Asymptotically Free Memories

I am applied mathematician specialising in functional analysis, complex analysis in multiple variables, probability theory and geometric deep learning. I am presently  based at the Collège de France  and CNRS as a researcher in AI and research engineer in the Multiscale Physics of Morphogenesis group lead by Prof. Hervé Turlier at the Centre Interdisciplinaire de Recherche en Biologie (CIRB). Before this I worked in Porto in Portugal as a research scientist in geometric deep learning. 

Prior to this, I completed my Ph.D in the area of quantum integrable systems (a very short introduction is given in here) from the Ecole Normale Supérieure de Lyon in France, supervised by Prof. Karol K. Kozlowski. 

My present research focusses on developing and formalising certain aspects of high-dimensional probability theory of combinatorial optimisation (CO). In particular, I am interested in the characterisation of the search space of said CO problems as adequate metric spaces that approximate Riemannian manifolds. The value of such work is to formalise the understanding dimensional reduction in geometric deep learning and to further understand the construction of adequate metric spaces of high dimensional data rigorously.

I am also interested in understanding optimal transport (OT) based approaches for optimisation on manifold of fixed-rank positive semi-definite (PSD) matrices. The value of this research is to provide better understanding of OT based optimisation approaches for non-convex problems in a first instance.

I also occasionally share about my hiking trips (places, routes, equipment, etc…) :).

You can reach me directly by email at goomanee.salvish@gmail.com or find me on LinkedIn.