Home Page of McKenzie Wang

Contact Information

e-mail: wang@mcmaster.ca

phone: (905)-525-9140 extension 23405

fax: (905)-522-0935

snail mail: Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

Research Area

Differential geometry, geometric analysis, group actions on manifolds

Teaching

Math 2X3 (Calculus III) Fall 2023

Math 1XX3 (Calculus II) Winter 2024

Math 3X3 (Complex Analysis) Winter 2024

Recent Publications/Preprints/Notes

(with M. Buzano, A. Dancer and M. Gallaugher) Non-kahler expanding Ricci solitons, Einstein metrics and exotic cone structures, Pacific J. Math., Vol. 273, (2015), 369-394, arXiv:1311.5097

(with M. Buzano, A. Dancer and M. Gallaugher) A family of steady Ricci solitons and Ricci-flat metrics, arXiv:1309.6140

(with M. Buzano and A. Dancer) A family of steady Ricci solitons and Ricci-flat metrics, Comm. Anal. Geom., 23 (2015), 611-638

(with A. Betancourt de la Parra, A. Dancer) A Hamiltonian approach to the cohomogeneity one Ricci solitons equations, J. Math. Phys., 57 (2016), 122501

(with P. Lu) Ancient solutions of the Ricci flow on bundles, Adv. Math., 318 (2017), 411-456.

(with P. Lu) Ancient solutions bundles with non-abelian structural groups, Comm. Anal. Geom., 28 (2020), 141-187, arXiv:1610.07709.

(with I. Adeboye and Guofang Wei) On the volume of orbifold quotients of symmetric spaces, Diff. Geom. Appl., 71 (2020), 101639, arXiv:1808.05747

(with U. Semmelmann and Changliang Wang) On the linear stability of nearly Kahler 6-manifolds, Ann. Glob. Anal. Geom., 57 (2020), 15-22.

(with Changliang Wang) Stability of Einstein Metrics on fibre bundles, J. Geom. Anal., 31 (2021), 490-515, arXiv:1808.05679.

(with U. Semmelmann and Changliang Wang) The linear stability of Sasaki Einstein and nearly parallel G_2 manifolds, Int. J. Math., 33 (2022), arXiv: 2011.11965.

(with Changliang Wang) Instability of Riemannian manifolds with real Killing spinors, Comm. Anal. Geom., 33 (8) (2022), 1895-1931, arXiv:1810.04526.

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The following file contains a listing of the 2-dimensional faces which need to be analysed for the results in

A. Dancer & M. Wang, Classification of superpotentials, Comm. Math. Phys., 284 (2008), 583-647.

2dfaces.pdf

Former Graduate Students

Here are my former and current students and some information about their research projects.

JUN WANG: (Ph. D. McMaster University 1996)

Thesis: Einstein metrics on bundles

J. Wang: Einstein metrics on principal circle bundles, Diff. Geom. Appl., 7 (1997), 377-388.

J. Wang and M. Wang: Einstein metrics on S^2 bundles, Math. Ann., 310 (1998), 497-526.

DEZHONG CHEN: (Ph. D. McMaster University 2010)

Thesis: Bundle construction of Einstein metrics

D. Chen: A notes on Ricci signatures, PAMS 137 (2009), 273-278

D. Chen: Examples of Einstein manifolds in odd dimensions, Ann. Glob. Anal. Geom., 40 (2011), 339-377.

D. Chen: Construction of conformally compact Einstein manifolds, arXiv:0908.1430

DAVID WILLIAMS: (M. Sc. McMaster University 2000)

Thesis: Construction of closed constant mean curvature surfaces

AMI MAMALO: (M. Sc. McMaster University 2005)

Project: Exploring spacetimes and singularities

JASON HARADYN: (M. Sc. McMaster University 2010)

Project: Invariant Einstein metrics and Ricci curvature on the exceptional Aloff-Wallach spaces

CONG ZHOU: (M. Sc. McMaster University 2013)

Thesis: On complete non-compact Ricci-flat cohomogeneity one manifolds

VINCENT CHIU: (M. Sc. McMaster University 2016)

Thesis: A numerical study of cohomogeneity one manifolds

HANCI CHI: (Ph. D. McMaster University 2019)

Thesis: Cohomogeneity one Einstein metrics on vector bundles

Hanci Chi: Invariant Ricci-flat metrics of cohomogeneity one with Wallach spaces as principal orbits, Ann. Glob. Anal. Geom., 56 (2019), 361-401.

SEBASTIAN ZWARICH: (M. Sc. in progress)

DYLAN McGINLEY: (M. Sc. in progress)

Former Undergraduate Research Students

CLARA BLAKELOCK (USRA 2005): Painleve analysis of the Einstein equations

LAURA WALTON (USRA 2010): Iterating the Ricci tensor of homogeneous metrics

MICHAEL GALLAUGHER (USRA 2013): Numerical analysis of Einstein and soliton equations

JONATHAN BAKER (USRA 2014): Numerical analysis of Einstein and solitons equations

MARTIN BLOTSTEIN (USRA 2014): Iterating the Ricci tensor of homogeneous metrics

MEGAN HARTWELL (USRA 2015): Finding superpotentials for Einstein equations with nonzero cosmological constant

CISSY SUEN (USRA 2015): Numerical analysis of soliton and Einstein equations

MATTHEW JORDAN (Arts and Science USRF 2016): Special relativity as told by the luminaries

NICHOLAS PLATI (USRA 2019): Numerical investigations of calibrated submanifolds

MARK BOUMAN (USRA 2020): Numerical investigation of Ricci solitons

NICHOLAS PLATI (J. Stewart Award 2020): Cohomogeneity one Einstein metrics with principal orbit Spin(8)/G2

ALEXANDER KAYSSI (Senior Thesis 2021): Linear stability analysis of higher dimensional Schwarzschild black holes

MATTHEW HOW-CHUN-LUN (J. Stewart Award 2022): Scalar curvature and surgery

MATTHEW HOW-CHUN-LUN (USRA 2023): Superpotentials and the Ricci-flat equations on the compact rank one symmetric spaces