Equivalently we will show the mechanism that creates big effects after applying arbitrarily small forces for a sufficiently large time. In the language of Hamiltonian Systems, we will consider small periodic in time perturbations of an integrable system. It is known that the energy is preserved in an integrable system, as well as other quantities known as actions. We will show that an arbitrarily small perturbation can create big increments in the energy (and in the actions) and we will explore the dynamic mechanism that is behind this phenomenon.

Further Info: Download the Poster - Click here
Streaming Link for join the webinar: Zoom Link
Passcode: 216273
Connection details for the Zoom webinar.
When: May 20, 2022 1:45 PM Lisbon (14:45 CEST)
Topic: EMS Women in Mathematics Day


Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 


GEOMETRY SEMINAR

Date: Tuesday May 17, 2022
Schedule: 14:30 Rome Time
Where: Room 1201 "R. Dal Passo"
Speaker: Gregory Sankaran (University of Bath)
Title: "(Uni)rationality of moduli of abelian varieties "

Abstract: With one partial exception, the birational type of the moduli space of principally polarised complex abelian g-folds is now known, and there are also results for related spaces such as Prym moduli spaces, universal families, non-principal polarisation and others. In general such spaces are of general type for large values of the parameters (g, degree etc.) and at least uniruled for small values. A few of the moduli spaces are known to be rational. In this talk I shall start to address questions of rationality and unirationality for these spaces over non-closed fields, usually the field of rational numbers. Little seems to be known but I hope to give some answers in simple cases, and to describe some consequences that follow or would follow from such results.

This talk is part of the activity of the M.I.U.R. Excellence Department Project MATH@TOV C.U.P.: E83C18000100006.

Organizing Committee: Giulio Codogni (mail to), Guido Maria Lido (mail to), Roberto Fringuelli (mail to), Claudio Onorati (mail to).
Further Info: Click here
Streaming Link (MS Teams):


Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 


COMPLEX ANALYSIS SEMINAR

Date: Tuesday May 17, 2022
Schedule: 16:00 Rome Time
Where: Room 1101 "D'ANTONI"
Speaker: Simone Diverio (Università La Sapienza di Roma)
Title: "Sviluppi recenti sulla congettura di Lang: quozienti di domini limitati"

Abstract: La congettura di Lang (1986) caratterizza le varietà complesse proiettive (o, più generalmente, Kähler compatte) iperboliche nel senso di Kobayashi come quelle di tipo generale assieme a tutte le loro sottovarietà. Lungi dall’essere dimostrata al momento, la congettura è però nota in una serie di casi paradigmatici ancorché particolari. Ci concentreremo in particolare su una direzione della congettura, spiegando come sia possibile verificare ad esempio che un quoziente libero e compatto di un dominio limitato dello spazio affine complesso abbia tutte sottovarietà di tipo generale (lavoro in collaborazione con S. Boucksom). Tempo permettendo, descriveremo alcune variazioni sul tema, considerando tipi di quozienti più generali: non più necessariamente lisci, né compatti (lavoro in collaborazione con B. Cadorel e H. Guenancia).

Organizing Committee: Leandro Arosio (mail to) - Filippo Bracci (mail to)
Further Info: Click here
Streaming Link (MS Teams): Only in presence


Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 


ALGEBRA AND REPRESENTATION THEORY SEMINAR (A.R.T.S.)

Date: Friday, May 20th, 2022
Schedule: 14:30 Rome Time
Where: Room 1201 "Roberta Dal Passo"
Speaker: Fabio GAVARINI (Università di Roma "Tor Vergata")
Title: "Multiparameter quantum groups: a unifying approach"

Abstract: The original quantum groups - in particular, quantized universal enveloping algebras, in short QUEA's - have been introduced as depending on just one "continuous" parameter. Later on, multiparameter quantum groups - in particular, multiparameter QUEA's - have been introduced in differente ways, with the new, "discrete" parameters either affecting the coalgebra structure or the algebra structure (while leaving the dual structure unchanged). Both cases can be realized as special type deformations - namely, either by twist, or by 2-cocycle deformation - of Drinfeld's celebrated QUEA Uh(g). In this talk I will introduce a new, far-reaching family of multiparameter QUEA's that encompasses and generalizes the previous ones, while also being stable with respect to both deformation by twists and deformations by cocycles. Taking semiclassical limits, these new multiparameter QUEA's give rise to a new family of multiparameter Lie bialgebras, that in turn is stable under both by twist and deformations by 2-cocycles (in the Lie bialgebraic sense).
This is a joint work with Gastón Andrés García - cf. arXiv:2203.11023 (2022).

Organizing Committee: Fabio Gavarini mail to) - Martina Lanini (mail to)
Further Info: Click here
Streaming Link (MS Teams): Click here


Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 


ALGEBRA AND REPRESENTATION THEORY SEMINAR (A.R.T.S.)

Date: Friday, May 20th, 2022
Schedule: 16:30 Rome Time
Where: Room 1201 "Roberta Dal Passo"
Speaker: Iain GORDON (University of Edinburgh)
Title: "Gaudin algebras, RSK and Calogero-Moser cells in type A"

Abstract: A few years ago, Bonnafé-Rouquier defined 'Calogero-Moser cells' through the representation theory of rational Cherednik algebras. These cells partition the elements of a complex reflection group G, but are currently difficult to calculate except in small rank examples. In the special case when G is a finite Coxeter group, the cells are conjectured to be the same as Kazhdan-Lusztig cells. In other words, conjecturally 'Calogero-Moser cells' generalise Kazhdan-Lusztig cell theory from Coxeter groups to complex reflection groups. I will discuss a confirmation of this conjecture for G being the symmetric group. The proof uses ideas from integrable systems (Gaudin algebras), algebraic geometry (moduli of points on genus zero curves), and combinatorics (crystals). This is joint work with A.Brochier and N.White.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

Organizing Committee: Fabio Gavarini (mail to) - Martina Lanini (mail to)
Further Info: Click here
Streaming Link (MS Teams): Click here


Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 


DIFFERENTIAL EQUATIONS SEMINAR

Date: Tuesday 17 May 2022
Schedule: 16:00 - Rome Time
Where: Room 1201 "R. Dal Passo"
Speaker: Chaona Zhu (Università di Roma "Tor Vergata")
Title: "Prescribing scalar curvatures: the negative case"

Abstract: The problem of prescribing conformally the scalar curvature on a closed manifold of negative Yamabe invariant is always solvable, if the function to be prescribed is strictly negative, while sufficient and necessary conditions are known in the case that function is non positive. Still in the case of a negative Yamabe invariant, Rauzy (Trans. Amer. Math. Soc. 1995) showed solvability, if the function to be prescribed is not too positive, as quantified by Aubin-Bismuth (J. Funct. Anal. 1997) later on. In this talk we will review these results variationally and shed some light on the case, when Rauzy’s conditions fail. This talk is joint work with Martin Mayer.


This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.

Organizing Committee: Riccardo Molle (mail to) - Alfonso Sorrentino (mail to)
Further Info: DIFFERENTIAL EQUATIONS PAGE: Click Here
Streaming Link (MS Teams): CLICK HERE


Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 


TOPOLOGY AND ALGEBRA SEMINAR

Date: Thursday May 19, 2022
Schedule: 16:00 - Rome Time
Where: Room 20 - MACROAREA DI SCIENZE
Speaker: TOMAMSO ROSSI (Università degli Studi di Roma "Tor Vergata")
Title: "Calcolare i numeri di Betti di $\bar{M_{0,n}}$ usando la Dualità di Koszul"

Abstract: Gli spazi dei moduli delle superfici di Riemann di genere g con n punti evidenziati $M_{g,n}$ e le loro compattificazioni sono oggetti di grande interesse sia per i geometri algebrici che per i topologi. In questo seminario ci concentreremo nel caso g=0 e vedremo come $M_{0,n}$ e la sua compattificazione di Deligne Mumford $\bar{M_{0,n}}$ siano strettamente collegati. In effetti mostreremo come la conoscenza dei numeri di Betti di uno dei due spazi permetta di calcolare i numeri di Betti dell'altro. Il motivo che sta dietro a questa interconnessione è la dualità di Koszul, di cui proverò a spiegare i concetti di base.

Organizing Committee: Paolo Salvatore (mail to)
Further Info:
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Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

 


NUMERICAL ANALISYS SEMINAR

Date: Wednesday 18 May 2022
Schedule: 14:00 - Rome Time
Where: Room 2001
Speaker: Tom Lyche (University of Oslo)
Title: " A C1 simplex spline basis for the Alfeld split "

Abstract: Piecewise polynomials over triangles and tetrahedrons have applications in several branches ranging from finite element analysis, surfaces in computer aided design... The smoothness on tetrahedrons is obtained either by high degrees of polynomials or using smaller degrees when splitting the tetraehedron into smaller pieces. Here we consider the Alfeld split which generalizes the Clough-Tocher split of a triangle. Simplex splines with arbitrary knots are the natural generalization of univariate B-splines to several variables. We consider degrees d = 2s-1 and construct a partition of unity basis for the space S12s-1;s on the Alfeld split, consisting of simplex-splines. We also show a Marsden like identity for s ≤ 5. Joint work with Jean-Louis Merrien.

This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.

Organizing Committee: Carla Manni ( Mail to)
Further Info:
Streaming Link (MS Teams):


Università degli Studi di Roma Tre
Dipartimento di Matematica - Fisica

 


MATHEMATICAL ANALISYS SEMINAR

Date: Wednesday 18 May 2022
Schedule: 14:30 - Rome Time
Where: "Largo San Leonardo Murialdo,1 - Pal.C Room 211
Speaker: Antonio J. Fernandez (I.C.M.A.T. - Madrid)
Title: "Singular limits for a half-Laplacian Liouville type equation "

Abstract: We consider the nonlocal Liouville type equation (-Delta)^(1/2)u = epsilon * k(x) e^u, u > 0 in I u = 0 in R I where I is a union of d >= 2 disjoint bounded intervals, k is a smooth bounded function with positive infimum and epsilon > 0 is a small parameter. For any integer 1 <= m <= d, we construct a family of solution u_epsilon which blow-up at m distinct points of I and for which epsilon *(integral of k(x) e^u) --> 2m*pi as epsilon --> 0$. Moreover, we show that, when d = 2 and m is suitably large, no such construction is possible. The talk is based on a joint work with Matteo Cozzi (Milano, Italy).

Organizing Committee: ( )
Further Info:
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Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 


PROBABILITY SEMINAR

Date: Friday May 20, 2022
Schedule: 14:00 Rome Time
Where: Room 1200
Speaker: Giacomo Giorgio
Title: "Convergence in Total Variation for nonlinear functionals of random hyperspherical harmonics "

Abstract: Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit d-dimensional sphere (d ≥ 2). We study the convergence in Total Variation distance for their nonlinear statistics in the high energy limit, i.e., for diverging sequences of Laplace eigenvalues. Our approach takes advantage of a recent result by Bally, Caramellino and Poly (2020): combining the Central Limit Theorem in Wasserstein distance obtained by Marinucci and Rossi (2015) for Hermite-rank 2 functionals with new results on the asymptotic behavior of their Malliavin-Sobolev norms, we are able to establish second order Gaussian fluctuations in this stronger probability metric as soon as the functional is regular enough. Our argument requires some novel estimates on moments of products of Gegenbauer polynomials that may be of independent interest, which we prove via the link between graph theory and diagram formulas.

Organizing Committee: Lucia Caramellino (mail to), Michele Salvi (mail to), Domenico Marinucci (mail to).
Further Info:
Streaming Link (MS Teams):


Università degli Studi Roma Tor Vergata
Dipartimento di Matematica

 


PROBABILITY SEMINAR

Date: Friday May 20, 2022
Schedule: 15:00 Rome Time
Where: Room 1200
Speaker: Edoardo Lombardo
Title: "High order approximations for the Cox-Ingersoll-Ross process using random grids "

Abstract: We present new high order approximations schemes for the Cox-Ingersoll-Ross (CIR) process that are obtained by using a recent technique developed by Alfonsi and Bally (2021) for the approximation of semigroups. The idea consists in using a suitable combination of discretization schemes calculated on different random grids to increase the order of convergence. This technique coupled with the second order scheme proposed by Alfonsi (2010) for the CIR leads to weak approximations of order $2k$ for all $k\in\N$. Despite the singularity of the square-root volatility coefficient, we show rigorously this order of convergence under some restrictions on the volatility parameters. We illustrate numerically the convergence of these approximations for the CIR process and for the Heston stochastic volatility model.

Organizing Committee: Lucia Caramellino (mail to), Michele Salvi (mail to), Domenico Marinucci (mail to).
Further Info:
Streaming Link (MS Teams):


Università degli Studi di Roma Tre
Dipartimento di Matematica - Fisica

 


ONE WORLD NUMERATION SEMINAR

Date: Tuesday 17 May, 2022
Schedule: 14:30 - Rome Time
Where: "Largo San Leonardo Murialdo,1 - Pal.C Room 311
Speaker: Vilmos Komornik (Université de Strasbourg)
Title: "Topology of univoque sets in real base expansions"

Abstract: We report on a recent joint paper with Martijn de Vries and Paola Loreti. Given a positive integer M and a real number 1 < q ≤ M+1, an expansion of a real number x ∈ [0,M/(q-1)] over the alphabet A = {0,1,...,M} is a sequence (c_i) ∈ A^N such that x = Σ_{k=1}^∞ c_i q^{-i}. Generalizing many earlier results, we investigate the topological properties of the set Uq consisting of numbers x having a unique expansion of this form, and the combinatorial properties of the set U'q consisting of their corresponding expansions.

Organizing Committee: ( )
Further Info:
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Comunication


It is a pleasure to announce the opening of a ONE YEAR POSITION with possible renewal (pending on funds availability) of the following post-doct position at the Department of Mathematics of UNIVERISTÀ DI ROMA TOR VERGATA: Cod: F3-2022-0007.

"NONLINEAR PDE’S AND GEOMETRIC ANALYSIS IN GEOMETRY AND PHYSICS (MUR DIPARTIMENTI DI ECCELLENZA–CUP:E83C18000100006) DEPARTMENT OF MATHEMATICS"

ON LINE APPLICATIONS and further information at the following link: Click here for site
APPLICATIONS should be send from May 09-2022 (12:00) to May 29-2022 (12:00).

All the best,

Gabriella Tarantello


 

Eventi

 

 

Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

Corso di Dottorato
Cluster expansion in statistical mechanics and its connection with the Lovász Local Lemma in combinatorics

Period: 2022.11.04 - 2022.06.06
Schedule:

DayPeriodTime
Monday11.04.2022 14:00 - 16:00
Wednesday13.04.2022 14:00 - 16:00
Monday20.04.2022 14:00 - 16:00
Wednesday27.04.2022 14:00 - 16:00
Monday02.05.2022 14:00 - 16:00
Wednesday04.05.2022 14:00 - 16:00
Monday09.05.2022 14:00 - 16:00
Wednesday11.05.2022 14:00 - 16:00
Monday16.05.2022 14:00 - 16:00
Wednesday18.05.2022 14:00 - 16:00
Monday23.05.2022 14:00 - 16:00
Wednesday25.05.2022 14:00 - 16:00
Monday03.05.2022 14:00 - 16:00
Wednesday01.06.2022 14:00 - 16:00
Monday06.06.2022 14:00 - 16:00
Where: Common Room
Organizing Committee: Benedetto Scoppola (Contatto E-Mail).
Speaker: Aldo Procacci (University Federal of the Minas Gerais, Belo Horizonte, Brasile)
Title: Cluster expansion in statistical mechanics and its connection with the Lovász Local Lemma in combinatorics

Abstract:

Course program:

Part 1. Continuous particles in the Grand Canonical Ensemble interacting via a pair potential
1. Conditions on the pair potential: stability and regularity
2. The infinite volume limit. Existence (the case of the finite range pair potential)
3. Properties of the pressure. Continuity.
4. The Mayer series
5. The combinatorial problem
6. The Penrose tree graph identity: partition schemes.
7. Analyticity at low density/high temperature

    a) The hard sphere gas (via the original Penrose partition scheme)
    b) gas of particles interacting via a stable and regular pair potential (via the Kruskal algorithm partition scheme)

Part 2. Discrete systems
1. The abstract polymer gas
2. Convergence of the cluster expansion
3. Convergence criteria: Kotecký-Preiss; Dobrushin; Fernández-Procacci.
4. Elementary examples.
5. Gas of non-overlapping subsets
6. Applications: spin systems at high temperature
7. Ising model at low temperature.
8. Antiferromagnetic Potts model at zero temperature on a graph G (complex zeros of the chromatic polynomial of G).

Part 3. The Connection with the probabilistic method in combinatorics
1. A powerful tool in combinatorics: The Lovász Local Lemma
2. Shearer criterion.
3. Scott-Sokal formulation of the Shearer Criterion via the abstract polymer gas.
4. The cluster expansion Local lemma
5. Example: colorings of a graph.
6. The Moser-Tardos algorithmic version of the Lovász Local Lemma
7. Entropy-compression method.

Further Info: Click here
Streaming Link (MS Teams):


Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

Corso di Dottorato
Introduction into Neural Networks and Deep Learning

Period: 2022.05.11 - 2022.06.30
Schedule:

DayPeriodTime
Wednesday2022.05.1116:00 - 18:00
Thursday 2022.05.1216:00 - 18:00
Wednesday2022.04.1916:00 - 18:00
Thursday 2022.05.2616:00 - 18:00
Wednesday2022.06.0116:00 - 18:00
Thursday 2022.06.0816:00 - 18:00
Wednesday2022.06.0916:00 - 18:00
Thursday 2022.06.1516:00 - 18:00
Wednesday2022.06.1616:00 - 18:00
Thursday 2022.06.2216:00 - 18:00
Wednesday2022.06.2316:00 - 18:00
Thursday 2022.06.3016:00 - 18:00
Where: Room 1101 D'Antoni
Organizing Committee: Bracci Filippo (Contatto E-Mail)
Speaker: Dmitri Koroliouk (National Academy of Sciences of Ukraine)
Title: "Introduction into Neural Networks and Deep Learning"

Abstract: Program is below:

Further Info: Prof. Koroliouk is available to meet anyone who is interested talking about the topics of the course, you can contact directly writing an E-Mail to: Prof. Koroliouk
Streaming Link (MS Teams):


Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

Corso di Dottorato
Introduction to rough paths

Period: 2022.05.05 - 2022.05.24
Schedule:

DayPeriodTime
Wednesday2022.05.05 14:00 - 16:00
Tuesday2022.05.11 14:00 - 16:00
Wednesday2022.05.12 14:00 - 16:00
Tuesday2022.05.18 14:00 - 16:00
Wednesday2022.05.19 14:00 - 16:00
Tuesday2022.05.23 14:00 - 16:00
Wednesday2022.05.24 14:00 - 16:00
Where: Room 1201 Dal Passo
Organizing Committee: Lucia Caramellino (Contatto E-Mail).
Speaker: Vlad Bally (Université Gustave Eiffel, France)
Title: "Introduction to rough paths"

Abstract: Rough path theory has been initiated in the last 90's by Terry Lyons in [1]. Then, in the last 20 years it has had a tremendous development, including the "regularity structures" theory of Hairer (we will not touch to this last topic in our course). And nowadays this is still an extremely active area of research. The aim of this theory is to construct a variant of the stochastic integral which is "pathwise". Moreover one solves Stochastic Differential Equations (SDEs) with the usual stochastic integral replaced by the "rough integral". This gives an application defined on the space of continuous functions C([0,T]) which, under the Wiener measure, produced the solution of the SDE. We stress that the classical theory of stochastic flows (due to Kunita, Bismut, and many others) produces a "strong solution" of the SDE, which is exactly such an application. But there is a crucial progress here: in the classical case, the flow produces a solution "almost surely" with an exception set depending on the coefficients of the SDE, whereas in the rough path theory the exception set is independent of the coefficients (in some sense it is universal). Moreover, a continuity property of the application, with respect to a specific norm (the "rough path norm") is proved. Nowadays there are many text books devoted to this subject. They are more or less difficult to read because of a rather heavy technical background. The aim of this introductory course is to give an elementary and simple approach to the main ideas in this theory. But of course, this is just a first step and a deep knowledge of the theory needs to read one of these books. I strongly recommend the beautiful book [2] of Friz and Hairer (which I will more or less follow).

Further Info: Click here
Streaming Link (MS Teams): The lessons will be streamed via Microsoft Teams. Those interested can request to be included in the Teams classroom of the course or to receive the link to follow the lessons by writing an email to Lucia Caramellino.


Università degli Studi di Roma "Tor Vergata"
Dipartimento di Matematica

Corso di Dottorato
On some classes of nonlinear and nonlocal elliptic PDEs on R^N

Period: 2022.05.16 - 2022.06.09
Schedule:

DayPeriodTimeRoom
Monday2022.05.16 11:00 - 13:00Dal Passo
Wednesday2022.05.18 16:00 - 16:00D'Antoni
Friday2022.05.20 16:00 - 18:00D'Antoni
Monday2022.05.23 16:00 - 18:00D'Antoni
Wednesday2022.05.25 16:00 - 18:00D'Antoni
Friday2022.05.27 16:00 - 18:00Dal Passo
Tuesday2022.05.31 11:00 - 13:00DAl Passo
Friday2022.06.03 11:00 - 13:00DAl Passo
Tuesday2022.06.07 14:00 - 18:00DAl Passo
Thursday2022.06.09 14:00 - 18:00DAl Passo
Where: see the schedule
Organizing Committee: Riccardo Molle (Contatto E-Mail).
Speaker: Carlo Mercuri (Swansea University, U.K.)
Title: "On some classes of nonlinear and nonlocal elliptic PDEs on R^N"

Abstract: This is an introductory course to 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 the variational formulation of these equations, to their functional setting and relevant compactness properties. Known results will be discussed, as well as suggestions for new research projects in this area. 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, characterised in terms of 'energy levels'. Some exercises will be discussed, as a preparation to 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. We will give a more detailed description of the program later.

Further Info: Click here
Streaming Link (MS Teams): .