Home Page of McKenzie Wang

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

Differential geometry, geometric analysis, group
actions on manifolds

Math 2X3 (Calculus III) Fall 2023

Math 1XX3 (Calculus II) Winter 2024

Math 3X3 (Complex Analysis) Winter
2024

(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.

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)

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

McMaster
University Department of Mathematics and Statistics homepage: http://www.math.mcmaster.ca

For information
about GAP (Geometry and Physics) meetings: http://www.math.uwaterloo.ca/~gap

For
information about Geometric analysis colloquium at Fields: http://www.fields.utoronto.ca/programs/scientific/14-15/geomanalysis

Updated August 23, 2023.