Page 55 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 55
INVITED SPEAKERS
reduced modeling strategies for complex physical problems described by parametric problems.
This lecture will first review two significant results in this area that concern (i) the practical con-
struction of optimal spaces by greedy algorithms and (ii) the preservation of the rate of decay
of widths under certain holomorphic transformation. It will then focus on recent attempts to
propose non-linear version of n-widths, how these notions relate to metric entropies, and how
they could be relevant to practical applications.
An invitation to Poisson Geometry
Marius Crainic, m.crainic@uu.nl
Utrecht University, Netherlands
Poisson structures originate in the work of Lagrange and Poisson on the motion of planets in
the solar system; the process of understanding them was long and it prompted the discovery
of several fundamental concepts in mathematics, such as: Jacobi identity, Maurer-Cartan equa-
tions, etc. Poisson Geometry (the geometric study of Poisson structures) can be traced back to
the work of Lie and Kirilov; the first systematic studies are found in the work of Lichnerowicz
in the 1970s and Weinstein in the 1980s. Its remarkable development over the last few decades
was driven by several problems (such as integrability or Conn’s linearization theorem) and led
to surprising new connections with various other fields. All these led to the present-day un-
derstanding of Poisson Geometry: it is an amalgam of Lie Theory, Symplectic Geometry and
Foliation Theory, offering the framework for exciting interactions between these theories, as
well as others. In the talk I will try to expand this abstract.
Tackling discrete optimization problems by continuous methods
Mirjam Dür, mirjam.duer@math.uni-augsburg.de
Augsburg University, Germany
Many NP-hard discrete and combinatorial optimization problems can be formulated with the
help of quadratic expressions. These in turn can be linearized by lifting the problem from
n-dimensional space to the space of n by n matrices. We show that this leads to a conic opti-
mization problem, i.e., an optimization problem in matrix variables where a constraint requires
the matrix to be in the cone of so called copositive or completely positive matrices. The com-
plexity of the original problem is entirely shifted into the cone constraint. We discuss the pros
and cons of this approach, and we review the state of the art in this area, covering both theory
and numerical solution approaches.
Modelling the genetics of spatially structured populations
Alison Etheridge, etheridg@stats.ox.ac.uk
University of Oxford, United Kingdom
The last century has seen remarkable developments in the nature and scale of genetic data,
and the tools with which to interrogate them. Nonetheless fundamental questions remain unan-
swered. The genetic composition of a population can be changed by natural selection, mutation,
53
reduced modeling strategies for complex physical problems described by parametric problems.
This lecture will first review two significant results in this area that concern (i) the practical con-
struction of optimal spaces by greedy algorithms and (ii) the preservation of the rate of decay
of widths under certain holomorphic transformation. It will then focus on recent attempts to
propose non-linear version of n-widths, how these notions relate to metric entropies, and how
they could be relevant to practical applications.
An invitation to Poisson Geometry
Marius Crainic, m.crainic@uu.nl
Utrecht University, Netherlands
Poisson structures originate in the work of Lagrange and Poisson on the motion of planets in
the solar system; the process of understanding them was long and it prompted the discovery
of several fundamental concepts in mathematics, such as: Jacobi identity, Maurer-Cartan equa-
tions, etc. Poisson Geometry (the geometric study of Poisson structures) can be traced back to
the work of Lie and Kirilov; the first systematic studies are found in the work of Lichnerowicz
in the 1970s and Weinstein in the 1980s. Its remarkable development over the last few decades
was driven by several problems (such as integrability or Conn’s linearization theorem) and led
to surprising new connections with various other fields. All these led to the present-day un-
derstanding of Poisson Geometry: it is an amalgam of Lie Theory, Symplectic Geometry and
Foliation Theory, offering the framework for exciting interactions between these theories, as
well as others. In the talk I will try to expand this abstract.
Tackling discrete optimization problems by continuous methods
Mirjam Dür, mirjam.duer@math.uni-augsburg.de
Augsburg University, Germany
Many NP-hard discrete and combinatorial optimization problems can be formulated with the
help of quadratic expressions. These in turn can be linearized by lifting the problem from
n-dimensional space to the space of n by n matrices. We show that this leads to a conic opti-
mization problem, i.e., an optimization problem in matrix variables where a constraint requires
the matrix to be in the cone of so called copositive or completely positive matrices. The com-
plexity of the original problem is entirely shifted into the cone constraint. We discuss the pros
and cons of this approach, and we review the state of the art in this area, covering both theory
and numerical solution approaches.
Modelling the genetics of spatially structured populations
Alison Etheridge, etheridg@stats.ox.ac.uk
University of Oxford, United Kingdom
The last century has seen remarkable developments in the nature and scale of genetic data,
and the tools with which to interrogate them. Nonetheless fundamental questions remain unan-
swered. The genetic composition of a population can be changed by natural selection, mutation,
53
