**Detecting disease from brain signals – Mathematics in brain research**

*Jianzhong Su, Professor and Chair, Department of Mathematics, University of Texas at Arlington*

Mathematics plays an increasing role in brain research and medicine. The well-known Hodgkin-Huxley model for neurons laid a foundation for computational neuroscience. However, understanding activities in the whole brain remains a focus of active research. Full brain Electroencephalography (EEG) and its source localization is a brain imaging modality based on multi-channel EEG signals. It measures the brain field potential fluctuations on the entire scalp for a period of time, and then we can mathematically calculate the electric current density inside the brain by solving an inverse problem for a partial differential equation. In this talk, we introduce mathematical methods for the EEG imaging problems and discuss its applications. One application is in identifying abnormality in brain activities during seizures of an infant patient with Glucose Transporter Deficiency Syndrome. Another application is to find the neuronal signatures in response to pain stimulations. Our research shows these brain data can be further used to study the brain properties that glean into the inner working of brain functions using mathematical and statistical tools.

*Illya V. Hicks, Computational and Applied Mathematics, Rice University*

Graphs or networks are everywhere and network analysis has garnered significant attention in diverse fields as an effective tool for studying complex, natural and engineered systems. Novel network models of data arising from internet analytics, systems biology, social networks, computational finance, and telecommunications have led to many interesting insights. In this talk, we explore discrete optimization techniques for finding cohesive data within these network-based models. The goal is to detect cohesiveness in spite of missing information (linkages). In this regard, we will explore different aspects of cohesiveness and how they are used for different applications.

**The greatness of mathematics**

*Natalie Hritonenko*, *Department of Mathematics, Prairie View A&M University *

** **This talk explores magic and versatility of mathematics providing numerous examples. Importance and challenges of mathematical modeling will be also discussed. Using her diverse interdisciplinary expertise, the speaker will go over comprehensive mathematical concepts and present applications of mathematics in describing various real-life phenomena and solving open problems in economics, biology, and environmental sciences.

**An Introduction to Operator Algebras (or How to do Linear Algebra in Infinite Dimensions)**

*Mark Tomforde, Department of Mathematics, University of Houston*

Abstract: As an undergraduate student, you have probably studied n x n matrices in your Linear Algebra class and discovered that multiplication by such a matrix is a linear transformation (or operator) on the n-dimensional vector space R^n. The n x n matrices can be added, multiplied, or scalar multiplied by a real number, and these operations make the set of n x n matrices (i.e., the operators) into an object known as an “algebra”. In this talk I’ll discuss an active area of mathematical research, known as “Operator Algebras”, in which one studies algebras of operators on (possibly infinite-dimensional) vector spaces. I’ll present a few of the different kinds of operator algebras that mathematicians have found interesting. I’ll also explain some of the major results for operator algebras and describe how these results have found applications to other areas of mathematics.