# Research

## Faculty Research Areas

Uday Banerjee - Generalized finite element methods, elliptic PDE

Pinyuen Chen - Statistical signal processing, ranking and selection theory

Dan Coman - Complex analysis, pluripotential theory, dynamics

J. Theodore Cox - Probability, interacting particle systems

Steven Diaz - Algebraic geometry of curve families

Nicole Fonger - Mathematics education

Jack Graver - Combinatorics, graph theory

Duane Graysay - Mathematics education

Philip Griffin - Stochastic processes, mathematical finance

Tadeusz Iwaniec - Harmonic analysis, elliptic PDE

Lee Kennard - Riemannian geometry, algebraic topology, symmetry

Hyune-Ju Kim - Statistics, change-point problems, regression model selection

Mark Kleiner - Representations of finite dimensional algebras

Leonid Kovalev - Geometric mapping theory, metric spaces

Loredana Lanzani - Harmonic analysis, PDE, complex analysis

Graham Leuschke - Commutative algebra, non-commutative algebraic geometry

Wei Li - Nonparametric and semiparametric models, Bayesian inference

Jianxuan Liu - Semiparametrics, causal inference, measurement error models, high dimensional data, case-control studies

Adam Lutoborski - Variational problems, optimization on matrix manifolds

Joanna Masingila - Out-of-school mathematics practice, teacher development

Terry McConnell - Martingales, Banach spaces, potential theory

Claudia Miller - Commutative algebra, connections with algebraic geometry

Jani Onninen - Nonlinear analysis, geometric function theory

Eugene Poletsky - Complex analysis, pluripotential theory

Declan Quinn - Noncommutative rings, Galois theory, Hopf algebras

Minghao Rostami - Numerical linear algebra, computational fluid dynamics

Lixin Shen - Applied harmonic analysis, wavelets, image processing

John Ucci - Topological K-theory, homotopy theory

Gregory Verchota - Singular integrals, elliptic PDE in nonsmooth domains

Andrew Vogel - Elliptic PDE in nonsmooth domains

Stephan Wehrli - Low-dimensional topology, knots and links

William Wylie - Riemannian geometry, geometric analysis

Yuan Yuan - Complex geometry and several complex variables

Dan Zacharia - Homological algebra, representations of algebras

## Recent Publications

- Creating and flattening cusp singularities by deformations of bi-conformal energy (Tadeusz Iwaniec, Jani Onninen, Zheng Zhu)
- Analysis of regional global climate changes due to human influences (Igor G. Zurbenko, Amy L. Potrzeba-Macrina)
- The Combinatorial Structure of Graphene, a chapter in Handbook of Graphene: Physics, Chemistry, and Biology (Jack E. Graver, Elizabeth J. Hartung)
- Note on an eigenvalue problem with applications to a Minkowski type regularity problem in Rn (Murat Akman, John Lewis, Andrew Vogel)
- Positive curvature and symmetry in small dimensions (Manuel Amann, Lee Kennard)
- Fast algorithms for large dense matrices with applications to biofluids (Minghao W. Rostami, Sarah D. Olson)
- Periods in solar activity (Amy L. Potrzeba-Macrina, Igor G. Zurbenko)
- Radial symmetry of minimizers to the weighted Dirichlet energy (Aleksis Koski, Jani Onninen)
- Deformations of bi-conformal energy and a new characterization of quasiconformality (Tadeusz Iwaniec, Jani Onninen, Zheng Zhu)
- Pluricomplex Green functions on manifolds (Evgeny A. Poletsky)
- On the functoriality of sl(2) tangle homology (Anna Beliakova, Matthew Hogancamp, Krzysztof Karol Putyra, Stephan Martin Wehrli)
- Lp regularity of the Bergman Projection on domains covered by the polydisk (Liwei Chen, Steven G. Krantz, Yuan Yuan)
- Solar energy supply fluctuations to Earth and climate effects (Igor G. Zurbenko, Amy L. Potrzeba-Macrina)
- Plurisubharmonically separable complex manifolds (Evgeny A. Poletsky, Nikolay Shcherbina)
- Weighted regularity and two problems of Sadullaev on weighted regularity (Muhammed Ali Alan)
- Principal component projection with low-degree polynomials (Stephen D. Farnham, Lixin Shen, Bruce W. Suter)
- Meaningfulness in representational fluency (Nicole L. Fonger)
- Professional learning through teacher-researcher collaborations (Jennifer M. Mayer, Mary Ann Huntley, Nicole L. Fonger, Maria S. Terrell)
- Rician noise removal via a learned dictionary (Jian Lu, Jiapeng Tian, Lixin Shen, Qingtang Jiang, Xueying Zeng, Yuru Zou)
- Self-intersections of Laurent polynomials and the density of Jordan curves (Sergei Kalmykov, Leonid V. Kovalev)