Summer Conference on Topology and Its Applications 2025

About This Grant

This award supports participation in the 39th Summer Conference on Topology and Its Applications (SUMTOPO 2025) taking place August 11-15, 2025 at the University of South Alabama in Mobile, Alabama. Topology is an area of mathematics that emerged from analysis and geometry as its own discipline in the late 19th century. It has since become a foundational discipline of mathematics, underlying many other areas of mathematics as well as the application of mathematics to the sciences, including logic, computer science, data science, life sciences, game theory, and category theory. As the thirty-ninth event in its series, SUMTOPO 2025 will be an important international event, held in the EPSCoR state of Alabama, that reflects the ever-expanding world of topology and its applications, with sessions dedicated to low-dimensional topology, dynamics and continuum theory, topological graph theory, set-theoretic topology, and interactions with computing. Participants will comprise a diverse group of established researchers, junior researchers, and graduate students, with special emphasis on recruiting speakers and participants from populations underrepresented in STEM. SUMPTOPO 2025's session on Low-Dimensional Topology will feature talks related to knot theory and low-dimensional topology, which have seen recent invigoration through the interaction of different techniques from algebra, geometry, combinatorics, and representation theory, where breakthroughs have often resulted from exchanging tools between fields to resolve outstanding problems. A session on Topological Dynamics and Continuum Theory will feature the study of continua (a topological space that is connected, compact and Hausdorff, and often metric as well) and the continuous mappings between them, as well as dynamical systems, including the study of iterates of a continuous map from a topological space to itself. In recent years there has been increasing interaction between mathematicians working in continuum theory and dynamical systems; in particular, continua arise naturally in the study of the topology and dynamics of one-dimensional and planar systems. In Topological Graph Theory, participants will explore how graphs can be embedded in the 3-dimensional space and on surfaces. This area features several important topics, including the Hadwiger Conjecture, the Colin de Verdière mu invariant, outerplanarity, planarity, and linkless embeddability. The Set-Theoretic Topology session will focus on the study of techniques from set theory that are used to investigate topics in general topology. Such topics include topological games, homogeneity, hyperspaces, topological algebra, compactifications, and much more. Problems about topological topics or properties often require extra axioms of set theory to answer; advances in set theory, conversely, have applications in general topology. Finally, a special session on Topology and Computing will be featured at SUMTOPO 2025 to showcase and disseminate the growing applications of computing for topology, as well as applications of topology on computing, broadly construed. Any research related to both topology and computing will be welcome, including but not limited to, topological data analysis, formalization of topology, applications of artificial intelligence and machine learning on topology, and more. More information may be found on the conference website at https://www.southalabama.edu/colleges/artsandsci/mathstat/sumtopo.html This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.