**| ****February 27, 2019 | ****Theme: Mathematics **|

### Lecturer

Distinguished Professor **Vladimir Tonchev**

### Topic

*Coding Theory, Combinatorial Designs, and Finite Geometry*

TechTalks presented by the Department of Mathematical Sciences:

- Missy Keranen, Mathematical Sciences
- William Keith, Mathematical Sciences
- CK Shene, Computer Sciences

This special iteration of the Research Forum series will be a combination for a Distinguished
Lecture (20 minutes) and several TechTalks presentations (2 Minute. 2 Slides)

### Research Statement

Error-correcting codes are used to protect data from random errors in satellite and wireless communication systems, audio and video recording, and data storage. A large class of codes with many practical applications are based on finite geometry. The most notable example of such codes are the famous Reed-Muller codes that are being used in deep space and mobile communications. The subject of this talk is a class of codes based on combinatorial designs. These combinatorial codes posses remarkable error-correction properties, admit efficient decoding, and may provide a viable alternative to some of the Reed-Muller codes.

### Six Questions with Professor Tonchev

## Tech Talks -February 27, 2019

### Melissa Keranen, Department of Mathematical Sciences, "Combinatorial Designs and Graphs”

Combinatorial designs have their roots in the design of statistical experiments and in recreational math. In this talk, I will give a brief introduction to the ﬁeld of Combinatorial Designs and explain how you may have constructed a design without even knowing it! I will discuss how my research relates designs to graphs, and has applications to communication and coding theory.

### William Keith, Department of Mathematical Sciences,"Partitions Across Mathematics"

In how many ways can one divide half a dozen objects: four and two, three two and
one, and so forth? What if the divisions are constrained by desired properties?
These simple questions are the basis of partition theory, a subject that requires
a mix of cutting-edge mathematical techniques and creative intuition. The benefit
of studying such a fundamental object is that the results can inform many areas in
mathematics and other sciences: partitions index energy states in particle systems,
symmetric functions, irreducible representations, and a wide variety of other objects
where a counting is useful to have.

### CK Shene, Department of Computer Science, "Visualizing Everything in Computer Science - What We have Done

An old saying: "A picture is worth a thousand words" indicates that seeing is perhaps
a better way of understanding. The goal of ** Visualizing Everything in Computer Science** is to investigate ways of showing the unseen nature and inner working of important
topics/algorithms in computer science so that the hidden nature of an event could
be understood easily. To visualize, something has to be rendered by a computer.
This something is of course geometric. Consequently, how to make something into a
geometric object so that it can be rendered by a computer is a key question. The study
of geometric objects is an important topic in geometry and topology, standard topics
in mathematics. Therefore, visualization requires knowledge in computer science and
in mathematics. We have received several National Science Foundation grants for the
development of many tools and algorithms about visualization. This talk will discuss
briefly what we have done in the past 20+ years.