Rob Kusner

Rob

Professor

Faculty
A headshot of Rob Kusner.
Contact
Email
Email
Phone
Personal Webpage
Location
LGRT 1435G

Office Hours:
Right after each class and on Zoom (by appointment via email)

Alternate Email:
kusner@umass.edu

Editor, Journal of Experimental Mathematics (2023-present)

Editor, Experimental Mathematics (1995-2023)

Treasurer & Trustee, Association of Members of the Institute for Advanced Study, Princeton (2015-2023)

Education

Ph.D. University of California, Berkeley, 1988

C.Phil. University of California, Berkeley, 1984

B.A. Math, Haverford College, 1981

B.A. Physics, Haverford College, 1981

RESEARCH INTERESTS

Geometric analysis and variational problems, low dimensional geometry & topology, mathematical visualization

Selected Publications

  • On the index of minimal 2-tori in the 4-sphere, J. Reine Angew. Math. 806 (2024) 9-22  (see also DOI: https://doi.org/10.1515/crelle-2023-0066 or arXiv:1803.01615 – with P. Wang)
  • A Gordian Pair of Links, Geometriae Dedicata 217 (2023) Article 47 (see also DOI: https://doi.org/10.1007/s10711-023-00783-1 or arXiv:1908.05610 – with W. Kusner)
  • On the Canham Problem: Bending Energy Minimizers for any Genus and Isoperimetric Ratio, Arch. Rat. Mech. Anal. 247 (2023) Article 10 (see also DOI: https://doi.org/10.1007/s00205-022-01833-w or arXiv:2104.10045 – with P. McGrath)
  • On Steklov Eigenspaces for Free Boundary Minimal Surfaces in the Unit Ball, Amer. J. Math. 14? (202?) ???-??? (in press, see also arXiv:2011.06884 for an earlier version – with P. McGrath)
  • Numerical methods for biomembranes: Conforming subdivision methods versus non-conforming PL methods, Math. Comp. 90:328 (2021) 471-516 (see also DOI: https://doi.org/10.1090/mcom/3584 – with P. Brogan, J. Chen, Y. Yang, T. Yu & A. Zigerelli)
  • The Mathematics of Richard Schoen, Notices Amer. Math. Soc. 65:11 (2018) 1349-1376 (see also DOI: http://dx.doi.org/10.1090/noti1749 - with H. Bray, M. Eichmair, A. Fraser, L.H. Huang, F.C. Marques, C. Mese, W. Minicozzi, K. Uhlenbeck & S.T. Yau)
  • Configuration Spaces of Equal Spheres Touching a Given Sphere: The Twelve Spheres Problem, Bolyai Soc. Math. Study 27 (2018) 219-278 (New Trends in Intuitive Geometry – the Laszlo Fejes Toth Centenary volume; see also arXiv:1611.10297 v3 - with W. Kusner, J. Lagarias & S.Shlosman)
  • Willmore Bending Energy on the Space of Surfaces, MSRI Emissary (2016) 1 & 5-8 (see https://www.msri.org/system/cms/files/204/files/original/Emissary-2016-S..– with A. Mondino & F. Schulze)
  • The expected total curvature of random polygons, Amer. J. Math. 137 (2015), 411-438 (with J. Cantarella, A.Y. Grosberg & C. Shonkwiler)
  • Ropelength Criticality, Geometry & Topology 18 (2014) 1973-2043 (with J. Cantarella, J. Fu & J. Sullivan)
  • Topological Colloids, Nature 493 (2013) 200-205 (with R. Kamien, T. Lubensky, I. Smalyukh & al.)
  • There is no triangulation of the torus with vertex degrees 5, 6, . . . , 6, 7 and related results: Geometric proofs for combinatorial theorems, Geometriae Dedicata 166 (2013) 15-29 (with I. Ismestiev, G. Rote, B. Springborn & J. Sullivan)
  • Coplanar k-Unduloids Are Nondegenerate, Int. Math. Res. Notices (2009) 3391-3416 (with K.G. Brauckmann, N. Korevaar, J. Ratzkin & J. Sullivan)
  • Coplanar constant mean curvature surfaces, Comm. Anal. Geom. 15 (2007) 985-1023 (with K.G. Brauckmann & J. Sullivan)
  • Criticality for the Gehring Link Problem, Geometry & Topology 10 (2006) 2045-2105 (with J. Cantarella, J. Fu, J. Sullivan & N. Wrinkle)
  • On the nondegeneracy of constant mean curvature surfaces, Geom. and Funct. Analysis 16 (2006) 891-923 (with N. Korevaar & J. Ratzkin)
  • Conformal structures and necksizes of embedded constant mean curvature surfaces, Global theory of minimal surfaces, 585-596, Clay Math. Proc. 2 Amer. Math. Soc., Providence, RI, 2005
  • Topology, Geometry and Conformal Structure of Properly Embedded Minimal Surfaces, J. Differential Geom. 67 (2004) 377-393 (with P. Collin, W. Meeks & H. Rosenberg)
  • The second hull of a knotted curve, Amer. J. Math. 125 (2003) 1335–1348. (with J. Cantarella, G. Kuperberg & J. Sullivan) 
  • Embedded CMC Surfaces of genus zero and three ends, J. Reine Angew. Math. 564 (2003) 35-61 (with K.G. Brauckmann & J. Sullivan)
  • On the Minimum Ropelength of Knots and Links, Inventiones Math. 150 (2002) 257-286 (with J. Cantarella & J. Sullivan)
  • Constant Mean Curvature Surfaces with Three Ends, Proc. Nat. Acad. Sci. (USA) 97 (2000) 14067-14068 (with K.G. Brauckmann & J. Sullivan)
  • Tight knot values deviate from linear relations, Nature 392 (1998) 237-238 (with J. Cantarella & J. Sullivan)
  • The Spinor Representation of Surfaces in Space, arXiv:dg-ga/9610005 (1996) 37 pages plus appendices (with N. Schmitt)
  • The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces, Geom. and Funct. Analysis 6 (1996) 120-137 (with R. Mazzeo & D. Pollack)
  • The Global Structure of Constant Mean Curvature Surfaces, Inventiones Math. 114 (1993) 311-332 (with N. Korevaar)
  • Torus knots extremizing the Mobius energy, Experiment. Math. 2 (1993), no. 1, 1-9 (with Denise Kim)
  • The number of faces in a minimal foam, Proc. Roy. Soc. London, Ser. A 439 (1992), no. 1907, 683-686
  • Minimizing the squared mean curvature integral for surfaces in space forms. Experiment. Math. 1 (1992), no. 3, 191–207 (with L. Hsu & J. Sullivan)
  • Constant mean curvature surfaces in hyperbolic space, Amer. J. Math. 114 (1992), 1-43 (with N. Korevaar, W. Meeks & B. Solomon)
  • Bubbles, conservation laws, and balanced diagrams, Geometric analysis and computer graphics (Berkeley, CA, 1988) 103-108, Math. Sci. Res. Inst. Publ. 17 Springer, New York, 1991
  • The Structure of Complete Embedded Surfaces with Constant Mean Curvature, J. Differential Geom. 30 (1989) 465-503 (with N. Korevaar & B. Solomon)
  • Comparison Surfaces for the Willmore Problem, Pacific J. Math. 138 (1989) 317-345
  • Conformal Geometry and Complete Minimal Surfaces, Bull. Amer. Math. Soc. 17 (1987) 291-295