## Weekly Bulletin (it)

**Notiziario dei seminari di carattere matematico**

a cura del Dipartimento di Matematica

*G. Castelnuovo*, Sapienza Università di Roma

Settimana dal 14-10-2019 al 20-10-2019

**Lunedì 14 ottobre 2019**

Ore 14:30, Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

Seminario di Geometria Algebrica

Mark Andrea de Cataldo (Stony Brook University)
*I numeri di Hodge di O'Grady 10 via le stringhe di N^go*

Discuto il preprint omonimo recente in collaborazione con A. Rapagnetta e G. Sacca' dove calcoliamo i numeri di Hodge della' varieta' olomorfica simplettica 10-dimensionale nota col nome di O'Grady 10. [Seminario di Geometria Algebrica, nell'ambito delle attività relative al Progetto di Eccellenza MIUR 2018-2022 Mat@Tov, CUPE83C18000100006]

**Lunedì 14 ottobre 2019**

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

Seminario di Analisi Matematica

Elena Kosygina (Baruch College)
*Stochastic homogenization of viscous Hamilton-Jacobi equations with non-convex Hamiltonians: examples and open questions*

Homogenization of Hamilton-Jacobi equations with non-convex Hamiltonians in stationary ergodic random media is a largely open problem. In the last 5 years several classes of examples and counter-examples appeared in the literature. The majority of known examples concern inviscid Hamilton-Jacobi equations. We shall discuss two classes of viscous Hamilton-Jacobi equations with non-convex Hamiltonians in one space dimension for which homogenization holds and pose several open questions. The talk is based on joint works with Andrea Davini (Sapienza - Universita di Roma) and with Atilla Yilmaz (Temple University) and Ofer Zeitouni (Weizmann Institute and NYU).

**Martedì 15 ottobre 2019**

Ore 14:30, Aula 211, Dipartimento di Matemtica e Fisica Largo S. L. Murialdo, 1

Seminario di Probabilita'

Jonathan Hermon
*Anchored expansion in supercritical percolation on nonamenable graphs.*

Let G be a transitive nonamenable graph, and consider supercritical Bernoulli bond percolation on G. We prove that the probability that the origin lies in a finite cluster of size n decays exponentially in n. We deduce that: 1. Every infinite cluster has anchored expansion (a relaxation of having positive Cheeger constant), and so is nonamenable in some weak sense. This answers positively a question of Benjamini, Lyons, and Schramm (1997). 2. Various observables, including the percolation probability and the truncated susceptibility (which was not even known to be finite!) are analytic functions of p throughout the entire supercritical phase. 3. A RW on an infinite cluster returns to the origin at time 2n with probability \exp(-\Theta(n^{1/3})). Joint work with Tom Hutchcroft.

**Martedì 15 ottobre 2019**

Ore 14:30, Aula 311, Dipartimento di Matematica e Fisica Largo S. L. Murialdo,1

Seminario di Fisica Matematica

Prof. H. Knoerrer (ETH Zurich)
*On the BKL conjectures - Oscillatory singular, spatially homogenuous space times*

The vacuum Einstein equations for Bianchi space times (that is space times that can be foliated into three dimensional space like slices that are all omogenuous spaces) reduce to a system of ordinary differential equations. The conjectures of Belinskii, Khalatnikov and Lifshitz predict that for almost all initial data the solutions of these differential equation behave like trajectories of a billiard in a Farey triangle in the hyperbolic plane, that is, a triangle whose three vertices are ideal points. In joint work with M.Reiterer and E.Trubowitz we show that, for a set of initial data that has positive measure, this is indeed the case. We use ideas inspired by scattering theory for approximations of the system. The fact that billiard in a Farey triangle is chaotic leads us to small divisor problems similar to those of KAM theory in Hamiltonian dynamics.

**Martedì 15 ottobre 2019**

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

Seminario di Analisi Matematica

Giuseppe Riey (Università della Calabria)
*Regularity results for anisotropic elliptic equations *

We first prove local regularity estimates for positive weak solutions of quasi-linear anisotropic elliptic equations, defined on a smooth bounded domain: a weighted integral hessian estimate and the integrability of the inverse of the gradient. Moreover, we also prove a Hopf type Lemma and, thanks to this result, the local results are then extended to the whole domain. abstract

**Martedì 15 ottobre 2019**

Ore 16:00, Aula D'Antoni, Università di Roma 'Tor Vergata'

Seminario di analisi complessa

Gautam Bharali (Indian Institute of Science)
*Visibility spaces for the Kobayashi distance and applications*

Given a metric space, there are several notions of it being negatively curved. In this talk, we single out a weak notion of negative curvature (which, in fact, is a consequence of negative curvature in the Riemannian category) that turns out to be very useful in proving results about holomorphic maps. This property is a form of visibility, the underlying metric spaces being bounded domains in (/\mathbb{C}^n/) equipped with the Kobayashi distance. In this talk, we shall present a general quantitative condition for a domain to be a visibility space in the sense alluded to above. A class of domains known as Goldilocks domains -- introduced in joint work with Andrew Zimmer in 2017 -- possess this visibility property. Visibility domains form a broad class of domains that includes, for instance, all pseudoconvex domains of finite type. Throughout the talk, we shall refer to the Wolff-Denjoy theorem -- which was previously known to hold true on certain convex domains and on strongly pseudoconvex domains -- as a framing device for the sort of phenomena that extend to visibility domains. We shall also discuss methods for determining when a domain is a visibility space and for constructing new examples with rough boundaries. This is joint work with Andrew Zimmer and Anwoy Maitra.

**Mercoledì 16 ottobre 2019**

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

seminario di Algebra e Geometria

Jacopo Stoppa (SISSA)
*Deformed Hermitian Yang-Mills connections, extended gauge group and scalar curvature*

I will discuss joint work in progress with Enrico Schlitzer (SISSA). We introduce a new system of partial differential equations that describe special metrics on pairs formed by a Kaehler manifold together with a line bundle, thought of as an object in the derived category. These comprise the deformed Hermitian Yang-Mills equations of Leung-Yau-Zaslow, and specialise to the Kaehler Yang-Mills equations of Alvarez-Consul, Garcia-Fernandez and Garcia-Prada in the large radius limit. The first part of the talk will be devoted to geometric motivation, in particular through a moment map interpretation. The second part will be more analytic and will focus on abelian varieties, following ideas of Feng-Szekelyhidi.

**Mercoledì 16 ottobre 2019**

Ore 14:30, Dal Passo , Dipartimento di Matematica, Tor Vergata

Seminario

Bin Gui (Rutgers University)
*Categorical extensions of conformal nets*

Given a conformal net A, its representation category Rep(A) is a braided tensor category by the Doplicher-Haag-Robert superselection theory (adapted to the low dimensional cases by Fredenhagen-Rehren-Schroer). In this talk I give an alternative approach to the tensor and braid structure of Rep(A) by constructing a "universal", "free", and anyonic extension of A, called the categorical extension of A. I will explain the main idea of constructing categorical extensions, and explain how this construction will be useful in solving many equivalence problems in conformal field theory.

**Mercoledì 16 ottobre 2019**

Ore 16:00, Dal Passo, Dipartimento di Matematica, Tor Vergata

Seminario

Pinhas Grossman (UNSW Sydney)
*(Conjectural) infinite families of quadratic categories*

A fusion category is called quadratic if the set of simple objects has a unique non-trivial orbit under the tensor product action of the group of invertible objects. Examples of quadratic fusion categories are near-group categories and Haagerup-Izumi categories. In this talk we will discuss several conjectural families of quadratic categories and associated modular data, motivated by examples coming from the classification of small-index subfactors. The formulas for the modular data generalize conjectures of Evans and Gannon. This is joint work with Masaki Izumi.

**Giovedì 17 ottobre 2019**

Ore 14:30, Aula 211, Diprtimento di Matematica e Fisica Largo San Leonardo Murialdo, 1

Seminario di Geometria

Marta Pieropan (EPFL)
*On the distribution of Campana points on Fano varieties*

We call Campana points an arithmetic notion of points on Campana's orbifolds that has been first studied by Campana and Abramovich, and that interpolates between the notions of rational and integral points. In this talk we introduce Campana points and a Manin type conWe call Campana points an arithmetic notion of points on Campana's orbifolds that has been first studied by Campana and Abramovich, and that interpolates between the notions of rational and integral points. In this talk we introduce Campana points and a Manin type conjecture for Campana points on Fano varieties, and we present results for equivariant compactifications of vector groups (joint work with A. Smeets, S. Tanimoto, T. Várilly-Alvarado) and for toric varieties (joint work with D. Schindler).

**Giovedì 17 ottobre 2019**

Ore 14:30, Dipartimento di Ingegneria, Università di Roma III

corso di Dottorato

Paolo Podio-Guidugli
*Continuum Thermodynamics*

Date del corso: 17, 18, 24 e 25 Ottobre 2019, ore 14:30. Contents: Modern continuum thermodynamics is a field theory devised to handle a large class of processes that typically are neither spatially homogeneous nor sequences of equilibrium states. The course will address the continuum theory of heat conduction, in which the constitutive laws furnish a mathematical characterization of the macroscopic manifestations of those fluctuations in position and velocity of the microscopic matter constituents that statistical thermodynamics considers collectively. In addition to a nonstandard exposition of the conceptual steps leading to the classical heat equation, the crucial assumption that energy and entropy inflows should be proportional is discussed and a hyperbolic version of that prototypical parabolic PDE is presented. Thermomechanics will come next, a slightly more complex paradigmatic example of a field theory where microscopic and macroscopic manifestations of motion become intertwined. Finally, a virtual power format for thermomechanics will be proposed, whose formulation requires that temperature is regarded formally as the time derivative of thermal displacement. It will be shown that this format permits an alternative formulation of the theory of heat conduction, and a physical interpretation of the notion of thermal displacement will be given. The course will be taught by Paolo Podio-Guidugli and will be based on his recent book Continuum Thermodynamics (Springer Nature, 2019).

**Giovedì 17 ottobre 2019**

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

Seminario P(n)/N(p)

Gabrielle Saller Nornberg (Sapienza Università di Roma )
*Unique continuation principles for systems*

In this talk we discuss some recent unique continuation results for systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, we obtain nonexistence of nontrivial (not necessarily positive) radial solutions, in the critical and supercritical regimes, for the Lane-Emden posed in a ball. Some of our results also apply to general fully nonlinear operators, such as Pucci’s extremal operators, being new even for scalar equations. Joint work with Ederson Moreira dos Santos and Nicola Soave.

**Giovedì 17 ottobre 2019**

Ore 15:45, Aula 211, Dipartimento di Matematica e Fisica Largo S. L. Murialdo,1

Seminario di Geometria

Marco Andreatta (Universita' di Trento)
*Effective Adjunction Theory*

Let X be a projective variety, with canonical divisor K, and H a Cartier divisor on X. The effectivity, or non effectivity, of some adjoint divisors aK + bH, for suitable a,b, determines the geometry of X. I will first give a proof of the following version of the Termination of Adjunction: X with at most canonical singularities is uniruled if and only if for each very ample Cartier divisor H on X we have that mK+H is not effective for some m=m(H)>0. Then I will discuss the following Conjecture: Assume that X has terminal singularities, H is nef and big and s >0. K+tH is not effective for every integer t with 1 ≤ t ≤ s if and only if K+sH is not pseudo-effective; this is true if and only if the pair (X,L) is birational to a precise list of (uniruled) models. The Conjecture is true for s ≥ (dimX-1); this can be proved via the Theory of the Reductions, started by Fujita and Sommese, which nowadays can be interpreted as a Minimal Model Program with Scaling.

**Venerdì 18 ottobre 2019**

Ore 14:00, Aula D’Antoni, Dipartimento di Matematica, Università degli Studi di Roma “Tor Vergata”

Algebra and Representation Theory Seminar

Yusra Naqvi (University of Sydney)
* A gallery model for affine flag varieties*

Positively folded galleries in Coxeter complexes play a role in many areas of maths, such as in the study of affine Hecke algebras, Macdonald polynomials, MV-polytopes, and affine Deligne-Lusztig varieties. In this talk, we will define positively folded galleries, and then look at a new recursive description of the set of end alcoves of folded galleries which are positive with respect to alcove-induced orientations. This further allows us to find the images of retractions from points at infinity, giving us a combinatorial description of certain double coset intersections in the affine flag variety. This talk is based on joint work with Elizabeth Milićević, Petra Schwer and Anne Thomas. N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

**Venerdì 18 ottobre 2019**

Ore 14:30, 311, Dipartimento di Matematica e Fisica - Largo S. L. Murialdo,1

Seminario di Analisi e Sistemi Dinamici

Filippo Giuliani (Univ. Politecnica de Catalunya)
*Chaotic resonant dynamics for some PDEs*

In this talk we consider two PDEs on the 2-dimensional torus,the Hartree and Beam equation,and we show the existence of solutions which are essentially Fourier supported on 8 resonant modes and have a non trivial dynamics that involves exchanges of energy in a chaotic fashion. More precisely,at certain time scales some modes oscillate between two values and the exchange times can be chosen randomly within a certain range. This behaviour is due to the presence of an invariant horseshoe-like set for the truncated Birkhoff normal form. This is a work in progress with M. Guardia, P.Martin, S. Pasquali.

**Venerdì 18 ottobre 2019**

Ore 15:00, D'Antoni, Dipartimento di Matematica, Università di Roma TOR Vergata

Seminario di Geometria Algebrica

Mark Andrea de Cataldo (Stony Brook University)
*La congettura P=W in teoria di Hodge non abeliana.*

Discuto, in maniera spero accessibile ai non esperti, la congettura P=W in teoria di Hodge nonabeliana. [Seminario di Geometria Algebrica, nell'ambito delle attività del Progetto di Eccellenza MIUR 2018-2022 Mat@Tov, CUPE83C18000100006]

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