## Notiziario Scientifico

**Notiziario dei seminari di carattere matematico**

a cura del Dipartimento di Matematica

*G. Castelnuovo*, Sapienza Università di Roma

Settimana dal 06-05-2019 al 12-05-2019

**Lunedì 06 maggio 2019**

Ore 14:15, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma

Seminario di Analisi Matematica

Riccarda Rossi (Università di Brescia)
*Some results on Balanced Viscosity solutions to rate-independent systems*

Over the last 15 years, the vanishing-viscosity approach to the mathematical modeling of purely rate-independent systems has become an increasingly popular method to select solutions with a mechanically feasible behavior at jumps. Recently, vanishing-viscosity analyses have been performed in the case of multi-rate systems. The aim of this talk, based on joint work with A. Mielke and G. Savare', is to give an overview of the related results.

**Lunedì 06 maggio 2019**

Ore 16:30, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma

Colloquium "Guido Castelnuovo"

Caucher Birkar (University of Cambridge)
*Birational geometry of algebraic varieties*

Birational geometry has seen tremendous advances in the last two decades. This talk is a gentle introduction to some of the main concepts and recent advances in the field.

**Martedì 07 maggio 2019**

Ore 13:45, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma

Seminario di Probabilità

Dello Schiavo Lorenzo (Università di Bonn)
*The Dirichlet-Ferguson diffusion*

We define, via Dirichlet forms’ theory, a geometric diffusion process on the \(L^2\)-Wasserstein space over a closed Riemannian manifold. The process is associated with the Dirichlet form induced by the \(L^2\)-Wasserstein gradient and by the Dirichlet-Ferguson random measure with intensity the Riemannian volume measure on the base manifold. We discuss the closability of the form via an integration-by-parts formula, which allows explicit computations for the generator and a specification of the process via a measure-valued SPDE. We comment how the construction is related to previous work of von Renesse—Sturm on the Wasserstein Diffusion and of Konarovskyi—von Renesse on the Modified Massive Arratia Flow.

**Martedì 07 maggio 2019**

Ore 14:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

Algebra and Representation Theory Seminar

Gastón Andrés Garcìa (Universidad Nacional de La Plata)
*Classifying finite-dimensional Hopf algebras*

In this talk I will introduce the problem of classifying (finite-dimensional) Hopf algebras over an algebraically closed field of characteristic zero. This is a difficult question, since the theory of Hopf algebras includes as first examples group algebras and universal enveloping algebras of Lie algebras. Up to know, there are very few general results, hence all efforts are focused on solving the classification problem for certain families of Hopf algebras: e.g., the semisimple ones, the pointed ones, or those of small dimension. The main obstruction lies in the lack of enough examples. Although the appearance of Quantum Groups gave an strong impulse to the theory, drawing the attention of mathematicians from different areas (representation theory, mathematical physics, QCFT, etc.), the problem is far from being solved. In this talk I will present some structural results, different techniques for classifying particular families of Hopf algebras, and then describe the current situation of the classification problem for small dimension.

**Martedì 07 maggio 2019**

Ore 15:15, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

Algebra and Representation Theory Seminar

Gastón Andrés Garcìa (Universidad Nacional de La Plata)
*Pointed Hopf algebras, quantum groups and the lifting method*

This talk will focus on the classification of pointed Hopf algebras and the description of a general method (called "lifting method") that was the key stone to solve the problem of classifying finite-dimensional pointed Hopf algebras over Abelian groups. It turned out that Hopf algebras of this type are all isomorphic to variations of (Borel parts of) small quantum groups. The implementation of this method is based on the notions of Nichols algebras, braided spaces and PBW-deformations, and led to the development of generalized root systems and Weyl groupoids. Time permitting, I will present a generalized lifting method that allows to construct new examples of non-pointed Hopf algebras related to quotients of quantized coordinate algebras over simple algebraic groups.

**Mercoledì 08 maggio 2019**

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

Seminario di Algebra e Geometria

Federico Binda (Regensburg)
*Specialization theorems for cycles of relative dimension 0*

In this talk, we will present a relation between a certain group of algebraic cycles, with finite coefficients, on a regular quasi-projective scheme X, flat over an excellent Henselian DVR A with perfect residue field, and the motivic cohomology (with compact support) of the special fiber, in the range classically corresponding to the group of zero cycles. When X is projective over A, this relation was studied by Bloch and Esnault–Kerz–Wittenberg, generalizing previous works by Sato and Saito, and implies a finiteness result for the Chow group of zero cycles of a smooth projective variety over a p-adic field. Our main result can be interpreted as a proper base change theorem with compact support for relative 0-cycles. This is a joint work (in progress) with Amalendu Krishna.

**Giovedì 09 maggio 2019**

Ore 14:30, Aula 211, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S.L. Murialdo, 1 - Pal. C

Seminario di Geometria

Giovanni Cerulli Irelli (Sapienza Università di Roma)
*Quiver Grassmannians*

This is an introductory talk concerning quiver Grassmannians. A quiver Grassmannian is a projective variety which parametrizes the subrepresentations of a quiver representation which have a fixed dimension vector. If the quiver representation has good homological properties one can hope to study the geometry of the associated quiver Grassmannians by using the representation theory of quivers. The main open problem on this subject is if the quiver Grassmannians associated to a rigid quiver representation admit a cellular decomposition. I will report on recent developments on this problem. This is joint work with F. Esposito, H. Franzen and M. Reineke.

**Giovedì 09 maggio 2019**

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

Seminario Fisica Matematica

Eveliina Peltola (Università di Ginevra)
*Crossing probabilities of multiple Ising interfaces*

I discuss crossing probabilities of multiple interfaces in the critical Ising model with alternating boundary conditions. In the scaling limit, they are conformally invariant expressions given by so-called pure partition functions of multiple \( SLE(\kappa) \) with \( \kappa=3 \). I also describe analogous results for critical percolation and the Gaussian free field.

**Giovedì 09 maggio 2019**

Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

Seminario di Analisi Matematica

Wei Cheng (Nanjing University, China)
*Herglotz variational principle and Hamilton-Jacobi equation of contact type*

In this talk, I will discuss our recent work on the Herglotz' variational principle with the applications to Hamilton-Jacobi equations in the form \( D_tu(t,x)+H(t,x,u(t,x),D_x u((t,x))=0 \). We will mainly focus on the regularity of the minimizers of the variational problem. This is joint work with Piermarco Cannarsa, Liang Jin, Kaizhi Wang and Jun Yan. (This seminar is part of the activity of the MIUR Excellence Department Project)

**Giovedì 09 maggio 2019**

Ore 15:00, Sala Biblioteca - area geotecnica, Dipartimento Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma

Seminario della serie "Challenges in Mechanics"

Mark Warner (Cavendish Lab, University of Cambridge, UK)
*Inducing curvature in materials gives a “metric mechanics”*

Liquid crystalline elastomers and glasses, change shape by 100\(\%\) following changes in temperature or illumination. Shape changes, that is elongation along a particular direction, rather than simply change of volume, can be imaginatively arranged to induce intrinsic curvature in initially flat spaces. Light-induced curvature suggests new mechanics paradigms to be exploited in strong actuation of slender materials without Euler failures\(^1\). I will give, with many demonstrations, examples of the materials and geometry arising\(^{2,3}\). Deformations can be large. Hence in-plane, in-material trajectories, along with integral curves of the director field, are substantially advected and distorted with the change. Calculating these distortions of in-material lengths will specify the evolving topography\(^4\)– both forward from a given director field, and inversely giving the director field required to obtain a desired shape.

\(^1\)Guit et al., Nature Comms 9, 2531 (2018).

\(^2\)Modes et al., Phys.Rev. E 81, 060701(R) (2010) & Proc.Roy.Soc.A467, 2128 (2011)

\(^3\)Mostajeran et al., Proc.Roy.Soc.A472, 2189 (2016)

\(^4\)Warner and Mostajeran, Proc.Roy.Soc.A474, 2210 (2018)

**Venerdì 10 maggio 2019**

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

Seminario di Probabilità

Mauro Mariani (National Research University Higher School of Economics, Moscow)
*Scaling limit of a continuous model of active particles*

A free energy functional arising from kinetic mean field models of interacting particles is considered. We study the variational limit, in the regime of long time and strong interaction. While the density of particles only features a weak limit in the phase space (say position and velocity), the projection of such a density on the spacial coordinates has a meaningful limit, which satisfies a hydrodynamic equation. We characterizes the tensors appearing in the hydrodynamic limit, in terms of the interaction and velocity field of the original model.

**Venerdì 10 maggio 2019**

Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata

Seminario di Geometria Algebrica

Chiara Camere (Università di Genova)
*Some isogenies between complex K3 surfaces *

The aim of this talk is to construct special isogenies between K3 surfaces, obtained by following quotients by symplectic automorphisms, and to determine the families of K3 surfaces for which this construction is possible. To this purpose we will prove that there are families of K3 surfaces of large dimension which both admit a finite symplectic automorphism and are desingularization of quotients of other K3 surfaces by a symplectic automorphism. In the second part of the talk we will consider the special case of involutions, and exhibit infinitely many sets of infinitely many K3 surfaces which are isogenous to each other. This is joint work in progress with A. Garbagnati.

[Algebraic Geometry Seminar - in the framework of the Research Project "Families of curves: their moduli and their related varieties" - Mission Sustainability Tor Vergata, CUP: E81|18000100005, Principal Investigator: F. Flamini]

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