Post-Doctoral Associate - SME

Postdoctoral Research Associate: Mathematical and Topological Foundations of Knowledge Analysis in the Science of Science
Carlson School of Management, University of Minnesota

We are seeking a motivated Postdoctoral Research Associate to join a project at the Carlson School of Management, University of Minnesota, working with Professor Russell Funk. This position focuses on developing and applying mathematical and computational methods to understand how scientific knowledge evolves over time.

About the Project
The core of this research lies in the "science of science"-using large-scale data from scientific articles, patents, and grants to characterize the dynamics of research and innovation. A central methodological theme involves understanding the geometric and topological structure of knowledge: how concepts cluster, how new ideas deform or extend existing structures, and how the shape of a knowledge landscape constrains or enables discovery.

The project draws on tools from topological data analysis (e.g., persistent homology, Euler characteristic curves, discrete curvature), machine learning (e.g., encoder models, multi-modal embeddings, large language models), and mathematical modeling to map scientific concepts and their relationships, tracing how they change, merge, or diverge across time.

Your Role
You will develop and apply mathematical models and computational algorithms to analyze the structure and evolution of scientific literature. An ideal candidate would bring deep mathematical maturity-particularly in topology, geometry, or related fields-and would also take genuine interest in thinking about how formal models can inform sociological theories regarding the structure and process of science. The work involves both proving things and computing things, often in the same week.

What We Offer
This is a full-time, one-year appointment with the possibility of renewal contingent on funding availability and performance. You will have the opportunity to dive deeply into a cutting-edge research area that sits at the intersection of pure mathematics and empirical social science, publish in leading journals, and be part of a supportive and collaborative research environment at a top-tier

Start Date: Determined at hire

Required Qualifications:

A recent PhD (or expected PhD) in mathematics, applied mathematics, physics, computer science, computational topology, or a related quantitative discipline.

A strong foundation in algebraic topology and/or differential geometry (e.g., homology theory, simplicial complexes, manifold theory, fiber bundles, curvature). Familiarity with topological data analysis-persistent homology, filtrations, stability theorems-is particularly valued.

Extensive experience with mathematical modeling and comfort with formal reasoning across algebraic, geometric, and analytic frameworks.

A deep foundation in linear algebra, tensor calculus, and functional analysis; and the ability to bring these tools to bear on problems in data analysis and complex systems.

Experience designing and implementing mathematical measures of complex systems, ideally on graph- or simplicial-complex-structured data.

The ability to translate abstract mathematical concepts into intuitive frameworks and analogies, creating interpretable models and clearly explaining complex results to an interdisciplinary audience.

Skill in modeling the collective behavior of complex systems, understanding how micro-level interactions drive macro-level structure and evolution.

Practical experience with high-performance computing (HPC) and parallel processing to enable the analysis of massive datasets.

Experience in advanced statistical inference (e.g., Bayesian statistics, spectral methods) for extracting robust patterns from noisy, high-dimensional data.

Strong programming skills (e.g., Python, R, C++) for handling large datasets and implementing models.

A genuine curiosity about how science works and a desire to ask big-picture questions.

Preferred Qualifications:

Experience with computational topology software (e.g., GUDHI, Ripser, giotto-tda, or similar).

Familiarity with natural language processing (NLP), network science, or embedding methods.

Experience with machine learning libraries such as PyTorch, TensorFlow, or scikit-learn.

Interest in or exposure to the philosophy or sociology of science, scientometrics, or innovation studies.

The ability to work both independently and collaboratively.

Pay Range: $61,008 per year; depending on education/qualifications/experience

Please visit the Benefits for Postdoctoral Candidates website for more information regarding benefit eligibility.

• Competitive wages, paid holidays, and generous time off
• Continuous learning opportunities through professional training
• Medical, dental, and pharmacy plans
• Healthcare and dependent care flexible spending accounts
• University HSA contributions
• Disability and life insurance
• Employee wellbeing program
• Financial counseling services
• Employee Assistance Program with eight sessions of counseling at no cost

Applications must be submitted online. To be considered for this position, please click the Apply button and follow the instructions. You will have the opportunity to complete an online application for the position and attach a cover letter and resume or CV.

To Apply

1. Fill out this application
2. Submit the following as a single PDF file to rfunk@umn.edu:

• A brief cover letter describing your research interests and why you are a good fit for this specific project.
• Your CV.
• A representative publication or working paper (if available).

This position will remain open until filled. Priority application deadline is March 26, 2026.

To request an accommodation during the application process, please e-mail employ@umn.edu or call (612) 624-8647.

The University recognizes and values the importance of diversity and inclusion in enriching the employment experience of its employees and in supporting the academic mission. The University is committed to attracting and retaining employees with varying identities and backgrounds.

The University of Minnesota provides equal access to and opportunity in its programs, facilities, and employment without regard to race, color, creed, religion, national origin, gender, age, marital status, disability, public assistance status, veteran status, sexual orientation, gender identity, or gender expression. To learn more about diversity at the U: http://diversity.umn.edu

Any offer of employment is contingent upon the successful completion of a background check. Our presumption is that prospective employees are eligible to work here. Criminal convictions do not automatically disqualify finalists from employment.

The University of Minnesota, Twin Cities (UMTC)

The University of Minnesota, Twin Cities (UMTC), is among the largest public research universities in the country, offering undergraduate, graduate, and professional students a multitude of opportunities for study and research. Located at the heart of one of the nation's most vibrant, diverse metropolitan communities, students on the campuses in Minneapolis and St. Paul benefit from extensive partnerships with world-renowned health centers, international corporations, government agencies, and arts, nonprofit, and public service organizations.

At the University of Minnesota, we are proud to be recognized by the Star Tribune as a Top Workplace for 2021, as well as by Forbes as Best Employers for Women and one of America's Best Employers (2015, 2018, 2019, 2023), Best Employer for Diversity (2019, 2020), Best Employer for New Grads (2018, 2019), and Best Employer by State (2019, 2022).