### Discrete Structure Analysis

Department Head: Professor Akihiro Munemasa

In the Department of Discrete Structure Analysis, we mostly work on the mathematical analysis of combinational structures and their application. Specifically, we work on the paradigm of building an analysis for discrete structures with the utilization of big data at the forefront of our research. We work to contribute to the reliability of communications by creating a new theory of algebraic coding through our work on quantum codes and DNA codes.

#### New developments in algebraic coding theory

One of our new developments in algebraic coding theory is to use not only algebraic approaches to quantum codes and DNA codes, but to also incorporate computer-aided combinatorial analysis approaches to large, yet finite, objects. In doing this, we hope to create a completely new paradigm for the mathematical analysis for combinational structures.

#### Mathematical approach to large networks

We contribute to the mathematical foundation of large complex networks, its structure and dynamics, by combining both discrete and continuous mathematics. Applications are explored, for example, in gene expression in biological science, decision-making in social science, network-type big data in information science, and so forth.

We also work on research related to other fields such as computational mathematics (discrete geometry, computational learning theory), foundations of mathematics, in particular computability theory, algebraic geometry (algebraic cycles, motif theory, triangulated categories), number theory and its applications (algebraic varieties over finite fields, and cohomology).