Research overview

Geometric models in pure and applied mathematics.

I work across geometry and mathematical physics, focusing on the geometry of moduli spaces of decorated bundles and on data‑informed models for networks and pattern formation.

In practice, I often start from simple, tractable settings and build toward more complex applications—because small changes in complex systems can have unpredictable effects, while simpler systems make those effects clearer.

Geometry & Quantization (pure)

Moduli spaces of decorated bundles. I study the geometry and topology of moduli spaces of decorated bundles, especially Higgs bundles and Hitchin systems, and the geometric structures they parametrize. Research on the moduli spaces of Higgs bundles has yielded deep connections between fundamental areas of mathematics and theoretical physics, blending ideas from algebraic and differential geometry, Lie theory, representation theory, and string theory.

Representative papers

  • Nonabelianization of Higgs bundles — J. Differential Geom. (2014, with N. Hitchin). A geometric mechanism that turns abelian data back into non‑abelian Higgs‑bundle data via spectral curves.
    JDG 97(1), 79–89.

  • Higgs bundles and (A,B,A)-branes — Comm. Math. Phys. (2014, with D. Baraglia). Constructs (A,B,A) branes via real structures and relates them to real integrable systems on the moduli space.
    CMP 331, 1271–1300.

  • Spectral data for U(m,m)-Higgs bundles — IMRN (2015). Introduces explicit spectral data and invariants for U(m,m)‑Higgs bundles, giving a concrete picture of the moduli.
    IMRN 2015(11), 3486–3498.

  • Higgs bundles and exceptional isogenies — Adv. Theor. Math. Phys. (2016, with S. Bradlow). Relates Higgs‑bundle moduli across groups via low‑dimensional exceptional isogenies using fiber products of spectral curves.
    ATMP 20(5), 1143–1190.

  • Higgs bundles—Recent applications — Notices of the AMS (2020). A concise expository snapshot of how the Hitchin fibration and integrable structure echo across mathematics and physics.
    Notices 67(5), 625–635.

More geometry → /publications/

Networks & Patterns (applied)

Geometric questions within different areas of science. My current projects lie along two intertwined directions—virus and society—with the overall aim of building novel techniques useful across many domains. Themes include: geometric insights (symmetries and patterns), repurposing stock‑market indicators for time‑series data in the social and natural sciences, and graph/network‑theoretic approaches to contagion and collective behavior.

Representative papers

  • A carbon‑aware ant colony system (CAACS) for sustainable GTSP — Nature Scientific Reports (2025, with M. Lin). Bi‑objective routing balances solution quality and estimated carbon impact, offering a practical sustainability lens on GTSP.

  • Modeling social cohesion with coupled oscillators: synchrony & fragmentation — Chaos, Solitons & Fractals (2025, with S. Hsu & R. Dunbar). A semicoupled‑oscillator model explains when activity schedule mismatch fractures groups—and how bonding mitigates it.

  • Correlations between COVID‑19 and dengue — Nature Scientific Reports (2023, with P. Bergero & G. Wang). Neural‑network models link signals across diseases and climates to improve dengue estimates where data are scarce.

  • A Physarum swarm Steiner‑tree algorithm — Nature Scientific Reports (2022, with S. Hsu & F.I. Schaposnik Massolo). A slime‑mold‑inspired, explore‑and‑fuse strategy that competes with leading solvers and handles obstacles naturally.

  • Modified age‑structured SIR model for COVID‑19‑type viruses — Nature Scientific Reports (2021, with V. Ram). Shows how contact patterns and age structure shape outcomes and policy trade‑offs.

More applied → /publications/

How to cite

Please see the individual paper pages or my Google Scholar profile for canonical citations.

Last updated: November 04, 2025