## Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma

Settimana dal 04-03-2019 al 10-03-2019

Lunedì 04 marzo 2019
Ore 14:15, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Barbara Nelli (DISIM, Università dell'Aquila)
TBA

Lunedì 04 marzo 2019
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Algebra and Representation Theory Seminar
Viola Siconolfi (Università di Roma Tor Vergata)
Wonderful models for generalized Dowling lattices
Given a subspace arrangement, De Concini and Procesi in the '90s described the construction of a variety associated to it, namely its wonderful model. An important feature of these model is that some of its geometric aspects are linked to some combinatorial properties of the subspace arrangement, in particular the description of its boundary and its Betti numbers. During the talk I will consider the subspace arrangement associated to a generalized Dowling lattice, a combinatorial object introduced by Hanlon. The aim is to study the wonderful model associated to it and to give a description of its boundary. To deal with this I will use a bijection between the set of boundary components of the wonderful model and a family of graphs. This is a joint work with Giovanni Gaiffi.

Martedì 05 marzo 2019
Ore 15:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellista Differenziale Numerica
Corrado Mascia (Sapienza Università di Roma)
Modelling reaction-diffusion beyond the Fourier law
The classical modelling of diffusion processes posits that the flux is proportional to the gradient of the density, with the final output that the resulting equation is parabolic. Such description has a number of flaws, the most famous being the infinite speed of propagation. The main problem lies in the fact that the system's response is assumed to be instantaneous. Differently, the presence of a time-lag, corresponding to the presence of inertial terms, has to be taken into account. In fact, philosophically speaking, parabolicity is an exceptional event, and the generic case (which preserves well-posedness) is the hyperbolic one. In this presentation, attention is given to the Maxwell-Cattaneo law -a constitutive equation for the evolution of the flux- which is the simplest mechanism to incorporate the presence of a relaxation time-scale and furnishing a hyperbolic model. Specifically, the talk concentrates on the main differences when the standard balance equation is coupled with the Maxwell-Cattaneo law in place of the Fourier law. Specific attention will be given to the presence of propagating fronts and their (analytical and numerical) stability.

Mercoledì 06 marzo 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Joel Kamnitzer (Toronto)
Mirkovic-Vilonen cycles, preprojective algebra modules and Duistermaat-Heckman measures
Via the geometric Satake correspondence, the Mirkovic-Vilonen cycles give bases for representations of semisimple Lie algebras. Similarly, by work of Lusztig, generic preprojective algebra modules give bases for these representations as well. It is a long-standing open problem to compare these bases. We will explain a new geometric way to make this comparison. As an application, we will show that these bases do not agree in $$SL_6$$.

Giovedì 07 marzo 2019
Ore 14:30, Aula 211, Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo S. L. Murialdo, 1
Seminario di Geometria
Harold Blum (University of Utah)
Uniqueness of K-polystable degenerations of Fano varieties
K-stability is an algebraic notion that characterizes when a smooth Fano variety admits a Kahler-Einstein metric. A key motivation for understanding K-stability is to construct moduli spaces for Fano varieties. In this talk, I will explain that a K-polystable degeneration of a family of Q-Fano varieties is necessarily unique. The result is a key step in the program to construct a proper moduli space parameterizing K-polystable Q-Fano varieties and essentially verifies the separateness of said moduli space. This is joint work with Chenyang Xu.

Venerdì 08 marzo 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario MoMA
Antonio De Simone (SISSA, Trieste)
Flagellar swimming and amoeboid motion in Euglena gracilis: the how and why of a behavioral change in a unicellular organism
Euglena gracilis is a unicellular protist exhibiting different motility strategies: swimming by flagellar propulsion, or crawling thanks to large amplitude shape changes of the whole body (a behavior known as amoeboid motion, or metaboly). Swimming is propelled by the non-planar beating of a composite flagellum powered by an axoneme, with molecular motors sliding over microtubule bundles (arranged according to the “standard” 9+2 architecture).The non-planar beating of the flagellum leads in turn to helical trajectories coupled with body rotations, and these rotations play an important role in the phototactic behavior of E. gracilis. Confinement triggers a behavioral change, namely, E. gracilis switches from flagellar swimming to ameboid motion, which is propelled by peristaltic waves along the body of the organism. These are powered by molecular motors driving the relative sliding of pellicle strips lying underneath the plasma membrane. The mechanisms controlling the gait switch in this unicellular organism are still unknown. Our most recent findings on the motility of E. gracilis, which are the result of a combined theoretical and experimental analysis, will be surveyed.

Venerdì 08 marzo 2019
Ore 15:00, Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Analisi Complessa
Eleonora Di Nezza (Università di Parigi 6 - Marie Curie)
Log-concavity of volume
In this talk we present a proof of the log-concavity property of total masses of positive currents on a given compact Kähler manifold, that was conjectured by Boucksom, Eyssidieux, Guedj and Zeriahi. The proof relies on the resolution of complex Monge-Ampère equations with prescribed singularities. As corollary we give an alternative proof of the Brunn-Minkowsky inequality for convex bodies. This is based on a joint work with Tamas Darvas and Chinh Lu.

Venerdì 08 marzo 2019
Ore 16:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario per Insegnanti (Piano Lauree Scientifiche)
Annalisa Malusa*, Donatella Ricalzone**, Marina Mayer**, Noemi Stivali***, Gualtiero Grassucci (* Sapienza Università di Roma, ** Liceo Pascal, *** Liceo Newton, **** Liceo Grassi)
La matematica da Medaglia Fields. Una proposta per il Liceo Matematico.

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