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KOUSHIK RAMACHANDRAN 

EMAIL : koushik "dot" tifrbng "dot" res "dot" in 

I am currently an Assistant Professor at TIFR Bangalore. 

From 2015-2018, I was a Visiting Assistant Professor at Oklahoma State University. Prior to that, in 2014-2015, I was a postdoc working with Siva Athreya in the Stat-Math unit of ISI Bangalore

I graduated with a Ph. D in Mathematics from Purdue University in May 2014. My thesis advisors were Alexandre Eremenko and Svitlana Mayboroda.

RESEARCH INTERESTS 

My research interests are in Complex Analysis, Potential theory, and Probability. I have worked on various quantities associated with the Laplacian (e.g Martin kernels, harmonic measures, and exit times of Brownian motion), and general Euclidean potential theory. I am currently thinking about analytic problems with a probabilistic flavor.

PUBLICATIONS 

1) Asymptotic behavior of positive harmonic functions in certain unbounded domains (Potential Analysis, Vol 41, Issue 2, (2014), 383-405).  PDF.

2) (with E. Lundberg) Electrostatic skeletons (Ann. Acad. Sci. Fenn. Math, Vol 40, (2015), 397-401) PDF
  
3) (with I. Pritsker) Equidistribution of Zeros of Random Polynomials (Journal of Approximation theory, Vol 215, (2017), 106-117).  PDF

4) (with E. Lundberg) The arclength and topology of a random lemniscate (Journal of the London Mathematical Society, Vol. 96, Issue 3, (2017) 621-641PDF

5) (with A.-K. Gallagher and J. Lebl) Convexity of level lines of Martin functions and applications (Analysis and Mathematical Physics, online first, (2018), DOI : 10.1007/s13324-017-0207-3PDF

6) (with S. Athreya) Harnack inequality for non-local Schrodinger operators (Potential Analysis, Vol 48, Issue 4, (2018), 515-551). PDF

7) (with I. Pritsker) Natural boundary and zero distribution of random polynomials in smooth domains (submitted) PDF

8) (with I. Pritsker) Random Bernstein-Markov factors (submitted).