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Talks & Seminars
Title: Mathematics, Proofs and Computation
Prof. Madhu Sudan, Harvard University
Date & Time: January 7, 2015 04:00
Venue: Center for Basic Sciences, Kalina Campus, Mumbai University
Abstract:
While it is well-understood that Proofs form the foundations of Mathematics, it is less well-known that Proofs and Computers are intimately related. Indeed a common perception is that the only link between Proofs and Computing is that sometimes computers can assist in the search for proofs. In this talk I will describe a more historically significant, and intrinsic, connection. Proofs are by definition "Computational Objects" - and to understand to the difference between a theorem and its proof, one needs to understand computational complexity of tasks - namely the number of steps on a computer needed to solve a given task. In this talk, I will talk about the historical role of proofs in computation, leading to the "prototype" of the modern computer in the 1930s, to the conception of the famous "Is P = NP?" question in the 1970s and some modern variation like interactive proofs, zero-knowledge proofs and probabilistically checkable proofs. I will explain how at each stage the study of proofs has revolutionized our understanding of what computers can or can not do!
Speaker Profile:
Professor Madhu Sudan is from the Computer Science department at Harvard University. Professor Sudan has a large body of highly influential work in many areas of Theoretical Computer Science, including Error Correcting Codes, Probabilistically Checkable Proofs, and Property Testing. He has been the recipient of many awards, notably the Nevanlinna Prize awarded in 2002, and the Infosys Prize awarded in 2014. Professor Sudan has recently been offered the Jubilee Professorship by Indian Academy of Sciences. The distinguishing feature envisaged in this professorship is that students, teachers and researchers from India should draw maximum benefits and inspiration by their close interaction with Jubilee Professor. Professor R. K. Shyamsundar, CSE department, IIT Bombay, has been instrumental in coordinating this visit.
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