Bio: Alain Berthoz, neurophysiologist, engineer and psychologist is one of the leading specialists in integrative physiology and cognitive functions. He first located and analyzed the neural activities of eye control and renewed understanding of the relationships between the vestibular system and eye movement control networks. He highlighted the role of otoliths and semicircular canals in spatial orientation, as well as that of gravity and its changes during evolution. He also discovered the fundamental role of the head and the anticipation of the gaze in the guidance of locomotion and its pathology. He participated in the first spacecraft science experiments to study the effects of weightlessness on sensorimotor functions. He recently studied the neural bases of spatial memory, the use of non-Euclidean geometries for movement and navigation, and pointed out the neurological and psychiatric dysfunctions in children and adults. Finally he proposed on these various themes mathematical modeling and uses of the principles of living in humanoid robotics.
Abstract: I will describe recent brain imaging data concerning brain networks involved in the ability to “change perspective” and “point of view”. This cognitive ability is indeed fundamental to orient and navigate, but also for all high-level intellectual operations. I will describe new experiences and paradigms that track and measure child development and pathology in young people with autism, schizophrenia, visuo-spatial disorders, and even anorexia nervosa. She is involved in empathy and exchanging emotions with others and plays a vital role in pedagogy. It reaches the elderly and is therefore a complex and diversified trans-noso- graphical feature. Finally, data from neurology and brain imaging reveal that these treatments of space depend on the spatial scale and that the brain uses different geometries for the different spaces of the body, the immediate or the distant environment of action. The study of possible mathematical models of these different geometries will be exposed by Daniel Bennequin.
Bio: Daniel Bennequin studied at the Ecole Normale Supérieure (ENS) Ulm in Paris and defended his thesis at Paris VII under the direction of Alain Chenciner in 1982. He was a graduate student at ENS Ulm, Professor at University of Strasbourg, then at the University Paris VII where he is emeritus since 2018. During the 80s he was the initiator of the topology of contact with Yakov Eliashberg. During the 1990s, he worked on integrative systems and geometry in physics. Since 2000 Daniel Bennequin also works in neuroscience, on the time of human movements, the flow of visual-vestibular information, the relation form and function in the labyrinth, the role of gaze in locomotion, primary visual maps. His most recent publications focus on the geometry of elementary particles (Arxiv Physics 2016), the information topology (with P. Baudot), psychic pain (with M. Bompard-Porte), the geometries of topos of voluntary movements ( with A. Berthoz).
Abstract: To guide the adaptation of actions and perceptions, the brains of animals put in place a variety of geometries and dynamics. The presentation will present a mathematical framework, inspired by the theory of singularities of differentiable applications and Galois theory, according to om, Brieskorn and Looijenga, which shapes the relations between neuronal functions, their regulations and certain geometries. We will present some examples and conjectures about these constructions (spaces of colors or kinematics of movements of the body), involving the affine group and its subgroups. Then we will introduce a new kind of geometry, which takes into account the organization and control of most actions, and the need to combine several types of actions and perceptions: a topos of spaces above a category (site), following Grothendieck and Verdier, representing the preparation and the execution of a class of movements, and taking into account the physical dimensions; eg, prehension, locomotion, navigation, imagination, …. We will show how these dynamic structures connect with the flow of information and optimal learning.