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-)

    Associate Dean for the Natural, Physical and Mathematical Sciences, College of Letters ans Sciences, UW-Madison, (2018-)


    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. On Poisson structures arising from a Lie Group actions, with Elizabeth Mansfield, submitted.

    2. Integrable Evolutions of twisted polygons in centro-affine Rm, with Anna Calini, to appear in Int Math Res Notices. CentroRnDisc_ForSubmission_FINAL.pdf

    3. The pentagram map on Grassmannians, with Raul Parada, Annales de l'Institut Fourier, Volume 69 (2019) no. 1, p. 421-456. Pentram map in G(n,mn)June23.pdf

    4. 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

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

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

    7. 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 .

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

    9. 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

    10. 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

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

    12. 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

    13. 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

    14. 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

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

    16. 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

    17. 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

    18. 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

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

    20. 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

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

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

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

    24. 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.

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

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

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

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

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

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

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

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

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

    34. 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).

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

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

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

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

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

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

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

    42. 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).

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

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

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

    46. 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