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My research is concerned with geometry, geometric flows, and data science. This includes work on Ricci flow, discrete versions of the heat equation, curve shortening flow, discrete Riemannian manifolds, graph theory drawing, and deep neural networks. Some of my recent collaborative projects are:VOSviewer
Courses
- MMMathematical Modeling
- CIICalculus II
- GDGGlobal Differential Geometry
- TGTopology-Geometry
- MAEMathematical Analysis for Engineers
- TGTTopics in Geometry and Topology
- FMRWFormal Mathematical Reasoning and Writing
- LALinear Algebra
- TGNTheory of Graphs and Networks
- CICalculus I
Grants
- Assessing Clinical Effectiveness and Implementation of Worksite Sleep Health Coaching in Firefighters
Co-Investigator (COI)
2023
$875.5K
Active - Enhancing Pathways to PhD in the Mathematical Sciences
Principal Investigator (PI)
2021
$150.0K
Active - RTG: Applied Mathematics and Statistics for Data-Driven Discovery
Co-Investigator (COI)
2020
$1.7M
Active - FRG: Collaborative Research: Geometric and Topological Methods for Analyzing Shapes
Principal Investigator (PI)
2018
$283.7K
Active - TRIPODS: UA-TRIPODS - Building Theoretical Foundations for Data Sciences
Co-Investigator (COI)
2017
$1.4M
- Examining Sleep and Social Rhythms as Mechanisms for Weight Gain After Job Loss
Co-Investigator (COI)
2014
$3.1M
- Career: Discrete and Generalized Riemannian Geometry and Curvature Flows
Principal Investigator (PI)
2008
$401.7K
News
- Flandrau Exhibition Goes Beyond the Mere Facts in Math
2016
- Interactive Math Exhibit Opens at Flandrau
2015
Publications (57)
Recent
- The impact of social rhythm and sleep disruptions on waist circumference after job loss: A prospective 18‐month study
2022
- 0139 Work Duration Affects How Prior-Night Sleep Predicts Next-Day Energy Expenditure in Emergency Response System Telecommunicators
2022
- Inconsistent social rhythms are associated with abdominal adiposity after involuntary job loss: An observational study
2021
- 086 Sleep midpoint after job loss predicts breakfast skipping patterns
2021
- Editorial: Mathematical Fundamentals of Machine Learning
2021
- Persistent Classification: A New Approach to Stability of Data and Adversarial Examples
2021
- 1049 Sleep Fragmentation And Sleep Restriction Are Associated With Increased Energy Intake Among Individuals Who Have Involuntarily Lost Their Jobs
2020
- Topology Lectures—Integration workshop 2020
2020
- 1047 Social Rhythm Instability Is Associated With Abdominal Adiposity After Involuntary Job Loss
2020
- Sleep fragmentation an sleep restriction are associated with increased energy intake among individuals who have involuntarily lost their jobs
2020
- Longer Sleep Duration Precedes Greater Water Intake at Breakfast
2019
- Social rhythm instability is associated with abdominal adiposity after involuntary job loss.
2019
- 0176 Longer Sleep Duration Precedes Greater Water Intake At Breakfast
2019
- Inconsistent Social Rhythms are Associated with Higher Waist Circumference Following Job Loss
2019
- Asymptotic Behavior of -Polygon Flows
2018
- A Bug’s Eye View: The Riemannian Exponential Map on Polyhedral Surfaces
2018
- Asymptotic Behavior of beta-Polygon Flows
2018
- Make PVC Polyhedra
2018
- DimReader: Axis lines that explain non-linear projections
2018
- Multi-Level Steiner Trees
2018
- PVC Polyhedra
2017
- Soliton metrics for two-loop renormalization group flow on 3D unimodular Lie groups
2017
- HIGH PREVALENCE OF OVER THE COUNTER SLEEP AID USE AMONG INDIVIDUALS WHO HAVE EXPERIENCED INVOLUNTARY JOB LOSS
2017
- Longitudinal assessment of daily activity patterns on weight change after involuntary job loss: the ADAPT study protocol
2017
- Duality structures and discrete conformal variations of piecewise constant curvature surfaces
2017
- Distortion estimates for barycentric coordinates on Riemannian simplices
2016
- Euclidean formulation of discrete uniformization of the disk
2014
- Covering Spaces
2011
- Discrete conformal variations and scalar curvature on piecewise flat two-and three-dimensional manifolds
2011
- Regge's Einstein-Hilbert functional on the double tetrahedron
2011
- DISCRETE CONFORMAL VARIATIONS AND SCALAR CURVATURE ON PIECEWISE FLAT TWO- AND THREE-DIMENSIONAL MANIFOLDS
2011
- The Ricci flow: techniques and applications. Part II: analytic aspects (Mathematical Surveys and Monographs 144)
2010
- Introduction to flows on Riemannian metrics
2009
- Ricci flow on three-dimensional, unimodular metric Lie algebras
2009
- Math 443/543 Graph Theory Notes 7: Small world phenomenon and decentralized search
2008
- Open Problems for PNGS
2008
- The Ricci flow: techniques and applications. Part III
2008
- Hamilton’s Ricci flow (Graduate Studies in Mathematics 77) By Bennett Chow, Peng Lu and Lei Ni: 608pp., US $79.00, isbn 0-8218-4231-5 (American Mathematical Society, Providence …
2008
- Riemannian Groupoids and Solitons for Three-Dimensional Homogeneous Ricci and Cross-Curvature Flows
2008
- The Ricci flow: techniques and applications
2007
- A monotonicity property for weighted Delaunay triangulations
2007
- Ni Lei: The Ricci Flow: Techniques and Applications, Part I: Geometric Aspects, 536 pp. SURV 135
2007
- Semidiscrete geometric flows of polygons
2007
- Geometric aspects
2007
- Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature
2006
- A combinatorial Yamabe flow in three dimensions
2005
- Geometric triangulations and discrete Laplacians on manifolds
2005
- A maximum principle for combinatorial Yamabe flow
2005
- Precompactness of the Ricci flow and a maximum principle on combinatorial Yamabe flow
2003
- Metric transformations under collapsing of Riemannian manifolds
2003
- University of California, San Diego January 7, 2003
2003
- Precompactness of solutions to the Ricci ow in the absence of injectivity radius estimates
2003
- Estimates on the Metric Tensor
2000
- The Legendre Transform
2000
- Nonlinear self-similar measures and their Fourier transforms
1996
- Nonlinear Self–similar Measures and their Fourier Transforms
1996