- Foliation of an asymptotically flat end by critical capacitors. (joint with M. M. Fall and I. A. Minlend) preprint, arxiv:2007.05323
- On an fourth order conformal invariant. preprint, arxiv:2002.05939
- On constant Q-curvature metrics with isolated singularities. preprint, arxiv:2001.07984
- On the rate of change of the best constant in the Sobolev inequality. (joint with T. Carroll and M. M. Fall), Math. Nachr. 290 (2017), 2185–2197.
- Monotonicity of the first Dirichlet eigenvalue of the Laplacian on manifolds with nonpositive curvature. (joint with T. Carroll), Indiana Univ. Math. J. 65 (2016), 353–376.
- A reverse Hölder inequality for extremal Sobolev functions. (joint with T. Carroll), Potential Anal. 42 (2015), 283–292.
- A numerical investigation of level sets of extremal Sobolev functions. (joint with S. Juhnke), Involve 8 (2015), 787–799. (This paper is essentially S. Juhnke’s 2013 honors dissertation.)
- An isoperimetric inequality for extremal Sobolev functions. (joint with T. Carroll), RIMS Kôkyûroku Bessatsu, B43 (2013), 1–16.
- Two isoperimetric inequalities for the Sobolev constant. (joint with T. Carroll), Z. Angew. Math. Phys., 63 (2012), 855–863.
- Isoperimetric inequalities and variations on Schwarz’s lemma (joint with T. Carroll), arXiv:SP/1006.2310 (This paper has been subsumed by the above paper in Z. Angew. Math. Phys.)
- Interpolating between torsional rigidity and principal frequency (joint with T. Carroll), J. Math. Anal. Appl., 379 (2011), 818–826.
- Eigenvalues of Euclidean wedge domains in higher dimensions, Calc. Var. PDE, 42 (2011), 93–106.
- A Payne-Weinberger estimate for wedge domains on spheres (joint with A. Treibergs), Proc. Amer. Math. Soc. 137 (2009), 2299–2309.
- Coplanar k-unduloids are nondegenerate (joint with K. Grosse-Brauckmann, N. Korevaar, R. Kusner, and J. Sullivan), Int. Math. Res. Not., 2009 (2009), 3391–3416.
- A capture problem in Brownian motion and eigenvalues of spherical domains (joint with A. Treibergs), Trans. Amer. Math. Soc. 361 (2009), 391–405.
- On the nondegeneracy of constant mean curvature surfaces (joint with N. Korevaar and R. Kusner), Geom. Funct. Anal. 16 (2006), 891–923.
- An end to end gluing construction for metrics of constant positive scalar curvature, Indiana Univ. J. Math. 52 (2003), 703–726.
- Wissenschaftlicher Mitarbeiter, Institut für Mathematic, Universität Würzburg, Nov 2017-present
- Permanent Lecturer, University of Cape Town, August 2010–June 2016 (this is equivalent to a tenured assistant professor position in the US)
- Visiting Lecturer, University College Cork, Sept. 2009–June 2010
- Postdoctoral Fellow (under B. McKay), University College Cork, Sept. 2008–Sept. 2009
- Temporary Assistant Professor, University of Georgia, August 2007–May 2008
- Postdoctoral Fellow, University of Connecticut, August 2004–May 2007
- Postdoctoral Fellow, University of Utah: August 2001–May 2004
- geometric analysis
- specifically mean curvature
- scalar curvature, Q-curvature,
- eigenvalues of the Laplace-Beltrami operator,
- isoperimetric inequalities in the spirit of Pólya and Szegő
- August 2001:Ph.D. in mathematics, University of Washington, , Thesis: An End to End Gluing Construction for Surfaces of Constant Mean Curvature, Advisor: Daniel Pollack
- May 1995: B.A. in mathematics, University of California at Berkeley
Honors, Awards, and Funding
- rated researcher by the National Research Foundation of South Africa, Jan. 1, 2013- June 30, 2016(This entitled me to R40, 000 per year towards research.)
- Carnegie Research Development Grant, funded by the University of Cape Town
- Postdoctoral Fellow Sept. 2008-June 2009, funded by the Science Foundation of Ireland
- VIGRE fellow, January–June 2001, funded by the National Science Foundation of the US
- Online Geometric Analysis Seminar, May 2020 (https://blatt.sbg.ac.at/onlineseminar.php)
- Analysis seminar, University College Dublin, Dublin, Ireland, Feb. 2016
- Special session on geometries defined by differential forms at the Joint National Meeting of the American Mathematical Society and Mathematical Association of America, San Antonio, USA, Jan. 2015
- Special session on geometric variational problems at the Tenth American Institute of Mathematical Sciences conference on Dynamical Systems, Differential Equations, and Applications, Madrid, Spain, July 2014
- Workshop on Kähler geometry and geometric analysis, Cork, Ireland, May 2014
- Geometry/Topology/Analysis seminar, University of Massachusetts, Amherst, MA, USA, April 2014
- Differential geometry seminar, City University of New York, New York, NY, USA, April 2014
- Geometry seminar, University of Rochester, Rochester, NY, USA, April 2014
- Analysis seminar, University College Dublin, Dublin, Ireland, March 2014
- Colloquium, School of Mathematical Sciences, University College Cork, Cork, Ireland, Feb. 2014
- Special session on complex and geometric analysis at the Joint National Meeting of the American Mathematical Society and Mathematical Association of America, Baltimore, USA, Jan. 2014
- Special session on analysis and PDE at the Joint National Meeting of the American Mathematical Society and the Mathematical Association of America, Baltimore, USA, Jan 2014
- Special session on geometry at the national congress of the South African Mathematical Society, Pietermaritzburg, South Africa, Nov. 2013
- Special session on geometry and differential equations at the national congress of the South African Mathematical Society, Port Elizabeth, South Africa, Dec. 2011
- Geometric Analysis Seminar, University of Helsinki, Helsinki, Finland, Sept. 2011
- Workshop on de Giorgi’s conjecture, Banff International Research Station, Banff, Canada, Aug. 2010
- Workshop on Geometry, Analysis, and String Theory, Leibniz University, Hannover, Germany, July 2009
- Irish Geometry Conference, University College Cork, Cork, Ireland May 2009• Geometry Day, Granada, Spain, Dec. 2008
- Geometry Seminar, Stanford University, Palo Alto, USA, May 2008
- 18th Southeast Geometry Conference, Columbia, SC, USA, March 2008
- Geometry Seminar, Georgia Institute of Technology, Atlanta, USA, Dec. 2007
- Progress in Surface Theory, workshop at Oberwolfach, Germany, May 2007
- Differential Geometry seminar, City University of New York, New York, USA, Oct.2006
- Differential Geometry Seminar, Massachusetts Institute of Technology, Cambridge, USA, April 2006
- Valley Geometry Seminar, UMass, Amherst, USA, Feb. 2006
- Differential Geometry/PDE seminar, Univ. Washington, Seattle, USA, May 2005
- 16th Southeast Geometry Conference, Columbia, SC, USA, March 2005
- Geometry seminar, University of Massachusetts, Amherst, USA, April 2001, Feb. 2002,
- October/November 2004, April 2005
- Geometry seminar, Idaho State University, Pocatello, USA, June 2004
- Special session on nonlinear partial differential equations at the Joint National Meeting of the American Mathematical Society and Mathematical Association of America, Phoenix, AZ, USA, Jan. 2004
- Topology seminar, Georgia Institute of Technology,Atlanta, USA, Dec. 2002
- Special session in the Winter Meeting of the Canadian Mathematical Society, Toronto, Canada, Dec. 2001
- Conference on Teaching and Learning, University of Cape Town, Oct. 2013
- Conference in Geometric Analysis, Universidad Autònoma de Barcelona, July 2013.
- Queen Dido Conference on Isoperimetry, Carthage, Tunisia, May 2010
- Summer School in Conformal Geometry, Potential Theory, and Applications, NUI Maynooth, Ireland, June 2009
- Lehigh University Geometry and Topology Conference, Oct. 2007
Academic and Professional Service
- member of the editorial board, Quaestiones Mathematicae
- member of the planning committee, Department of Mathematics and Applied Mathematics, University of Cape Town, July 2014–Dec. 2015
- member of the executive committee of the African Mathematical Sciences Institute, Muizenberg, South Africa, Feb. 2012–Dec. 2015
- external examiner for third year complex analysis, University of the North West, South Africa, 2014-2015
- external examiner of the MSc dissertation of C. A. Emereuwa, University of Pretoria, South Africa, 2015
- chair of a committee to reorganize the second and third year courses in pure and applied mathematics at the University of Cape Town
- member of a search committee to find a new head of the mathematics department at the University of Cape Town
- introduction and pioneer use of WebWork, an online homework tool, for first and second year mathematics courses at the University of Cape Town
- overhaul of the departmental webpage for the Department of Mathematics and Applied Mathematics, University of Cape Town (with Rob Martin and Julian Gordon [the departmental IT officer])
- referee for Inventiones Mathematicae, Experimental Mathematics, Annales de la Faculté des Sciences de Toulouse, Colloquium Mathematicum, Bulletin of the London Mathematical Society, Publicaciones Matemàtiques
- reviewer for Math Reviews
- organizer for a workshop in geometric analysis at the African Institute of Mathematical Sciences, Dec. 2012
- organizer for a special session in geometric differential equations at the 2011 South African Mathematical Society national congress in Port Elizabeth
- co-organizer for a special session in the fall 2006 American Mathematical Society northeastern sectional meeting
- co-organizer of research level Geometry seminar at U. Connecticut, September 2004–May 2007
- organizer for the spring 2004 meeting of the Pacific Northwest Geometry Seminar
- co-organizer of research level PDE/Differential Geometry seminar at U. Utah, August 2003–May 2004
- assisted with a VIGRE Minicourse in nonlinear wave phenomena, August 2003
- faculty advisor for the graduate student geometry seminar, August–December, 2002
- assisted with a VIGRE Minicourse in variation methods and nonlinear PDE, particularly
- in organizing a series of lectures on minimal surfaces, May 2002
- organizer of graduate student geometry seminar, 1998–2000
Outreach and Community Service
- guest lecturer in mathematical enrichment sessions for secondary school students in Cape Town, South Africa, March 2012 and August 2011 (three lectures, one each on the isoperimetric inequality, knots, and coloring of graphs)
- led mathematical enrichment sessions for secondary school students in Cork, Ireland, Febuary 2010 (two sessions, one each on inequalities and a discrete model for heat flow)
- led a series of three lectures on fractals in the University of Utah Math Circle, a high school outreach program, April 2003
- assisted with the Math Circle program, September 2002–May 2004
Mathematics for Computer Scientists 1: 5 hrs, Mon 10-12, Wed 11-14, J. Ratzkin
Exercises in Mathematics for Computer Scientists 1 in groups: 2 pc, Mon 12-14 ; Mon 14-16 ; Mon 16-18 ; Tue,Wed 8-10, J. Ratzkin
- At Universität Würzburg I have staffed exercise sessions in analysis II and III, function theory (complex analysis), first year mathematics for physicists, and differential geometry of curves and surfaces.
- I was a part of the lecturing team for the standard first year mathematics course at the University of Cape Town, July-Nov. 2012 and July-Nov. 2014.
- I have also assisted in teaching classes ranging from freshman calculus to graduate geometry and topology, led discussion sections, staffed drop-in tutoring centers, and graded for a variety of courses.
I have been the sole instructor or course leader (which includes writing syllabi, course notes, and exams) for the following courses.
- at the University of Cape Town:
– first year course for applied mathematics (MAM1044, 2011)
– fourth year (honors) course in PDE (2011, 2012, 2013, and 2015)
– second year linear algebra (MAM2000-2LA, 2012, 2013, and 2015)
– second year differential equations (MAM2000-2DE, 2013, 2014, and 2015)
- at University College Cork:
– real analysis II (MA3051, undergraduate, fall 2009)
– introductory mathematics (MA1003, fall 2009 and spring 2010)
– topology and metric spaces (MA3056, spring 2010)
- at the University of Georgia:
– abstract algebra (undergraduate, fall 2007)
– single-variable calculus (fall 2007)
– multi-variable calculus (spring 2008)
– Euclidean geometry (spring 2008)
- at the University of Connecticut:
– single-variable calculus (fall 2004, fall 2006)
– geometry (fall 2004, spring 2005),
– multi-variable calculus (spring 2005, fall 2005, fall 2006)
– ordinary differential equations (spring 2006, spring 2007)
– complex analysis (spring 2006)
– writing in mathematics (spring 2007)
- at the University of Utah:
– partial differential equations for engineers (fall 2003)
– topics in Riemannian geometry: the Yamabe problem (spring 2003)
– trigonometry (fall 2002)
– linear algebra (spring 2002)
– ordinary differential equations (fall 2001, spring 2004)
- at the University of Washington:
– multivariable calculus (summer 2000, spring 1999)
– ordinary differential equations (summer 1999)
– first year calculus (summer 1997)
– remedial algebra (winter 1997)
- Murray Christian, PhD at the University of Cape Town, May 2011-Feb. 2019 Dissertation, title: Constant mean curvature 12 surfaces in H 2 × R.
- Mogtaba Mohammed, AIMS postgraduate diploma, Feb.–June 2011. Topic: Weyl’s asymptotic formula for eigenvalues of the Laplacian.
- Humphrey Marufu, honours project at the University of Cape Town, March-Nov. 2012. Topic: extremal domains for three variational problems.
- Stefan Juhnke, honours project at the University of Cape Town, Feb–Nov. 2013. Topic: geometry of level sets of extremal Sobolev functions.
- 8 final year capstone projects in topics including the maximum principle for elliptic PDE, the classical isoperimetric inequality, maximal surfaces in Minkowski space, classification of hyperbolic isometries, and groups & three-dimensional manifolds.