In the second issue of bulletin of 2016, we present two articles with the recent trends in Dynamical Systems and in Numerical Analysis, an article about the Willmore Conjecture and the work of André Neves, as well as several summaries and reports of some of the activities partially supported by CIM. Inserted in the cycle of historical articles, we include a piece about the work developed by Pedro Nunes to celebrate the revival of the Pedro Nunes’ Lectures.

The Legacy of Claude Shannon
Tuesday - 13 December 2016, at 16:00 Salão Nobre, Instituto Superior Técnico, ULisboa, Portugal

The Centro Internacional de Matemática, in partnership with the Portuguese Mathematical Society and the Science Museum of the University of Coimbra, organized a one day international workshop on Literature and Mathematics, with the collaboration and support of the Centro de Matemática, Aplicações Fundamentais e Investigação Operacional of the University of Lisboa.
This initiative took place at the beautiful Bookstore santiago, on the occasion of the folio 2016 -  Óbidos International Literature Festival — organised and hosted by the medieval town of Óbidos

In the past days 15 to 17 June 2016, held the second edition of the so entitled Porto Meetings in Mathematics and Biology, with the promoting of the Faculty of Sciences of University of Porto, the Institute for Research and Innovation in Health (i3s),the Mathematics Center of the University of Porto (CMUP), andalso counted with the sponsorship of the CIM.

Jean-Pierre Bourguignon holds an engineering degree from École Polytechnique and a PhD in mathematical sciences from the University Paris VII. A differential geometer by training, he has since pursued his interest in the mathematical aspects of theoretical physics. He is the President of the European Research Council as of 1 January 2014. He was the Director of the Institut des Hautes Études Scientifiques (IHÉS) from 1994 till 2013 and president of the European Mathematical Society from 1995 to 1998

Pedro Nunes and the loxodrome
The 16th century was a period of great scientific and technological development in Europe. Portugal was no stranger to this general atmosphere, having developed new sailing techniques, which were necessary to navigate outside the Mediterranean, and below the Equator, where the North Star is not visible.

The great advances in computational mathematics over the last half century, driven by profound developments in numerical methods along with remarkable progresses in the field of high performance computing, are playing a major role in the scientific and engineering innovation.

Established in 1961, the Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society in recognition of a notable research memoir in geometry and topology. Presented every three years, this year’s edition of the prize distinguished the joint work of the Brazilian mathematician Fernando Codá Marques (Princeton University) and the Portuguese mathematician André Neves (Imperial College London), for their landmark achievement and major contribution to the use of variational methods in differential geometry, with a special highlight for the proof of the long-standing Willmore Conjecture.

After the notion of uniform hyperbolicity was coined in the seventies by Smale [26], it became the paradigm of chaotic dynamics. If, on the one hand, the local dynamics of a uniformly hyperbolic diffeomorphism is simple and conjugated to the one exhibited by linear saddles, on the other hand the global dynamics presents an unpredictable character due to sensibility to initial conditions, denseness of periodic trajectories and orbits with transitive and (ir)regular behavior. The geometric theory developed for uniformly hyperbolic dynamics guarantees the existence of local immersed submanifolds (called stable and unsta- ble manifolds) that are invariant by the dynamics and that constitute a crucial ingredient in the construction of finite Markov partitions. In consequence, subshifts of finite type can be used as combinatorial models for the dynamics and the powerfull techniques and ideas from statistical mechan- ics extend to this context. The geometric and functional analytic approaches (via construction of Markov partitions and the description of the spectrum of transfer operators, respectively) play a key role in the construction of physi- cal, Sinai-Ruelle-Bowen and equilibrium measures and the study of their statistical properties. We refer the interested reader to e.g. [5, 24] for a more complete account.

The International Conference on Semigroups and Automata (CSA 2016) was held in The Faculty of Sciences of the University of Lisboa, from the 20th to the 24th June 2016. CIM assumed the role of host institution.
This conference was organized with the purpose of celebrating the 60th birthdays of Professors Jorge Almeida (Univ. Porto) and Gracinda Gomes (Univ. Lisboa) for their extraordinary role over the years in the development of semigroup theory, in Portugal and abroad. Recognition of their work by the international community contributed decisively to achieve a record number of 117 participants for a semigroup conference and to the high quality of the program.

The conference Recent trends in Differential Equations held in Aveiro (Portugal) from 27 to 29 June, 2016, celebrated the 75th birthday of Professor Arrigo Cellina from the University Milano-Bicocca, Italy and the 60th birthday of Professor Alberto Bressan from Penn State University, USA.
Organized by the Functional Analysis and Applications group of the Center for Research and Development in Mathematics and Applications (CIDMA), and hosted by the Department of Mathematics of the University of Aveiro, the conference brought together mathematicians engaged in research on Differential Equations, Differential Inclusions and Set Valued Maps, Calculus of Variations, Control Theory and Applications. All these are areas where Professors Arrigo Cellina and Alberto Bressan have both made major contributions.