## Twenty Questions, Mastermind and Entropy

The speaker for the fall 2018 Howard Rowlee Lecture is Ruy Exel, currently a visiting professor of mathematics at Nebraska from the Universidade Federal de Santa Catarina. The lecture will be held at 4 p.m. Nov. 2 in Avery Hall, Room 115. All faculty, staff and students are welcome to attend.

#### Abstract

Imagine a table with a large number of objects of different colors, shapes, weights, sizes, flavors, smells … I’ll think of one of the objects and I’ll challenge you to guess it. You are allowed to ask what is the object’s color, or maybe its shape, which side of the table it is located or any other characteristic until you finally guess it. Which characteristic should you ask about first? If all objects are white, except for a red one, is it a good strategy to start by asking which color it is? If you get red as an answer, you win the game, but it is much more likely I’ll say white and you are back to square one!

The purpose of this lecture is to discuss, in a mathematically precise way, how to measure the value of information, leading up to the notion of entropy, and to show how it can be used to gauge how much information you should expect to get with each question in the above game, and also in games such as “Twenty Questions” or “Mastermind.” Should time allow, we will move on to other applications of these ideas, for example highlighting the famous Gibbs states of statistical mechanics which tell you how to compute the probability of each face of an uneven dice. Entropy is also highly relevant in physics, statistics, computer science, electrical engineering, natural language processing, cryptography, neurobiology, human vision, the evolution and function of molecular codes (bioinformatics), quantum computing, linguistics, plagiarism detection and pattern recognition.

## Symmetry in Mathematics

The speaker for the spring 2018 Howard Rowlee Lecture is Dave Benson, professor emeritus of mathematics at the University of Aberdeen in Scotland. The lecture will be held at 4 p.m. April 27 in Avery Hall, Room 115. All faculty, staff and students are welcome to attend.

#### Abstract

Benson’s talk, “Symmetry in Mathematics,” will discuss symmetry and cohomology of groups in nature, music, first-grade arithmetic, and crystallography.

#### About the Speaker

His research area is group theory, broadly interpreted, including the cohomology theory and representation theory of such, and the connections of these topics with algebraic topology, algebraic geometry and commutative algebra. Benson received his Ph.D. from Cambridge University under the direction of John Thompson and was a professor at the University of Georgia before moving to Scotland.

Early in his career, Benson was involved in the famed classiﬁcation of ﬁnite simple groups. He has nearly 150 publications to his name, including a popular two-volume manuscript on representation theory and cohomology. Benson is also the author of “Music: A Mathematical Oﬀering,” a 500-page treatise on the mathematics of music, including applications of groups to music theory. In 2017, Benson was elected as a Fellow of the Royal Society of Edinburgh.

There is also a one-day conference on Operator Algebras on Saturday, November 3rd.