Clément Pernet

Clément Pernet

Maître de conférence UGA
clement.pernet@univ-grenoble-alpes.fr
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Univ. Grenoble Alpes, LJK - CAS3C3,

Université Grenoble Alpes
Laboratoire Jean Kuntzmann
700, avenue Centrale, Bâtiment IMAG
CS 40700
38058 GRENOBLE Cedex 09 - France

Office: 108
tel: +33 (0)4 57 42 17 97


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Research interests

Keywords:

Computational Linear Algebra, Computer Algebra, Complexity, Coding Theory, Fault Tolerance, Secure Multiparty Computation, Security of Outsourced Computing, Parallel Computing, exact computations, Mathematic Software.

My research involves three complementary areas:

Algorithms and complexity in exact linear algebra, and its applications.

My work concerns the computational aspects of linear algebra problems in general, and more specifically problems in exact linear alebra related to the matrix multiplication, rank (rank profile, rank structure), the characteristic polynomial and matrix normal forms. My two major contributions in the field are:

Security of outsourced computing

In the context of outsourced or multi-party computations, I develop protocols to ensure security in the broad sense (trust, privacy, proof of correctness, etc) of these computations. My approach focuses on efficiency in practice, by developing problem specific approaches to avoid overheads of the generic approaches. More precisely I contribute to

Mathematic software development.

I seek to develop algorithms combining theoretical and practical efficiency, and therefore propose in a rather systematic way, their implementations in largely distributed, mainstream libraries and software. I am mainly working on 3 open-source software projects: FFLAS-FFPACK, a package of routines for dense linear algebra over a finite field; LinBox, a library for exact linear algebra over a finite field or integers; SageMath, a general purpose mathematic software.