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My main research focuses on the study of differential and difference equations using algebra, geometry and model theory. So far I have contributed to furthering our understanding of the Painlevé equations, the logarithmic equations and equations for the covering maps (e.g. the j-function). The Painlevé equations appear in many physical applications including for example statistical mechanics, random matrix theory, general relativity and fibre optics. The other equations are at the heart of important problems in number theory and functional transcendence theory. My recent work is supported by the National Science Foundation (DMS-1700336). Some of the work below (at BCC) was also supported by a PSC-CUNY Research Award (Traditional A).
I
mentored Manzour Bakere under the Louis
Stokes Alliances for Minority Participation (LSAMP)
undergraduate research program for academic year
2017-2018. Here
is a link to his poster.
The Tenth Differential Algebra and Related Topics (DART-X) webpage.
Here's
a link to the videos of some of the talks
I have given recently: video.
Paper in preparation