Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 17-06-2019 al 23-06-2019
Lunedì 17 giugno 2019
Ore 14:15, Sala di Consiglio, Dipartimento di Matematica
Seminario di Analisi Matematica
Jose M. Mazon (Universitat de Valencia)
Kurdyka- Lojasiewicz-Simon inequality for gradient flows in metric spaces
The classical Lojasiewicz inequality and its extensions by Simon and Kurdyka have been a considerable impact on the analysis of the large time behaviour of gradient flow in Hilbert spaces. Our aim is to adapt the classical Kurdyka- Lojasiewicz and Lojasiewicz-Simon inequalities to the general framework gradi- ent flow in metric spaces. We show that the validity of a Kurdyka- Lojasiewicz inequality imply trend to equilibrium in the metric sense, and the Kurdyka- Lojasiewicz inequality has the advantage to derive decay estimates of the trend to equilibrium and finite time of extinction. Also we study the relation be- tween Kurdyka- Lojasiewicz inequality and the existence of talweg. The entropy method have proved to be very useful to study the large time behaviour of solutions to many EDP’s. This method is based in the entropy-entropy pro- duction/disipation (EEP) inequality, which correspond to Kurdyka- Lojasiewicz inequality, and also in the entropy transportation (ET) inequality. We show that for geodesically convex functionals Kurdyka- Lojasiewicz inequality and entropy transportation (ET) inequality are equivalent. We apply our general results to gradient flow in Banach spaces and in spaces of probability measures with Wasserstein distances. For the energy functional associated with a doubly- nonlinear equations on RN we obtain the equivalence between Lojasiewicz- Simon inequality, generalized log-Sobolev inequality and p-Talagrand inequality; also we get decay estimates for its solutions. Finally we apply our results to metric spaces with Ricci curvature bounds from below, getting that, in this con- text, a p-Talagrand inequality is equivalent to a Lojasiewicz-Simon inequality. Joint work with Daniel Hauer (Sydney University)
Martedì 18 giugno 2019
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza
Seminario di Geometria
Hessel Posthuma (Universita` di Amsterdam )
Twisted K-theory and the classification of topological insulators
In this talk I will sketch, following Freed and Moore, how an exotic version of twisted equivariant K-theory classifies topological phases of free fermions in condensed matter physics. (This is an introduction to the subject, in particular no advanced background in physics is assumed.) This version of K-theory turns out to be mathematically interesting in its own right. After that I will illustrate the theory with some computations in some examples with crystal symmetries, based on joint work with de Boer, Kruthoff and Stehouwer.
Martedì 18 giugno 2019
Ore 14:00, Aula Dal Passo, Dipartimento di Matematica di Roma "Tor Vergata"
seminario di Analisi Matematica
Diego Souza (Federal University of Pernambuco, Recife, Brazil)
Positive and negative controllability results for some equations of Sobolev-Galpern's type
In this talk we deal with the controllability problem for some Sobolev's type equations. We show that the equations cannot be driven to zero if the control support is strictly contained within the domain. Nevertheless, we also prove that it is possible to control the equations asking the control support to move in time in order to cover the whole space domain. (*) this seminar is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Martedì 18 giugno 2019
Ore 15:00, Aula 2E, Pal. RM004, Dip. SBAI (Scienze di Base e Applicate per l'Ingegneria), Sapienza Università di Roma
Incontri di Algebra e Geometria allo SBAI
Jehanne Dousse (Université Lyon 1)
Partition identities of Capparelli and Primc
A partition of a positive integer n is a non-increasing sequence of positive integers whose sum is n. A Rogers-Ramanujan type identity is a theorem stating that for all n, the number of partitions of n satisfying some difference conditions equals the number of partitions of n satisfying some congruence conditions. Lepowsky and Wilson were the first to exhibit a connection between Rogers-Ramanujan type partition identities and representation theory in the 1980s. Shortly after, studying representations of a different Lie algebra, Capparelli discovered a partition identity yet unknown to combinatorialists. Since then, interactions between representation theory and partition identities have been very fruitful, giving rise to many new identities, such as Primc's identity from crystal base theory. After an introduction to the above-mentioned partition identities, we will show that Capparelli's identity can be deduced combinatorially from Primc's identity, even though they don't seem related from the representation theoretic point of view.
Martedì 18 giugno 2019
Ore 15:00, aula seminari DISG, Dipartimento di Ingegneria Strutturale e Geotecnica Via Eudossiana 18 Roma
Patrick Ballard (Institut d'Alembert Sorbonne Universités)
ANALYSIS OF THE COUPLING BETWEEN LINEAR ELASTICITY AND DRY FRICTION
Elastic solids in frictional contact are well-known to display a rich phenomenology: stick-slip, squeal, judder, etc... This phenomenology is still badly understood nowadays. One line of research consists in looking for the origin of these phenomena in complex friction laws (such as state and rate dependent friction laws). Another line of research consists in sticking to the most idealized friction law (the so-called Coulomb law of dry friction) and exploring the mathematical properties of its coupling with linear elasticity. This is this second approach which will be developed during the seminar. In particular, it will be shown that this coupling contains bifurcations which may account for the qualitative variety of response of the system. This line of research leads to the study of the effects of heterogeneous friction coefficients. The analysis yields non-intuitive new mechanical effects.
Mercoledì 19 giugno 2019
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Dylan Allegretti (Sheffield)
Quiver representations, cluster varieties, and categorification of canonical bases
Associated to a compact oriented surface with marked points on its boundary is an interesting class of finite-dimensional algebras. These algebras are examples of gentle algebras, and their representation theory has been studied by many authors in connection with the theory of cluster algebras. An important fact about these algebras is that their indecomposable modules come in two types: string modules, which correspond to arcs connecting marked points on the surface, and band modules, which correspond to closed loops on the surface. Thanks to the work of many mathematicians, the string modules are known to categorify generators of a cluster algebra. In this talk, I will explain how, by including band modules in this story, one can define a family of graded vector spaces which categorify Fock and Goncharov's canonical basis for the algebra of functions on an associated cluster variety. These vector spaces are of interest in mathematical physics, where they are expected to provide a mathematical definition of the space of framed BPS states from the work of Gaiotto, Moore, and Neitzke.
Mercoledì 19 giugno 2019
Ore 16:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Marielle Simon (INRIA, Lille)
Hydrodynamic limit for an activated exclusion process
In this talk we present a microscopic model in the family of conserved lattice gases. Its stochastic short range interaction exhibits a continuous phase transition to an absorbing state at a critical value of the particle density. We prove that, in the active phase (i.e. for initial profiles smooth enough and uniformly larger than the critical density 1/2), the macroscopic behavior of this microscopic dynamics, under periodic boundary conditions and diffusive time scaling, is ruled by a non-linear PDE belonging to the class of fast diffusion equations. The first step in the proof is to show that the system typically reaches an ergodic component in subdiffusive time. Joint work with O. Blondel, C. Erignoux and M. Sasada.
Giovedì 20 giugno 2019
Ore 14:30, Aula D'Antoni, Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
Algebra and Representation Theory Seminar
Kirill Zainoulline (University of Ottawa)
Hyperplane sections of Grassmannians and the equivariant cohomology
This is a joint work in progress with Martina Lanini. We study a family of hyperplane sections of Grassmannians from the point of view of the GKM-theory. Starting from the Schubert divisor which corresponds to the most singular section and has a natural torus action we provide a uniform description of the equivariant cohomology of the whole family of sections including the smooth one.
Giovedì 20 giugno 2019
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Ciclo di lezioni/corso di dottorato
Dejan Slepcev (Carnegie-Mellon University)
Variational problems on random structures: analysis and applications to data science - I
http://www.mat.uniroma2.it/~dott/Slepcev.html
Venerdì 21 giugno 2019
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Ciclo di lezioni/corso di dottorato
Dejan Slepcev (Carnegie-Mellon University, Pittsburgh)
Variational problems on random structures: analysis and applications to data science - II
http://www.mat.uniroma2.it/~dott/Slepcev.html
Venerdì 21 giugno 2019
Ore 15:00, Aula 311, Dipartimento di Matematica e Fisica Largo S. L. Murialdo, 1
Seminario di Analisi
Masahiro YAMAMOTO (The University of Tokyo)
Inverse problems for fractional partial differential equations
Fractional partial differential equations are recognized as useful model equations for several phenomena such as anomalous diffusions. For quantitative analyses, one has to estimate physical parameters governing fractional equations, which appears for example as orders of fractional derivatives, coefficients and source terms. Usually such physical parameters are not determined a priori but should be estimates by matching with available observation data of solutions. This type of problems belong to inverse problems and here we survey several types of inverse problems for partial differential equations with time-fractional derivatives.
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