Current and past fellows
Dr. Liviana Palmisano, Italy
Dynamical systems
I am an IMPACT posdoctoral fellow at Institute of Mathematics of PAN in Warsaw. I defended my Ph.D.-thesis "On the circle functions with a flat interval and Cherry flows" on 12 December 2013 at the Mathematical Department of the University of Orsay (Paris XI).My research work is essentially concentrated on dynamical systems in low dimensions. The centerpiece of my interest is a class of circle endomorphisms with a flat interval and its applications. The most interesting application is the study of a flow on the bi-dimensional torus: the Cherry flow. I study its topological, metrical and ergodic properties. This type of problems originate in theoretical physics, in particular in mechanics. My research can be considered to be at the interface between the more classical techniques in real dynamical systems theory and the more modern techniques in ergodic dynamics and theoretical physics.
At IMPAN there is an active research group in low dimensional dynamical systems. The research themes of this group corresponds very well to my current scientic interests concentrated on dynamics of the Cherry flows. My stay in Warsaw is provides me with a great opportunity to discuss and broaden my current research interests.
Period of stay: 13.01.2014-12.01.2016
Scientist in charge: Prof. Feliks Przytycki
Scientist in charge: Prof. Feliks Przytycki
Dr. Michal Doucha, Czech Republic
Department of Foundations of Mathematics
I studied at the Institute of Mathematics of the Czech Academy of Sciences and the Faculty of Mathematics and Physics of the Charles University in Prague under the supervision of Jindřich Zapletal. I am interested in applications of logic to other areas of mathematics. In particular, I specialize in descriptive set theory and countable and metric model theory. I try to follow the recent program of applying techniques from these disciplines to areas such as functional analysis, topological group theory, topological dynamics, etc., especially in cases where classical methods were not successful.My project in IM PAN consists mainly of extending the countable model theoretic methods (Fraïssé theory, Hrushovski construction,etc.), that were originally used to produce some countable discrete structures with certain properties, to a non-discrete metric (topological) context. Thus far, this led to constructions of certain universal Polish groups that are of interest to topological group theorists.
Another (closely related) activity is my search for a connection between model-theoretic properties of homogeneous structures and topological properties of their automorphism groups. A lot of research has been recently done on non-Archimedean Polish groups (closed subgroups of the permutation group of integers) as they precisely correspond to automorphism groups of ultrahomogeneous discrete countable structures. This correspondence turned out to be very useful. Similarly, general Polish groups correspond to automorphism groups of "almost ultrahomogeneous" metric structures, and this is a connection I plan to explore.
If one has a clear plan what to work on, and an idea how to approach problems he/she wants to solve (including optimism that it will work out), then working as an IMPACT-fellow enables him/her to fully focus on that project in a great working environment in IM PAN. There are no other duties than working on the project, and possibilities to travel and present results at conferences all year round.
Period of stay: 01.01.2014-30.06.2015
Scientist in charge: Dr. Marcin Sabok
Scientist in charge: Dr. Marcin Sabok
Dr. Van Luong Nguyen, Vietnam
Differential Equations
I am an IMPACT postdoctoral fellow at Institute of Mathematics of Polish Academy of Sciences. I was a former Marie Curie Ph.D fellow – under the SADCO project (website: http://itn-sadco.inria.fr/) - at the Department of Mathematics, University of Padova, Italy, under the supervision of professor Giovanni Colombo. I successfully defended my Ph.D thesis entitled: “On Regular and Singular Points of the Minimum Time Function” on September 24th, 2014. My thesis focuses on the regularity properties of the minimum time function for both linear and nonlinear control systems using techniques of non-smooth analysis and geometric measure theory.Another interesting topic I have worked on since I graduated from my undergraduate school is Fixed Point Theory and Its Applications. Specifically, together with some colleagues, we have proved various coupled fixed point and quadruple fixed point theorems in spaces with a partial order relation and presented their applications to the existence and uniqueness of solutions of integral equations and integro-differential equations.
My project at IMPAN mainly continues focusing on minimal time problem and, more generally, optimal exit time problems and related problems. In particular, I am going to study the regularity properties of the value function in more general setting.
In addition to offering me a great chance to work on my own research program, IMPAN is promisingly a global institution in an interconnected world. At IMPAN, there are different active groups working on different specific topics in control theory, e.g., geometric control theory, and stochastic control theory. Every researcher or fellow can naturally have great opportunities to discuss and broaden their current research interests in an inspiring and deeply rewarding educational enterprise.
Period of stay: 01.11.2014-31.10.2016
Scientist in charge: Prof. Bronisław Jakubczyk
Scientist in charge: Prof. Bronisław Jakubczyk
Dr. Réamonn O Buachalla, Ireland
Noncommutative Geometry
I obtained my PhD in mathematics in 2013 from the University of London, completed under the supervision of Prof. Shahn Majid. Subsequently, I spent two years as a postdoc of the Eduard Cech Institue at the Charles University in Prague. I started my current position at IMPAN at the beginning of 2015.My research lies in the intersection between quantum groups and noncommutative geometry. More specifically, I study the quantum flag manifolds as motivating examples for a possible theory of noncommutative complex geometry. My thesis was titled "Quantum Groups and Noncommutative Geometry".
IMPAN, given its long history of work on interaction between noncommutative geometry and quantum groups, is an ideal location for me to be based.
Period of stay: 01.01.2015-31.12.2016
Scientist in charge: Prof. Piotr M. Hajac
Scientist in charge: Prof. Piotr M. Hajac
Dr. Colin Mrozinski, France
Noncommutative Geometry
I completed my PhD in mathematics in December 2013, entitled "Fusion semiring of quantum groups" at University Blaise Pascal (Clermont II) under the supervision of Julien Bichon. Since then, I have been working at IMPAN, first with a local contract, and starting in September 2015, as an IMPACT fellow.My research interest are quantum groups and their representation theory. More precisely, my PhD was aimed to classify quantum groups according to some invariant coming from their representation theory. Also, a standard reconstruction procedure allows to construct new examples of quantum groups by prescribing their representation theory.
By its deep links with the history of quantum groups and the active life of its noncommutative geometry team, IMPAN is the place to be for my research interests.
Period of stay: 01.09.2015-29.02.2016
Scientist in charge: Dr. Adam Skalski
Scientist in charge: Dr. Adam Skalski
Dr. Karen Strung, Canada
Dynamical systems
My research focuses on the structure of separable nuclear C*-algebras with a specific interest in C*-algebras associated to dynamical systems, as well as the interactions between dynamical systems and operator algebras.I obtained my doctorate at Westfälische Wilhelms-Universität in Münster, Germany in January 2014 under the supervision of Wilhelm Winter. My thesis, ``On classification, UHF-stability, and tracial approximation of simple nuclear C*-algebras" focussed on classifing certain classes of C*-algebras. Since completing my doctorate, I have had postdoctoral positions at the Fields Institute in Toronto, University of Münster in Germany, and IMPAN in Warsaw.
I have been an IMPACT postdoctoral fellow since October 2015, where I work with the noncommutative geometry group.
Period of stay: 01.10.2015-30.09.2017
Scientist in charge: Dr. Tatiana Shulman
Scientist in charge: Dr. Tatiana Shulman