# Research

My research addresses computational, mathematical, and statistical problems in the study of complex systems. My interests include network data science, dynamical models of social structures, and data science applications supporting equity and sustainability.

## Methods of Network Data Science

How do we analyze and learn from network data? I build mathematical foundations for network data science algorithms, with recent focus on networks of higher-order interactions. Much of my work is devoted to developing novel random graph models and applying them in algorithms. Doing so often requires tools from probability, optimization, combinatorics, and random matrix theory.

Nonbacktracking spectral clustering of nonuniform hypergraphs
PSC, Nicole Eikmeier, and Jamie HaddockSIAM Journal on Mathematics of Data Science (2023) |

Generative hypergraph clustering: from blockmodels to modularity
PSC, Nate Veldt, and Austin BensonScience Advances (2021) |

Moments of uniformly random multigraphs with fixed degree sequences
PSCSIAM Journal on Mathematics of Data Science (2020) |

## Models of Polarization, Hierarchy, and Inequality

Human and animal societies are structured by persistent hierarchies, inequalities, and divisions. Dynamical and statistical models can help us understand the extent of these structures, how they form, and under what conditions they persist. I am especially interested in the role of social feedback loops in reinforcing these structures.

Emergence of polarization in a sigmoidal bounded-confidence model of opinion dynamics
Heather Zinn Brooks, PSC, and Mason PorterarXiv (2023) |

Emergence of hierarchy in networked endorsement dynamics
Mari Kawakatsu, PSC, Nicole Eikmeier, and Dan LarremoreProceedings of the National Academy of Sciences (2021) |

Local symmetry and global structure in adaptive voter models
PSC and Peter MuchaSIAM Journal on Applied Mathematics (2021) |

## Key Collaborators

- Nicole Eikmeier (Computer Science, Grinnell)
- Jamie Haddock (Mathematics, Harvey Mudd)
- Heather Zinn Brooks (Mathematics, Harvey Mudd)
- Kelly Finn (Psychology and Brain Sciences, Dartmouth)
- Mason Porter (Mathematics, UCLA)
- Alice Schwarze (Mathematics, Dartmouth)
- Nate Veldt (Computer Science, Texas A&M)
- Austin Benson (Computer Science, Cornell)
- Mari Kawakatsu (Applied and Computational Mathematics, Princeton)
- Dan Larremore (Computer Science, CU Boulder)
- Peter Mucha (Mathematics, Dartmouth)
- Marta González (City and Regional Planning, UC Berkeley)
- Andrew Mellor (Oxford, OxFORD Asset Management)
- Shan Jiang (Urban and Environmental Policy and Planning, Tufts)
- Mary Angelique Demetillo (Environmental Science, UVA)
- Sally Pusede (Environmental Science, UVA).

## Student Research

If you are a Middlebury student interested in working with me as a research collaborator, I have a whole list of FAQs just for you!

## Other Work

The research on this page is the best description of my current interests and activities. For my complete research record, see my Google Scholar page.