Logic List Mailing Archive

PhD student position on semidefinite programming, Paris (France), Deadline: 31 Dec 2018

A PhD position is available in the joint INRIA, CNRS, and Sorbonne 
Université (LIP6) team PolSys (https://polsys.lip6.fr/) in Paris.  The 
position is funded by the ANR JCJC program GALOP (Games through the lens 
of ALgebra and OPtimization).

Scientific context:

Semidefinite programming (SDP) extends linear programming and has become a 
fundamental ingredient in polynomial and combinatorial optimization, 
complexity theory, game theory, quantum computing, control, signal 
processing, and computational finance. The standard tool to solve SDP 
problems is interior point methods. One of the current challenges is to 
exploit the underlying algebraic formulation to cope with the reliability 
issues of SDP and deduce more efficient algorithms.  For such a task, we 
should exploit the algebraic and geometric structure of the polynomial 
systems that correspond to the optimization problem.  With these algebraic 
and optimization tools, we can study the complexity of special classes of 
(continuous) stochastic games and obtain precise bounds.

We invite applications for a full-time PhD position for three years at the 
intersection of algebraic algorithms, optimization, and theoretical 
computer science, with a view towards applications in game theory.

A successful PhD candidate will work on one, or on a combination, of
the following topics:
- Deduce efficient algorithms and precise complexity and degree bounds
   for important classes of stochastic games based on algebraic
   formulations.
- Exploit the algebraic formulation of SDP to deal with
   reliability issues.
- Exploit the structure of polynomial systems, for example
   multi-homogeneity, sparsity, symmetry, properties of determinantal
   varieties, to introduce improved algorithms for Groebner basis
   and/or solving.
- Provide an efficient and certified open-source software for real
   solving univariate polynomials and polynomial systems.


Profile:

- MSc in computer science or (applied) mathematics.
- Strong background in algorithms, knowledge of complexity theory.
- Skills in a programming language like C or C++ is a definitely plus.
- High command of written and oral language.
- Ability to work in a team.


Application:

The application should include:
- Letter of interest.
- Scientific CV.
- Contact information of two references (Title, Name, organization, 
e-mail).

The starting date of the PhD is expected to be early 2019 or soon after.

Potential candidates should send their application or questions by the end 
of December 2018 to Elias Tsigaridas (elias.tsigaridas@inria.fr).
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