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MATH AND INFLUENCE
VISUALIZING AND ANALYZING HUMAN COGNITION, DECISIONS, AND EMOTIONS
FRIDAY, APRIL 25, 2025
1 PM – 2 PM
ALKEK TEACHING THEATER
Reception with speaker in attendance follows the presentation
Open and accessible to the general public
Abstract:
Thoughts, decisions, and emotions shape our everyday lives, influencing everything from personal choices to societal trends. Yet, these processes are complex, often intangible, and difficult to measure. AI models attempt to replicate aspects of human decision-making by optimizing for specific rewards or targets, guiding outcomes toward predefined, or singular, objectives. However, their rigidity in often requiring a binary, black-and-white, outcomes make it challenging for AI to navigate the nuances of human emotions, shifting contexts, and the unpredictable nature of real-world decision-making. In contrast, human lives exist in shades of grey. People continuously learn, adapt, and balance multiple competing factors. This raises several important questions: What does it truly mean to learn and adapt to our surroundings? How do we determine whether decisions remain consistent over time? What other decision options are there? Can we detect whether data, shaped by these measurements, reflects human-like intent? More importantly, can we visualize and control individual decisions or outcomes? And what are the broader consequences of understanding these dynamics?
This presentation explores the mathematics behind sentiment and emotional regulation using balance theory techniques I have developed over the past 15 years. I will briefly share my journey in creating these techniques and how they bridge the theoretical and applied worlds. Through engaging visuals and real-world examples, we will see how these methods, by introducing more nuance —more “grey”— help bring clarity to the seemingly unpredictable nature of influence. I will discuss the universality of this approach, demonstrating its applications across psychology, crime pattern theory, epidemiology, voting behavior, business, education, physics, and beyond. Furthermore, we will examine how external influences can propagate through and shape the decisions we make, often in ways that are unseen but profoundly impactful.
Speaker: Dr. Lucas Rusnak
(click to expand) Dr. Rusnak has a PhD in Mathematics from Binghamton University and is Associate Professor of Mathematics at Texas State University.
He introduced oriented hypergraphs and hypergraphic balance theory, through which he provided a categorical unification of matrix algebra and hypergraphs. This allowed for exciting new generalizations for the Matrix-tree theorem, Kirchhoff’s Laws, and Laplacian dynamics. He also provided the first formula that calculates the solution to an 1893 conjecture for optimal matrices. The techniques to obtain these results also led to the discovery of sentiment-regulatory data science where Dr. Rusnak was a twice featured Innovator at South-by-Southwest (SXSW). He frequently collaborates with researchers at the NSA and has held a Health Research Fellowship. His contributions were recently featured in the book Higher Order Systems for motivating hypergraphic sentiment data analysis. Dr. Rusnak has supervised over 60 research students from the high school through the Doctoral level, and his research interests include anything that challenges the classical boundaries of mathematics, with a specific interest in graph theory, matrix theory, category theory and matroid theory.
Sponsored by: Department of Mathematics and Texas Mathworks.
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2022 – Math & Ethics: Algorithms, Fairness, and Social Good
2021 – Math & Epidemics: Mathematics, Data & Disease
2020 – Math & Politics: Graphs, Geometry & Gerrymandering
2019 – Math & Music: Creativity & Innovation
2018 – Math & Art: How To Mathematically Immerse Yourself in the Work of Art