Sahibzada Waleed Noor
Assistant Professor - University of Campinas (UNICAMP)
Sahibzada Waleed Noor began his doctoral studies in 2007 at the Abdus Salam School of Mathematical Sciences in Lahore, Pakistan and defended his thesis in 2012.
During this period he had the opportunity to stay at the University of Lille in France as part of a split-PhD fellowship with the French Embassy in Pakistan.
In 2013 he became a post-doctoral researcher at ASSMS and made a scientific stay at the mathematics section of the International Centre for Theoretical Physics (ICTP) in Trieste, Italy.
In 2014 he was offered a post-doctoral position at the University of Sao Paolo in Sao Carlos, Brasil and from 2016 to date he is a "Professor Doutor" (equivalent to assistant professor in the US system) at the University of Campinas (UNICAMP) in Brasil.
How would you define your field of study? What is your vision about it? Which are the topics you're most passionate about?
My research revolves around problems at the intersection of operator theory and complex analysis. In particular the focus is on using Hilbert spaces of holomorphic functions (such as the Hardy, Dirichlet and Bergman spaces) and the spectral theory of their operators as tools to investigate the relationships between seemingly unrelated open problems such as the Invariant Subspace Problem (ISP) in operator theory, the Riemann Hypothesis (RH) in analytic number theory, and the Periodic Dilation Completeness Problem (PDPC) in harmonic analysis.
How do you expect your experience in IMM to be? Why did you accept to teach for this project?
Almost all of my education from high school until the completion of my PhD took place in Pakistan. I am therefore a product of Pakistani education. I believe this gives me a good understanding of the experiences and challenges of mathematics students in Pakistan. I accepted to teach at the IMM program in order to share with students the many experiences I have had over the years. it is my hope that I can be a source of guidance for them. Personally speaking, I feel great excitement and an element of nostalgia in the possibility of "returning" to Pakistan and teaching at the same university where I myself was an undergraduate almost 15 years ago.
What is your teaching philosophy? What would you like to transmit to your students? How do you motivate them?
I believe that the best way to stimulate students towards a subject is to share with them the same child-like wonder and excitement oneself feels toward it. Rather than tell them that they have to wait many years before anything "mathematically significant" will be intelligible, I make an attempt to introduce them to some of the deepest mathematical mysteries of our times. For instance while introducing the rationals and real number in a first calculus course, I will introduce them to the "Continuum Hypothesis".
Similarly a discussion of integers and primes will be followed by a historical account of the "Prime Number Theorem". Such an approach creates excitement and makes students feel they are participating in an activity that has consumed the greatest of minds in human history.
Do you have one of two favorite quotes you would like to share and/or a personal “motto”?
"There is no such thing as a silly mathematical idea"..... Unknown
"Beauty is the first test: there is no permanent place in the world for ugly mathematics” ..... G. H. Hardy
"I sleep less so that I can live my dreams".......villain in the James Bond film "Die Another Day"
Selected Publications
(with Osmar R. Severiano) Complex symmetry and cyclicity of composition operators on H2(C+), Proc. Amer. Math. Soc. 148 (2020), 2469-2476.
A Hardy space analysis of the Báez-Duarte criterion for the RH, Adv. Math. 350 (2019) 242-255.
Complex symmetry of Toeplitz operators with continuous symbols, Arch. Math. 109 (2017), 455–460.
On an example of a complex symmetric composition operator on H² (D), J. Funct. Anal. 269 (2015), no. 6, 1899-1901.
Complex symmetry of composition operators induced by involutive ball automorphisms, Proc. Amer. Math. Soc. 142 (2014), no. 9, 3103–3107.
(with Dan Timotin) Embeddings of Müntz spaces: the Hilbertian case, Proc. Amer. Math. Soc. 141 (2013), no. 6, 2009–2023.