17/05/22  Seminario  16:00  17:00  1201 Dal Passo  Chaona Zhu  Chinese Academy of Sciences and Roma "Tor Vergata"  Prescribing scalar curvatures: the negative case
( MS Teams Link for the streaming )
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 AubinBismuth (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.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

13/05/22  Colloquium  15:00  16:00  1201 Dal Passo  Michela Procesi  Università di Roma Tre  May12: Celebrating Women in Maths
Order and chaos and wave dynamics
(Opening address by Gabriella Tarantello)
(MS Teams link for the streaming at the end of the abstract)
Many physical phenomena are well described as the propagation of waves: the motion of the sea, the transmission of sound, electromagnetic waves (light, radio waves). Their mathematical description is often extremely complicated, and characterized by the coexistence of stable and chaotic behaviors. I will discuss some models of wave propagation by nonlinear Partial Differential Equations illustrating briefly the main difficulties as well as some mathematical methods used to study them.
A small refreshment will be served at the end of the colloquium.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 
10/05/22  Seminario  16:00  17:00  1201 Dal Passo  Filippo Gazzola  Politecnico di Milano  Longtime behavior of partially damped systems modeling degenerate plates with piers
( MS Teams Link for the streaming )
We consider a partially damped nonlinear beamwave system of evolution PDE's modeling the dynamics of a degenerate plate. The plate can move both vertically and torsionally and, consequently, the solution has two components. We show that the component from the damped beam equation always vanishes asymptotically while the component from the (undamped) wave equation does not. In case of small energies we show that the first component vanishes at exponential rate. Our results highlight that partial damping is not enough to steer the whole solution to rest and that the partially damped system can be less stable than the undamped system. Hence, the model and the behavior of the solution enter in the framework of the socalled "indirect damping" and "destabilization paradox". These phenomena are valorized by a physical interpretation leading to possible new explanations of the Tacoma Narrows Bridge collapse.
Joint work with Abdelaziz Soufyane (University of Sharjah, UAE)
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 
10/05/22  Colloquium  14:30  15:30  1201 Dal Passo  Slava Rychkov  IHES, Bures sur Yvette, Paris 
COLLOQUIUM LEVICIVITA
“Bootstrap” method in physics and
mathematics
In the last 1015 years, “bootstrap” was applied to problems as disparate as critical exponents of secondorder phase transitions, scattering of elementary particles, chaotic dynamical systems, and Laplacian spectra on hyperbolic manifolds. This produced many new computerassisted bounds on various quantities of interest. I will explain common features of these problems, and what is this bootstrap method which applies to all of them. 
09/05/22  Colloquium  15:00  16:00  1201 Dal Passo  Lorenzo Rosasco  University of Genova  A guided tour of machine learning (theory)
In this talk, we will provide a basic introduction to some of the fundamental ideas and results in machine learning, with emphasis on mathematical aspects. We will begin contrasting the modern data driven approach to modeling to classic mechanistic approaches. Then, we will discuss basic elements of machine learning theory connected to approximation theory, probability and optimization. Finally, we will discuss the need of new theoretical advances at the light of recent empirical observations while using deep neural networks. 
06/05/22  Seminario  14:30  15:30  1201 Dal Passo  Peter FIEBIG  FriedrichAlexanderUniversität ErlangenNürnberg 
Algebra & Representation Theory Seminar (ARTS)
"Tilting modules and torsion phenomena"
 in live & streaming mode 
( click HERE to attend the talk in streaming )
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Given a root system and a prime number p we introduce a category X of “graded spaces with Lefschetz operators” over a ring A. Then we show that under a base change morphism from A to a field K this category specialises to representations of the hyperalgebra of a reductive group, if K is a field of positive characteristic, and of a quantum group at p^{l}th root of unity, if K is the p^{l}th cyclotomic field. In this category we then study torsion phenomena (over the ring A) and construct for any highest weight a family of universal objects with certain torsion vanishing conditions. By varying these conditions, we can interpolate between the Weyl modules (maximal torsion) and the tilting objects (no torsion). This construction might shed some light on the character generations philosophy of Lusztig and LusztigWilliamson.
N.B.: please click HERE to attend the talk in streaming.

04/05/22  Seminario  14:00  15:00  2001  Marjeta Knez  University of Ljubljana  A supersmooth C^{1} spline space over planar mixed triangle and quadrilateral meshes
In the talk a C^{1} spline space over mixed meshes composed of triangles and quadrilaterals, suitable for FEMbased or isogeometric analysis, will be introduced. The mesh is considered to be a partition of a planar polygonal domain into triangles and/or quadrilaterals. The proposed space combines the Argyris triangle element with the C^{1}
quadrilateral element for polynomial degrees d ≥ 5. The spline space is assumed to be C^{2} at all vertices and C^{1} across edges, and the splines are uniquely determined by C^{2}data at the vertices, values and normal derivatives at chosen points on the edges, and values at some additional points in the interior of the elements.
The motivation for combining the Argyris triangle element with a recent C^{1} quadrilateral construction, inspired by isogeometric analysis, is twofold: on one hand, the ability to connect triangle and quadrilateral finite elements in a C^{1} fashion is nontrivial and of theoretical interest. On the other hand, the construction facilitates the meshing process by allowing more flexibility while remaining C^{1} everywhere. This is for instance relevant when trimming of tensorproduct Bsplines is performed.
As it will be demonstrated by numerical examples the presented spline space can be employed to various applications like interpolation and least square approximation of a given function or to solve the biharmonic equation via its weak form and Galerkin discretization.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006. 
03/05/22  Seminario  16:00  17:00  1201 Dal Passo  Francesco Fidaleo  Università di Roma  Spectral actions for qparticles and their asymptotic
( MS Teams Link for the streaming )
For spectral actions made of the average number of particles and arising fromopen systems made of general free qparticles (including Bose, Fermi and classical ones corresponding to q= pm 1 and 0, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cutoff. We treat both relevant situations relative to massless and massive particles, where the natural cutoff is 1/eta=k_eta T and 1//sqrt{eta}, respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium. We briefly discuss the appearance of condensation phenomena occurring for Boselike qparticles, for which qin (0,1], after passing to the continuum. We also compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 
22/04/22  Seminario  16:00  17:00  1201 Dal Passo  Andrea APPEL  Università di Parma 
Algebra & Representation Theory Seminar (ARTS)
"SchurWeyl duality for quantum affine symmetric pairs"
 in live & streaming mode 
( please click HERE to attend the talk in streaming )
N.B.: This talk is part of the activity of the MIUR Excellence
Department Project MATH@TOV CUP E83C18000100006
In the work of Kang, Kashiwara, Kim, and Oh, the SchurWeyl duality between quantum affine algebras and affine Hecke algebras is extended to certain KhovanovLaudaRouquier (KLR) algebras, whose defining combinatorial datum is given by the poles of the normalised Rmatrix on a set of representations.
In this talk, I will review their construction and introduce a "boundary" analogue, consisting of a SchurWeyl duality between a quantum symmetric pair of affine type and a modified KLR algebra arising from a (framed) quiver with a contravariant involution. With respect to the KangKashiwaraKimOh construction, the extra combinatorial datum we take into account is given by the poles of the normalised Kmatrix of the quantum symmetric pair.
N.B.: please click HERE to attend the talk in streaming.

22/04/22  Seminario  14:30  15:30  1201 Dal Passo  Lleonard RUBIO y DEGRASSI  Università di Verona 
Algebra & Representation Theory Seminar (ARTS)
"Maximal tori in HH^{1} and the homotopy theory of bound quivers"
 in live & streaming mode 
( please click HERE to attend the talk in streaming )
N.B.: This talk is part of the activity of the MIUR Excellence
Department Project MATH@TOV CUP E83C18000100006
Hochschild cohomology is a fascinating invariant of an associative algebra which possesses a rich structure. In particular, the first Hochschild cohomology group HH^{1}( A) of an algebra A is a Lie algebra, which is a derived invariant and, among selfinjective algebras, an invariant under stable equivalences of Morita type. This establishes a bridge between finite dimensional algebras and Lie algebras, however, aside from few exceptions, fine Lie theoretic properties of HH^{1}( A) are not often used.
In this talk, I will show some results in this direction. More precisely, I will explain how maximal tori of HH^{1}( A), together with fundamental groups associated with presentations of A, can be used to deduce information about the shape of the Gabriel quiver of A. In particular, I will show that every maximal torus in HH^{1}( A) arises as the dual of some fundamental group of A. By combining this, with known invariance results for Hochschild cohomology, I will deduce that (in rough terms) the largest rank of a fundamental group of A is a derived invariant quantity, and among selfinjective algebras, an invariant under stable equivalences of Morita type. Time permitting, I will also provide various applications to semimonomial and simply connected algebras.
This is joint work with Benjamin Briggs.
N.B.: please click HERE to attend the talk in streaming.
