## Clément PernetProfesseur Grenoble INP - UGAclement.pernet@univ-grenoble-alpes.fr |
Grenoble INP - UGA,
LJK -
CAS^{3}C^{3},
Grenoble INP - UGA
Office: 108 |

My research involves three complementary areas:

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.

- 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.

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.