Postdoctoral researcher in computational neuroscience ©

I got my Ph.D in Sydney, Australia. My achievements in the area of Higher Category Theory relate to four important aspects of it : I built higher operads for all weak higher transformations on the globular setting; I discovered a notion of fractal property which may be possessed by an ω-operad. Thanks to this notion, the difficult problem of the existence of the weak ω-category of weak ω-categories is replaced by a precise technical problem, which is to prove that a specific ω-operad of coendomorphism is contractible; I discovered the first algebraic models of (∞,n)-categories (for each n ∈ N): My models of (∞,n)-categories are algebras for specific monads on the category of globular sets. Recently I described in the IHES the first globular approach of Grothendieck ∞-topos. A paper related to this subject should be available soon. This approach is more natural than those proposed by Jacob Lurie using quasicategories for three reasons : First my ∞-toposes are very natural, in the sense that their constructions follow exactly the classical definition of Grothendieck toposes, just by using pure categorical methods. When truncated in the level 1, my ∞-toposes, provide exactly classical Grothendieck toposes. Secondly a notion of higher stacks emerged when we build it, which shows straight-away that our model of higher stacks do form an ∞-topos, where other didn’t prove such important fact. Also, our approach of Grothendieck ∞-topos is more general than those of Jacob Lurie, because he has built them with quasicategories which are well known models of (∞,1)-categories, whereas with our approach we use algebraic models of ∞-categories, where cells greater than 1 are not necessary invertibles. Very recently I found of a whole technical philosophy to build, probably, all kind of weak higher geometries by using natural models of higher moduli stacks under a suitable interaction between higher operads and some beautiful Quillen model structures. Sorry to say that, but my work must go beyond than those of Jacob Lurie, that I respect a lot, where applications of my approach much be much more easier and flexible for the future. At the moment I try to understand the simplicial approach of Lurie (unfortunately, even basics of simplicial sets is still mysterious for me at the moment; I will try to ask basics questions about it in this site) in order to be able to claim such thing. Last thing : I live alone in Paris (I am french). I have the Asperger Syndrom, which makes me difficult to apply anywhere, because I have some problems with applications, etc. My conditions (no moneys) makes me slow to interact, finish my work, etc. Also I do love other mathematics : Especially I had written a lot of manuscripts of others mathematics alone (Algebraic Geometry, Differential Geometry, Fiber Bundles, Measure Theory, Sets Theory, Forcing Methods, etc.) Please, feel free to contact me. ©

Masters candidate terminating in Semester 1 2019. ©