Yingying Wu
Assistant Professor, Department of Mathematics, University of Houston
Adjunct Assistant Professor, Department of Mathematics, Rice University
About me
I am an Assistant Professor in the Department of Mathematics at the University of Houston and an Adjunct Assistant Professor in the Department of Mathematics at Rice University.
My research is in geometric analysis, gauge theory, and algebraic geometry. I construct and study singularity models for ℤ/2-harmonic forms and spinors in three and four dimensions, together with the associated spectral problems. I also investigate eigenvalue inequalities comparing the spectra of embedded surfaces and the domains they bound. In algebraic geometry, I develop comparison theorems relating tree and network spaces to algebraic fans and moduli of curves, and study the operadic structure of moduli spaces of SUSY curves.
Here is my CV.
Ads: I am looking for motivated Ph.D. students interested in differential geometry, algebraic geometry, and supersymmetry. Please send me your CV and transcript to ywu68@uh.edu if interested.
Research
My research brings together the analysis of singular geometric objects and the geometry of moduli spaces. A central direction is to establish comparison theorems between toric varieties and moduli spaces of desingularization pathways for ℤ/2-harmonic forms and spinors, using toric geometry to reveal their structure, stratification, and degeneration.
Harmonic singularities and gauge theory. With Clifford Taubes, I constructed homogeneous ℤ/2-harmonic forms and spinors with nonsmooth branching loci in [three dimensions] and new models from regular polytopes in four dimensions. We also investigated the topology and variational structure of the associated twisted spectral problem on the two-sphere.
Spectral geometry. With Ricardo Gloria-Picazzo and Shing-Tung Yau, I proved the eigenvalue-ratio bound proposed by Yau, relating the intrinsic spectrum of an embedded surface to the Dirichlet spectrum of the domain it bounds.
Algebraic geometry and moduli spaces. I proved comparison theorems relating tree and network spaces to algebraic fans and moduli of curves. With Enno Keßler and Yuri I. Manin, I studied moduli spaces of SUSY curves and their operads], describing how combinatorial structures encode geometric gluing and degeneration.
Alongside this work, I develop geometric and spectral methods for machine learning and biomedical applications.
See [Research & Publications] for papers and further details.
Mentoring & Seminars
I advise doctoral students and mentor postdoctoral researchers in geometric analysis, algebraic geometry, and related areas. My mentoring emphasizes sustained mathematical discussion, careful reading, and the development of independent research questions and proofs.
I co-organize the Houston–College Station Learning Seminar with Simone Cecchini and Christos Mantoulidis, bringing together students and faculty from the University of Houston, Texas A&M University, and Rice University. I also organize the University of Houston Mathematics Colloquium. Visit [People & Seminars] for my research group, current activities, and past seminars.