It has been observed that motor neuron synapses in the worm C. elegans are remarkably evenly spaced, even during growth and development. In this work, we propose a novel mechanism for Turing pattern formation that provides a possible explanation for the regular spacing of synapses along the ventral cord of C. elegans during development. The […]

The Navier-Stokes existence and smoothness problem is one of the most important open problems in modern mathematics.   Ya. Sinai and D. Li have proposed a renormalization approach to constructing a counter-example to existence. In this approach, existence of  a blow-up solution (a solution whose energy becomes infinite in finite time) is equivalent to existence of fixed […]

Joint work with Larry Shepp & Philip Ernst In this paper we develop a mathematical model to address an ongoing politico-economic debate between Democrats and Republicans. Democrats in the US say that government spending can be used to “grease the wheels’ of the economy, create wealth, and increase employment; the Republicans say that government spending […]

I will discuss the concept of transfinite ζ-metrics. In some details I will discuss transfinite Apollonian metric in the settings of semi-metric spaces. I will discuss specific examples of domains where the transfinite Apollonian metric can be computed explicitly. This is a preliminary work.