Julien Bernat

Julien Bernat is a Lecturer in Mathematics at the University of Lorraine, specifically at INSPÉ (National Higher Institute for Teaching and Education) of Lorraine, where he has held teaching and research positions since 2007. He is affiliated with the Analysis and Number Theory research team at IECL (Institut Élie Cartan de Lorraine), a joint research unit of CNRS and the University of Lorraine.

Bernat's research centers on non-standard number systems, aperiodic structures, and word combinatorics. His work bridges theoretical computer science and pure mathematics, with significant contributions to β-numeration systems, substitution dynamics, fractal geometry of number representations, and combinatorial properties of infinite words. Key methodologies include geometric modeling of substitutions, analysis of aperiodic tilings, and computational approaches to Pisot number systems.

His publication record from 2006-2011 reveals consistent focus on the intersection of number theory and discrete structures. Dominant themes include geometric interpretations of substitution systems, topological properties of β-integers, factor complexity of infinite words, and arithmetic operations in non-standard numeration. The research demonstrates strong connections between abstract combinatorics and concrete geometric realizations, particularly in fractal set theory.

Beyond research, Bernat holds substantial educational responsibilities as coordinator for mathematics at INSPÉ's Nancy site and head of the M2 MEEF mathematics program. He actively develops mathematical outreach through the IREM group "games in the teaching of mathematics," creating innovative activities like "well-colored squares," "escape of the clones," and particle dynamics demonstrations that make advanced concepts accessible.

His public engagement includes science festival presentations on mathematical paradoxes, knot theory, and societal roles of mathematics, alongside publications in outreach journals like "Découverte" and "le Petit Vert" covering polyominoes, quadrilaterals, and mathematical divination techniques.