ZEROS, CRITICAL POINTS, AND COEFFICIENTS OF RANDOM FUNCTIONS

It has been a long journey- almost half a decade- and this journey would not have been possible without some truly exceptional and amazing people! I would first like to thank my advisor, Robin Pemantle, for guiding me through my years at Penn. He’s been incredibly helpful and encouraging and I’ve learnt a lot from him. Apart from being a prolific mathematician, he’s also an amazing human being, and it has been a great privilege to work with him. I was lucky to have Andreea Nicoara, Tony Pantev, Stephen Shatz, J. Michael Steele (Statistics) instruct me in courses that have formed strong foundations. I want to thank Philip Gressman and Andreaa Nicoara for stimulating discussions and helpful suggestions that changed the way I was thinking about my very first research problem and led to my first ever Eureka! moment. Also, I’m grateful to Andreea Nicoara and J. Michael Steele for serving on my orals ’ committee, and Jerry Kazdan and J. Michael Steele for being a part of my defense committee. In my second year at Penn, I was a teaching assistant to Jerry Kazdan and Nakia Rimmer and learnt a lot from them about teaching mathematics