Erick HERBIN

Since 2011, as head of the department, I've been working to redefine the content of mathematics teaching. The aim was to strengthen the theoretical foundations for all students of Ecole Centrale Paris, which represented a real change for this engineering school. Advanced mathematics courses were defined for students wishing to specialize further in mathematics.
From 2015 to 2018, I was a member of the team led by John Cagnol that defined the new engineering curriculum, following the merger between Ecole Centrale Paris and Supélec. In particular, I was involved in identifying the characteristics of the engineer we wanted to train: endowed with strong abstraction and formalization skills.
What kind of mathematics for 21st-century engineers dealing with complex systems? Talk in French at IHP (may, 2018)

1st year (eq. Bachelor)	Lectures of Convergence, Integration, Probability (40h), since 2018
	In 2021, I'm handing over responsibility for this 900-student course to devote myself to an original format for a small group of selected students. In this Free Math Group, learning is centered on the objective of gaining a better grasp of concepts, and sessions are organized around presentations by the students.
	Lectures of Measure Theory, Hilbert and Fourier Analysis (25h), 2017-2018
	Lectures of Probability (25h), 2007-2018
	Tutorials of Real Analysis (20h), 2004-2016
	Tutorials of Probability and Statistics (20h), 1999-2006
2nd year (eq. Master 1)	Lectures of Advanced Probability (36h), since 2008
3rd year (eq. Master 2)	Lectures of Conformal invariance and Loewner evolution (30h), since 2022
	Lectures of Disordered Systems and Percolation (24h), 2015-2021
	Lectures of Brownian motion and stochastic calculus (with Jacques Lévy-Véhel, 30h), 2009-2014
	Lectures of Functional Analysis (20h), 2005-2006

In 2012, I initiated the creation of a Research program at Ecole Centrale Paris. The aim was to offer certain students the possibility of an apprenticeship-type curriculum, where they would spend 1 or 2 days a week in a research laboratory. They would work for 3 years on a real research topic, under the supervision of a mentor.
My 1st student in this program went on to a PhD under my supervision.

2023-2027	Hausdorff dimension of continuous random trees with irregular coding function
	(F. Miskdjian, Research program of CentraleSupélec).
2019-2021	Hausdorff dimension of continuous random trees constructed by aggregation
	(E. Gallière, Research program of CentraleSupélec).
2017-2021	Fractal dimensions of stochastic processes defined by scaling limits
	(A. Bois-Verdière, Research program of ECP).
2016-2020	Packing dimension of fractional processes
	(F. Bencherif, Research program of ECP).
2016-2019	Scaling limits and random matrices
	(T. Pham-Mariotti, Research program of ECP).
2016-2019	Hausdorff dimension of tangent stochastic processes
	(L. Gradt, Research program of ECP).
2015-2019	Link between local regularity of stochastic processes and Hausdorff dimension of their graph
	(J. Devianne, Research program of ECP).
2015-2016	Definition of set-indexed stochastic processes from projections on flows
	(Y. Thanwerdas, Research program of ECP).
2015-2016	Scaling limits and local regularity of stochastic processes
	(A. Bernardi, 3rd year student of Ecole Polytechnique).
2013-2017	Geometric properties of generalized stochastic processes
	(B. Hannebicque, Research program of ECP).
2013-2014	Hausdorff dimension of stochastic processes defined as Wiener integrals.
2012-2013	Integral representation of stationary processes indexed by functions,
	Hausdorff dimension of level sets of non-stationary Gaussian processes,
	Hausdorff dimension of Wiener integrals.
2010-2011	Geometrical properties of set-indexed Brownian motion,
	Hausdorff dimension of irregular multifractional Brownian motion,
	Convergence of discrete stochastic processes to fractional Brownian motion.
2009-2010	2-microlocal analysis of semi-martingales,
	Sample paths properties of irregular multifractional Brownian motion.
2008-2009	Local times and sample paths properties of Gaussian processes,
	Holder regularity and Hausdorff dimension of Gaussian processes.
2006-2008	Several projects on advanced probability.

2007-2011	Continuing education: "Engager une démarche incertitudes" (IMdR-LNE)
2008-2011	Continuing education: "Elaborer une démarche incertitudes" (IMdR-LNE)