Curriculum Vitae

  • Personal Data
  • Position
  • Degrees
  • Awards
  • Publications and preprints
  • Talks given as invited speaker
  • In the future...
  • Other responsabilities

  • Personal Data

    Name : Gloria Marí Beffa.

    Nationality: Spain/USA.

    Mailing address: Van Vleck hall, Dept. of Mathematics, U. of Wisconsin, Madison WI 53706.

    Telephones: Office -- (608) 263-1634

    e-mail address: maribeff(at)


    Assistant Faculty Associate, Mathematics Department, University of Wisconsin - Madison (1997-2000)

    Associate Faculty Associate, Mathematics Department, University of Wisconsin - Madison (2000-2003)

    Faculty Associate, Mathematics Department, University of Wisconsin - Madison (2003-2006)

    Associate Professor, Mathematics Department, University of Wisconsin - Madison (2006-2010)

    Professor, Mathematics Department, University of Wisconsin - Madison (2010-)

    Chair of the Mathematics Department, UW-Madison (2014-)


    Ph.D. in Mathematics , University of Minnesota, June 1991 (Thesis advisor: Prof. Jack F. Conn; thesis title: Poisson Geometry of the Virasoro algebra).

    Licenciatura con grado , Universidad de Malaga , Spain , July 1985.

    Licenciatura , Universidad de Malaga , Spain , June 1985.


    Letters and Science Academic Staff Excellence Mid-Career Award, 2006.

    Letters and Science Faculty Advising Award, 2007-08.

    Philip R. Certain Award for outstanding research, teaching, and service contributions to the College, 2011-12.

    Simons Fellowship by the Simons Foundation, 2012-13.

    Publications and preprints

    1. Integrable Evolutions of twisted polygons in centro-affine Rm, with Anna Calini, in progress.

    2. The pentagram map on Grassmannians, with Raul Parada, to appear in the Annales de l'Institut Fourier. Pentram map in G(n,mn)June23.pdf

    3. On the integrability of the shift map on twisted pentagram spirals, J. Phys. A: Math. Theor. 48 (2015) 285202. spiral-int.pdf

    4. On integrable generalizations of the pentagram map, Int Math Res Notices (2015) 2015 (12): 3669-3693;doi: 10.1093/imrn/rnu044. penta-scaling.pdf

    5. Discrete moving frames on lattice varieties and lattice based multispaces, with L. Mansfield, Foundations of Computational Mathematics, 18(1) 181-247 (2018). latticemovingframe-for-submission.pdf

    6. Hamiltonian evolutions of twisted polygons in parabolic manifolds: the Lagrangian Grassmannian, Pacific Journal of Mathematics 270-2 (2014), 287--317. DOI 10.2140/pjm.2014.270.287 Parabolic-discrete-Grassmannian.pdf .

    7. Hamiltonian structures and integrable evolutions of twisted gons in RPn, with J.P. Wang, Nonlinearity 26 (2013) 2515-2551. Projective-discrete.pdf

    8. Discrete moving frames and integrable systems, with Elizabeth Mansfield and Jing Ping Wang, Foundations of Computational Mathematics, Volume 13, Issue 4 (2013), Page 545-582 (DOI) 10.1007/s10208-013-9153-0. discrete-moving-frames-integrable systems.pdf

    9. An integrable flow for starlike curves in centroaffine space, with A. Calini and T. Ivey, Symmetry, Integrability and Geometry: Methods and Applications, 9 (2013), 022.R3paperSept5-2012.pdf

    10. On generalizations of the pentagram map: discretizations of AGD flows, Journal of Nonlinear Science: Volume 23, Issue 2 (2013), Page 303-334. pentagrammap1.pdf

    11. Geometric Poisson brackets on Grassmannians and the conformal sphere, with Mike Eastwood, Proceedings of the Royal Society of Edinburgh, 142A, 519-555, (2012). Grassmannian-Conformal.pdf

    12. Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors, Annales de l'Institut Fourier, Volume 61, number 6 (2011) p. 2405-2434. O2n-spinors.pdf

    13. A completely integrable flow of star-shaped curves on the light cone, with Theresa Anderson, J. Phys. A: Math. Theor. 44 (2011) 445203. lightcone-conformal.pdf

    14. Poisson structures for Geometric curve flows in semi-simple homogeneous spaces, with Peter Olver, Regular and Chaotic Dynamics 15 (2010) 532-550. psgs.pdf

    15. Integrable Systems Associated to Curves in Flat Galilean and Lorentzian Manifolds, with S. Squires, Applicable Analysis special issue, "Solitons", V 89, 4 (2010), pp 571-592. Galilean-Lorentz.pdf

    16. On bi-Hamiltonian flows and their realizations as curves in real semisimple homogeneous manifolds, Pacific Journal of Mathematics, 247-1 (2010), pp 163-188. semisimple-sphere.pdf

    17. Remarks on KdV-type flows of star-shaped curves, with T. Ivey and A. Calini, Physica D: Volume 238, Issue 8, Pages 788-797 (2009). CaliniIveyMari-Beffa.pdf

    18. Hamiltonian evolutions of curves in classical affine geometries, Phys. D 238 (2009), no. 1, 100-115, affine-geometries.pdf.

    19. Projective-type differential invariants and geometric curve evolutions of KdV-type in flat homogeneous manifolds, Annales de l'Institut Fourier, Tome 58,4 (2008) 1295-1335. Schwarzian-KdV1.pdf

    20. Geometric Hamiltonian structures on flat semisimple homogeneous manifolds, the Asian Journal of Mathematics, v. 12, 1, (2008) 1-33.

    21. Transvection and differential invariants of parametrized curves, with Jan Sanders, Journal of Lie Theory, v. 18, #1, (2008) pp 93-123.

    22. Geometric realizations of Bi-Hamiltonian completely integrable systems, Symmetry, Integrability and Geometry: Methods and Applications, 4 (2008), 034, 23 pages; arXiv:0803.3866.

    23. Projective Type differential invariants for curves and their associated PDEs of KdV type, IMA volumes in Mathematics and its Applications, v. 144 (2008) pp 265-276.

    24. On completely integrable geometric evolutions of curves of Lagrangian planes, Proceedings of the Royal Society of Edinburg, 137A (2007), 111--131.

    25. Poisson geometry of differential invariants of curves in some nonsemisimple homogenous spaces, Proc. Amer. Math. Soc. 134 (2006) 779-791, nonsemisimple.pdf , Corrigenda

    26. Poisson brackets associated to the Conformal geometry of curves, Trans. Amer. Math. Soc. 357 (2005) 2799-2827.

    27. Poisson brackets associated to invariant evolutions of Riemannian curves , Pacific Journal of Mathematics, 215 (2) (2004) 357-380.

    28. On Relative and Absolute Differential invariants of conformal curves, Journal of Lie Theory, 13 (2003) 213-245.

    29. On Integrable systems in 3--dimensional Riemannian Geometry , with J. Sanders and J.P. Wang, J. Nonlinear Sci. V. 12, pp. 143--167 (2002)

    30. KdV Hamiltonian systems and differential invariants in projective and conformal geometries, Contemporary Mathematics, AMS, V. 285 pp:29-38 (2001).

    31. Corrigenda to Conformal analogue of the ADG bracket in two dimensions , J.Phy.A: Math Gen 33(2000) 8601.

    32. Conformal analogue of the ADG bracket in two dimensions , J. Phy.A: Math Gen 33 (2000) 4689--4707.

    33. The Theory of Differential Invariance and Infinite dimensional Hamiltonian evolutions , in Poisson Geometry, Banach Center Publications, V. 51, Institute of Mathematics, Polish Academy of Sc. Warszawa (2000).

    34. The Theory of differential invariants and KdV Hamiltonian evolutions , Bull. Soc. math. France, 127, pp 363--391, 1999.

    35. Differential Invariants for Parametrized Projective Surfaces , with Peter Olver, Communications in Analysis and Geometry, V. 7, no 4, 807--839, 1999.

    36. Invariant Differential Equations and the Adler-Gel'fand-Dikii bracket , with A. Lopez and R. Heredero, J. Math. Phy. 38, 5720--5738, (1997).

    37. The Second Hamiltonian Structure for the Periodic Toda Lattice , Proceedings of the Royal Math Soc of Edinburg, 127 A , 547-566, 1997.

    38. Transverse sections for the Second Hamiltonian KdV structure , The Journal of Geometrical Analysis, V.8, #3, 385--407 (1998).

    39. On the Poisson geometry of the Adler-Gel'fand-Dikii brackets , The Journal of Geometrical Analysis, v. 6-2 , 207-232, 1996.

    40. Poisson Geometry of Adler-Gel'fand-Dikii Manifolds , Proc. of the Cornelius Lanczos International Centenary Conference, Ed. Brown, Chu and Ellison, SIAM 1994.

    41. On the Virasoro algebra as a Poisson submanifold of a Kac-Moody algebra on the circle , Proc.of the American Mathematical Society, 122-3 , 859-869 (1994).

    42. A Transverse structure for the Lie-Poisson bracket on the dual of the Virasoro algebra , Pacific Journal of Mathematics 163-1 , 43-72 (1994).

    43. A symplectic realization for a nonlinearizable Poisson structure on $sl(2, \R)^{\ast}$ , with J. Conn, preprint.

    44. Modelos matem\' aticos no lineales con umbral en la Teor\' \i a de Epidemias , Proceedings of the CNEDA, Santander, Spain 1985.

    45. Los modelos SIS and SIRS en la Teoria de Epidemias , Proceedings of the Jornadas Hispano-Lusas de Matem\` aticas, Badajoz, Spain 1986.

    Talks given as invited speaker

    In the future..

    I am on sabbatical during 2012-13, back to teaching in Fall 2013.

    Other responsabilities

    I am Chair of the equity and diversity committee in Letters and Science, and member of the faculty executive graduate school committee and of the Undergraduate General education campus-wide committee.

    Also a member of the State of Wisconsin task force in charge of rewriting state wide math standards and alligning them with the National Math core standards.

    I am a referee for a number of Mathematics journals and I am co-editing SIGMA and FoCM special issues.

    Volunteer coordinator of the UW Mentorship program for women in Math and Science, a mentorship program connecting talented highschool girls to Math graduate students and Undergraduate Math/science/engineering majors.

    I am the mother of a thirteen and a eighteen years old, wife and we take care of a house. How we manage to do everything is beyond my understanding.

    Last modified: September 2011 by Gloria Mari Beffa