PhD in Applied Mathematics 2021, Technion University, Israel
I received my PhD in Applied Mathematics from Technion University in Israel. I am broadly interested in how function emerges in biological systems from the myriad of interacting elements which constitute them. The state of this elementary ensemble evolves in a high-dimensional space; despite this, the emergence of function often entails a low-dimensional structure for the dynamics. Examples can be found in the simplest of organisms such as bacteria – when genetic networks control the process of cell division – and in complex animals, when neural networks in the brain represent task-related signals from their environment. In my research, I aim to elucidate the mechanisms underlying these compact representations: how they form, what are the properties of interaction between units which enable proper function, and how function is maintained stable over time. I use tools from dynamical systems theory and control theory to build and analyze mathematical models of biological networks; these include numerical simulation and formal analytical treatments, which enable derivation of simplified models that capture the essence of the phenomena under study. Currently, my interest is focused on representation and function in neural networks. Viewing representations via the lens of dynamics unfolding over time, my work shows that it is possible to quantitatively link between their properties and the success of learning.