Clément Pernet Professeur Grenoble INP - UGA clement.pernet@univ-grenoble-alpes.fr

Grenoble INP - UGA, LJK - CAS3C3, Grenoble INP - UGA 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

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:

• a new matrix invariant, the rank profile matrix, and a characterization of the conditions on pivoting for a Gaussian elimination to reveal it. It finds a natural application in the field of rank structured matrices;
• a reduction of the complexity for computing the characteristic polynomial to that of matrix multiplication, with a probabilistic algorithm, and more recently a deterministic one.

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

• Coding theory applied to Algorithm Based Fault Tolerance.
• Interactive proofs, applied to two party verification protocols.
• Secure Multi-party Computations in linear algebra.
• Proof of retrievability.

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.