Andrew Salch

Andrew Salch is an Associate Professor in the Department of Mathematics at Wayne State University's College of Liberal Arts and Sciences. His research bridges algebraic topology, number theory, and data science, with a focus on stable homotopy theory, formal groups, and topological methods for fMRI analysis. He mentors graduate students and develops computational tools for mathematical research.

Education:

• Ph.D. in Mathematics, University of Rochester (2008)
• M.A. in Mathematics, University of Rochester (2005)
• B.S. in Mathematics, Portland State University (2003)

Research Interests: Salch's work explores the interplay between homotopy theory and number theory, particularly via L-functions, Iwasawa theory, and formal modules. He also applies topological data analysis (TDA) to neuroscience, developing tools for fMRI data. His computational projects include Sage scripts for Morava stabilizer group actions and persistent homology workflows.

Publication Trends: His articles primarily address algebraic topology (e.g., Morava stabilizer groups, cobordism) and number-theoretic connections (e.g., zeta-functions, Iwasawa invariants). Recent work expands into fMRI data analysis using persistent homology and statistical inference, reflecting interdisciplinary collaboration.

Advising and Collaborations: He advises students like Mohammad Behzad Kang and collaborates with labs (e.g., Diwadkar Lab at WSU Medical School) on fMRI projects. His pure mathematics collaborations include work with Luca Candelori on topological modular forms and with Gabe Angelini-Knoll on homotopy limits.

Tools and Software: Salch develops open-source tools for topological data analysis (e.g., fMRI pipelines) and computational topology (e.g., Sage scripts for formal group laws). His seminar notes on modular forms and L-functions are publicly shared.