# Journal

I gave an invited talk on “Generalized Hamiltonian Monodromy and Circle Actions” at the conference on Integrable Hamiltonian Systems that took place in Ascona from 19 to 24 June 2016. The conference was organized by Anton Alekseev, Sonja Hohloch, and Tudor Ratiu.

Monodromy in Hamiltonian systems has been traditionally associated to singularities of the integrable Hamiltonian fibration and, in particular, to singularities of focus-focus type. In a recent work with Nikolay Martynchuk, we showed that in 2 degree of freedom Hamiltonian systems with a circle action, to understand monodromy, one should look at the fixed point of the circle action. This result follows from the fact that, in such systems, a 2-torus bundle $E$ over a circle $\Gamma$ can be also viewed as a principal circle bundle over a 2-torus $B$.

At the end of October I will be in Chicago. On 26 October I am giving a seminar on recent results on monodromy at the Geometry, Topology and Dynamics Seminar at the University of Illinois at Chicago. From 25-30 October I am attending Vis2015 where we present our most recent work on particle selection.
After Chicago I fly to Japan. First, to Kobe for SIGGRAPH ASIA 2015 and then, on 6 November, I will visit Kyoto University where I am giving an extended talk at the Kyoto Dynamical Systems Seminar.

A few years ago together with Lingyun Yu and Petra and Tobias Isenberg we presented CloudLasso, a method for selecting clusters in 3D particle data. We now introduce the CAST methods, novel context-aware algorithms for particle selection. For example, with PointCast one can select a whole particle cluster with a single mouse-click or touch; the algorithm infers an appropriate selection that can then be fine-tuned. For more details, check the paper and video.

Filippov systems are dynamical systems with discontinuities. They are being used to model the dynamics in cases where there is very rapid transition between different dynamical regimes. For example, if in a predator-prey system the number of prey crosses a threshold then the predation rate can increase discontinuously.
As the simplest case of a Filippov system one can consider a two-dimensional dynamical system where the phase space is separated into two regions.

From mid-April until mid-May 2015 I will be at Fudan University as a Senior Visiting Scientist at the Shanghai Key Laboratory of Contemporary Applied Mathematics. There I will be working with Prof. Lin Wei on the dynamics of pulse coupled oscillator networks.

I wrote a short article for the Nieuw Archief voor Wiskunde that appeared in the March 2015 issue. The article offers a bird’s eye view of my research, experiences, and aspirations.
The pictures of the Hopf fibration and the curled torus look much better in color; you can see them below.

Vacancy: PhD position Topic: Symmetry in classical mechanics Affiliation: University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science, Dynamical Systems and Mathematical Physics group Supervisor: Dr. Konstantinos Efstathiou Job description The PhD candidate will study the effect of symmetry on the dynamics and geometry of Hamiltonian systems and work on applications to physical problems. The position includes light teaching duties.
Requirements Candidates should hold an MSc degree in mathematics, applied mathematics, physics, or related fields.

Since mid-April I am Assistant Professor at the Johann Bernoulli Institute for Mathematics and Computer Science at the University of Groningen.

Our paper with Henk Broer on using covering spaces for proving, and better understanding, fractional monodromy has now been accepted for publication in Communications in Mathematical Physics. Fractional monodromy is a geometric property of integrable Hamiltonian fibrations which generalizes standard Hamiltonian monodromy. In this paper we show that by passing to an appropriate covering space the geometry of the fibration is considerably simplified allowing us to prove fractional monodromy for a very wide class of resonant Hamiltonian systems.

Since 1 February 2013 I am Lecturer (Assistant Professor) at the Department of Mathematical Sciences of Xi’an Jiaotong - Liverpool University.

TLDR: https://efstathiou.gr/unlinked/standard-map.
In the context of an introductory lecture on Hamiltonian systems it is interesting to demonstrate several phenomena related to perturbing an integrable Hamiltonian system: Poincaré-Birkhoff chains, stability islands, the persistence and destruction of invariant tori, the consequent transition to global stochasticity, homoclinic and heteroclinic tangles and the Smale horseshoe, and many more. The standard map is a great playground for exploring these phenomena.
Nevertheless, presenting only a static sequence of phase portraits would be a great injustice to the richness of the dynamical behavior that can be exhibited by Hamiltonian dynamical systems in general, and the standard map in particular.