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, Parallel Computing, exact computations, complexity, Mathematic Software, Coding and Fault Tolerance, Security of Outsourced Computing

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:

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.

Security and fault tolerance in distributed environment

In the context of outsourced or multi-party computations, we develop protocols to ensure security of these computations (trust, privacy, proof of correctness, etc). Our approach focuses on efficiency in practice, by developping problem specific approaches to avoid overheads of the generic approaches.