Speaker: Javier Morales (University of Maryland) -

Abstract: http://www.terpconnect.umd.edu/~lvrmr/2017-2018-F/Classes/RIT.shtml

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Speaker: Vladimir Matveev () - http://users.minet.uni-jena.de/~matveev/

Abstract: I will mostly speak about Finsler metrics of positive constant ﬂag curvature (I explain what is it) on closed 2-dimensional surfaces. The main result is that the geodesic flow of such a metric is conjugate to that of a Katok metric (recall that Katok metrics is are easy and well-understood examples of two-dimensional Finsler metrics of positive constant ﬂag curvature). In particular, either all geodesics are closed, and at most two of them have length less than the generic one, or all geodesics but two are not closed; in the latter case there exists a Killing vector field. Generalizations for the multidimensional case will be given; in particular I show that in all dimensions the topological entropy vanishes and the geodesic flow is Liouville integrable. I will also show that in all dimensions a Zermelo transformation of every metric of positive constant flag curvature has all geodesics closed. The results are part of an almost finsihed paper coauthored with R. Bryant, P. Foulon, S. Ivanov and W. Ziller.

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Speaker: Vladimir Matveev (Friedrich-Schiller-Universität Jena ) - http://users.minet.uni-jena.de/~matveev/

Abstract: We introduce a construction that associates a Riemannian metric $g_F$ (called the

Binet-Legendre metric) to a

given Finsler metric $F$ on a smooth manifold $M$. The transformation

$F \mapsto g_F$ is $C^0$-stable and has good

smoothness properties, in contrast to previously considered

constructions. The Riemannian metric $g_F$ also behaves nicely under

conformal or isometric transformations of the Finsler metric $F$ that

makes it a powerful tool in Finsler geometry. We illustrate that by

solving a number of named problems in Finsler geometry. In particular

we extend a classical result of Wang to all dimensions. We answer a

question of Matsumoto about local conformal mapping between two

Berwaldian spaces and use it to investigation of essentially conformally Berwaldian manifolds.

We describe all possible conformal self maps and all self similarities

on a Finsler manifold, generasing the famous result of Obata to Finslerian manifolds. We also classify all compact conformally flat

Finsler manifolds. We solve a conjecture of Deng and Hou on locally

symmetric Finsler spaces. We prove smoothness of isometries of Holder-continuous Finsler metrics. We construct new ``easy to calculate''

conformal and metric invariants of finsler manifolds.

The results are based on the papers arXiv:1104.1647, arXiv:1409.5611,

arXiv:1408.6401, arXiv:1506.08935,

arXiv:1406.2924

partially joint with M. Troyanov (EPF Lausanne) and Yu. Nikolayevsky (Melbourne).

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Speaker: George Tsironis (U of Crete)

"Macroscopic quantum devices are becoming reality not only for computational purposes but also as sensors and for other general applications In this talk we will focus on superconducting technology and analyze the emergence of coherence in coupled networks of meta-atoms made of units such as SQUIDS and Josephson junctions. These networks may operate classically in a negative permeability regime[1], induce intrinsic nonlinear localized modes and partial coherence in the form of chimeras[2], tame disorder through hysteretic loops or transmit through nonlinear frequency bands. In the quantum regime, on the other hand, meta-atoms may interact through injected electromagnetic fields and form propagating “quantum breathers”, i.e. compound semi-classical propagating modes induced by the nonlinearity of the qubit-field interaction [3]. These coherent modes generate self-induced transparency in the medium and in certain cases may also induce super-radiance.

[1] N. Lazarides and G. P. Tsironis, rf SQUID metamaterials, Appl. Phys. Lett. 90, 163501 (2007).

[2] N. Lazarides, G. Neofotistos, and G. P. Tsironis, Chimeras in SQUID metamaterials, Physical Review B 91, 054303 (2015).

[3] Z. Ivic, N. Lazarides, and G. P. Tsironis, Qubit lattice coherence induced by electromagnetic pulses in superconducting metamaterials, Scientific Reports 6, 29374(2016)."

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Speaker: Rob Stevenson (University of Amsterdam) - https://staff.fnwi.uva.nl/r.p.stevenson/

Abstract: We consider a Fictitious Domain formulation of an elliptic PDE, and solve the arising saddle-point problem by an inexact preconditioned Uzawa iteration.

Solving the arising `inner' elliptic problems with an adaptive finite element method, we prove that the overall method converges with the best possible rate.

So far our results apply to two-dimensional domains and lowest order finite elements (continuous piecewise linears on the fictitious domain, and piecewise constants on the boundary of the physical domain).

Joint work with S. Berrone (Torino), A. Bonito (Texas A&M), and M. Verani (Milano).

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