Gautam Neelakantan Memana

Gautam Neelakantan Memana

I am a fifth year graduate student at UW Madison mathematics department. I am on job market this year. My research interests lie in harmonic analysis, partial differential equations, and geometric measure theory.

Before joining UW Madison, I was a student at Indian Institute of Science Education and Research Mohali in the BS-MS dual degree program with a major in mathematics.

Research

  1. A regularity theorem for maximally subelliptic PDE. ▼

    This paper establishes regularity results for solutions to maximally subelliptic partial differential equations. We prove that weak solutions exhibit improved regularity properties under natural geometric conditions, extending classical elliptic theory to the subelliptic setting.

  2. With S. Maity, Uniform Poincaré inequalities on measured metric spaces, manuscripta math. (2022). ▼

    We establish uniform Poincaré inequalities on measured metric spaces with controlled geometry. Our results provide quantitative bounds that are independent of the specific metric space structure, with applications to analysis on fractals and singular spaces.

  3. MS thesis at Indian Institute of Science Education and Research Mohali. ▼

    We prove that the Abel sums of the spectral projections of $L^p(H^n)$ functions on Heisenberg group($H^n$) converges to the function almost everywhere for $1$< $p$ <$ \infty$ and hence an extension of the $L^p$ spectral theory proposed by R. Strichartz('91). We prove our result by establishing the $L^p$ boundedness of the Littlewood-Paley $g$-function for the heat semi-group of $(−\mathcal{L}) (iT)^{-1}$, where $\mathcal{L}$ is the Heisenberg sublaplacian and $T=\frac{\partial}{\partial t}$.

Contact

Email: neelakantanm "at" wisc "dot" edu
Office: Van Vleck Hall 620, 480 Lincoln Dr, Madison, WI 53706

Teaching

Currently I am a TA for Linear Algebra (MATH 340).