Heather Macbeth

Heather Macbeth

Department of Mathematics
Massachusetts Institute of Technology

Office: 2-246A
Mailing address: MIT, 77 Massachusetts Ave, Cambridge, MA 02139-4307
Email: hmacbeth at mit dot edu

I am a C. L. E. Moore Instructor in Mathematics at MIT, with research interests in Kähler geometry and in geometric analysis.

Before MIT I was a graduate student (2010-15) at Princeton, under the supervision of Gang Tian. Before Princeton I was a Part III student (2009-10) at Trinity College, Cambridge. Before Cambridge I was an undergraduate (2006-9) at the University of Auckland. My CV is available.

Preprints and recent publications:

  • Steady Kähler-Ricci solitons on crepant resolutions of finite quotients of Cn. With Olivier Biquard. Preprint, 2017.
  • Kähler-Einstein metrics and higher alpha-invariants. Preprint, 2014.
  • Conformal classes realizing the Yamabe invariant. Int. Math. Res. Not., to appear. [arXiv]
  • Detecting Einstein geodesics: Einstein metrics in projective and conformal geometry. With Rod Gover. Differential Geom. Appl. 33 (2014), suppl., 44-69. [arXiv] [MR]
  • Einstein metrics in projective geometry. With Andreas Čap and Rod Gover. Geom. Dedicata 168 (2014), 235-244. [arXiv] [MR]
  • Older publications:

  • Cayley graphs of given degree and diameter for cyclic, Abelian, and metacyclic groups. With Jana Šiagiová and Jozef Širáň. Discrete Math. 312 (2012), no. 1, 94-99. [MR]
  • Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter. With Jana Šiagiová, Jozef Širáň and Tomáš Vetrík. J. Graph Theory 64 (2010), no. 2, 87-98. [MR]
  • Some expository writings:

  • An introduction to equivariant cohomology and the equivariant first Chern class, by YiYu (Adela) Zhang, report on an undergraduate research project supervised by me.
  • Free translation of the introduction of Hopf's 1926 paper on the degree of the Gauss map of a hypersurface.
  • A compactness theorem for Yamabe metrics.
  • Explicit constants for Riemannian inequalities.
  • Moduli spaces of Einstein metrics. Notes for a talk in the Graduate Student Seminar, Princeton, 2011.
  • The Arnold chord conjecture. Part III essay, Cambridge, 2010, written under the supervision of Gabriel Paternain.

    Teaching highlights:

  • In Spring 2017 I was the writing instructor for 18.100P, a new MIT course, aimed at double- and non-majors, which covers elementary real analysis while developing mathematical writing skills. Materials I wrote for this course (including some fun multi-week projects exploring applications of real analysis to physics, computer science, economics, etc) available on request.
  • In Fall 2016 I taught 18.950, a course on elementary differential geometry.

    and some cool projects: I have supervised projects through MIT's Undergraduate Research Opportunities Program. I serve on the MIT math department's Diversity Committee. I organized the Princeton Noetherian Ring for two years. I have taught, mentored and graded extensively for the NZMOC, and less extensively for the BMOC and the USAMO. I have asked and answered some questions at MathOverflow.