Shannon Centenary

Abstract: We understand complex systems around us though predictive modelling – building algorithms that generate future predictions when given relevant past information. Each model encapsulates a way of understanding future expectations through past observations. In the spirit of Occam’s razor, the better we isolate the causes of what we observe, the greater our understanding. This philosophy privileges the simpler models; should two models make identical predictions, the one that requires less input information is preferred.
Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. This waste creates a significant overhead in memory costs when one seeks to use such models to simulate the world around us – one that becomes increasingly prohibitive as we seek to understand ever more complex systems. In this presentation, will introduce how information can behave differently in the quantum world, and why this allows us to systematically construct quantum models that surpass classical limits.
(No quantum background necessary, accessible to advanced undergrads )

Abstract: Information theory is an area of study which sits at the intersection of engineering, applied mathematics, and computer science. This talk will provide a gentle introduction to information theoretic ideas and connections to diverse areas such as wireless communications, languages, gambling, and life sciences. Along the way, we will discuss the life and times of Claude Shannon who is considered to be the father of information theory. Shannon was an engineer from Bell Labs, USA who established the mathematical foundations of the information age, helping to understand the basics of communication, computing, and cryptography. The talk should be accessible to a fairly wide audience, including undergraduate students, graduate students, and even members of the general public.

Abstract: As Hardy once put it, "there is no permanent place in the world for ugly mathematics". Conversely, there is always a place for fun mathematics particularly as a tool for explaining the crux of problems. Shannon was among the best proponents of this line of thinking. Indeed, the greatest homage to him is the extent to which simple abstractions pervade information theory even today. These abstractions, while elegant and simple to state, are sometimes very hard to solve. But they always capture something at the core of a physical, practical problem we want to solve. We will look at a series of puzzles of varying difficulties that highlight the research we are working on at the University of Hawaii today. These puzzles will be self contained, and we will go over how they dovetail into statistical problems underlying probabilistic modeling and community detection. These puzzles are used in the Open Houses we host at University of Hawaii for a broader audience, not necessarily in engineering. However, sections of the talk that delve deeper into these puzzles are meant for students at the upper division undergraduate and graduate level.