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)math.wisc.edu

    Positions
    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 (2014-2018)

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

    Interim Associate Dean for Research, College of Letters and Sciences, UW-Madison, (2020-Jan 2023)

    Associate Dean for Research, College of Letters and Sciences, UW-Madison (Jan 2023-)

    Degrees
    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.

    Awards
    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. Wm Algebras and Fractional Powers of Difference Operators, Nonlinearity, 37-9, 095011 (July 2024), centroRn-part3.pdf.

    2. What is a lattice Wm-algebra?, with Anton Izosimov, International Mathematics Research Notices, rnad151, July 2023, centroRn-part2.pdf.

    3. On Poisson structures arising from a Lie Group action, with Elizabeth Mansfield, preprint.

    4. Integrable Evolutions of twisted polygons in centro-affine Rm, with Anna Calini, International Mathematics Research Notices, V 6, (2022), 4318-4375. CentroRnDisc_ForSubmission_FINAL --- Correction

    5. 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

    6. 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

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

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

    9. 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 .

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

    11. 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

    12. 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

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

    14. 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

    15. 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

    16. 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

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

    18. 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

    19. 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

    20. 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

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

    22. 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

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

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

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

    26. 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.

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

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

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

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

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

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

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

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

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

    36. 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).

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

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

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

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

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

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

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

    44. 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).

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

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

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

    48. 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

  • From Geometric Invariants to Integrable Systems via Lie Groups, Symmetry, Invariants, and their Applications, AARMS, Halifax, August 2022.

  • Discrete Geometry of Polygons and Soliton Equations, Colloquium, North Carolina State University, Raleigh, March 2022.

  • Pseudo difference operators and discrete W_n algebras, Moving frames and their modern applications, Banff International Research Station, August 2021.

  • Adding Symmetry to discrete systems, A Celebration of Symmetry and Computation, University of Kent at Canterbury, July 2019.

  • Plenary talk at the XXVII International Fall Workshop on Geometry and Physics, Sevilla, Spain (2018).

  • Discrete Geometry of polygons and soliton equation, part I and II. Infinite Dimensional Algebra seminar, MIT (2018)

  • Discrete geometry of polygons and Soliton Equations, Colloquium, University of Illinois, Urbana-Champaign, October 2017.

  • Discrete Geometry of Polygons and Soliton Equations, Joint London Mathematical Society and Institute of Mathematics and Applications; Symmetry and Computation, London October 2017.

  • Discrete geometry of centro-affine polygons and Hamiltonian structures for discrete Wn-algebras, 10th IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory. Athens, Georgia, March 2017.

  • Discrete geometry of polygons and Hamiltonian structures, Integrability and near-integrability in mechanics and geometry, CMO, Oaxaca, June 2016.

  • Geometric realizations of completely integrable PDEs: continuous and discrete cases, (plenary speaker) WIMS, University of Illinois, Urbana, April 2016. Also at Women in Geometry, Banff, November 2015.

  • Lax representations for pentagram maps and spirals, Colloquium, University of Georgia, Athens, April 2015.

  • The Shift map on pentagram spirals, AMS regional meeting, Section: Integrable Combinatorics. East Lansing, March 2015.

  • The geometry of polygons and completely integrable systems, SIAM-NW14 (Conference on Nonlinear Waves and Coherent Structures), Churchill College, Cambridge, UKi, 2014.

  • The pentagram map and its generalizations, Differential Geometry seminar, CIMAT, Guanajuato, Mexico, 2013.

  • Generalizations of the pentagram map to higher dimensions, 2nd conference on Finite dimensional integrable systems, CIRM, Lumini, Marseille 2013.

  • Generalizations of the pentagram map, Differential Geometry Seminar, Arizona State University, Tempe, 2013.

  • Discrete moving frames, given at the Applied Math Seminar, U of Kent-Canterbury UK, November, 2012.

  • Discrete moving frames and applications to integrable systems, given at the Math-Physics Seminar, UMN-Minneapolis, September, 2012.

  • The pentagram map and generalizations: Integrable discretizations of AGD flows, I gave three different variations of this talk at three different conferences: Moving frames in Geometry, a workshop at the CRM, Montreal, May 2011; Foundations of Computational Mathematics, FoCM'11, Budapest July 2011; Workshop in discrete integrable systems, Lorentz center, Leiden July 2011.

  • Geometric realizations of KdV equations in semisimple parabolic manifolds, Spring Lecture Series on Conformal Differential Geometry and its interaction with Representation Theory, Fayetteville, Arkansas, April 2011.

  • Bi-Hamiltonian Flows and Geometric Realizations, plenary speaker, Fourth International Workshop on Differential Algebra and Related Topics (DART-IV), Beijing, China, October 30, 2010

  • Classical Geometry of curves and geometric realizations of soliton equations, given at the Differential Geometry Seminar, UC-Irvine, March, 2010.

  • On the preservation of invariants of arc-length type by geometric Hamiltonian curve flows, given at the AMS Spring sectional meeting, Raleigh, April 2009.

  • Classical Geometry of curves and Completely integrable systems, given at the Symplectic Geometry Seminar, Penn State, November 2007.

  • Geometric Realizations of Completely Integrable biHamiltonian systems, Seventh International Conference Symmetry in Nonlinear Mathematical Physics, Kiev, Ukraine, June 2007.

  • Projective type differential invariants for curves and their associated PDEs of KdV type , IMA Summer program on Symmetries and Overdetermined Systems of Partial Differential Equations , Minneapolis, July-August 2006.

  • Classical geometry of curves, Moving frames and Hamiltonian Structures of PDEs, Mathematics Department Colloquium, Vrije Universiteit, Amsterdam 2006.

  • Projective-type differential invariants of curves, and their associated PDEs of KdV-type, Applied Mathematics Seminar, University of Kent at Canterbury, 2005 and Geometric Analysis seminar, University of Wisconsin at Madison 2006.

  • Invariant evolutions of curves in flat homogeneous spaces, given at a meeting on Applications of invariant theory to Differential Geometry, CMS meeting at Dalhousie University in Halifax, Canada, June 2004.

  • Poisson structures associated to the geometry of curves in manifolds with a conformal structure, BIRS conference on Differential invariants and invariant differential equations, Banff, Canada, July 2003.

  • Hamiltonian structures associated to Riemannian curves , Formal Geometry and Mathematical Physics meeting, Utah State U, Logan 2002.

  • Hamiltonian systems of PDEs and Invariance Theory , Analysis Seminar, Leiden University, Leiden 2000.

  • KdV Hamiltonian systems and differential invariants in projective and conformal geometries , NSF-CBMS Conference on the "Geometrical Study of Differential Equations", Howard University, Washington DC June 2000.

  • Integrable systems and the periodic Toda Lattice, The Noetherian Ring, Madison Fall 1999.

  • The Theory of Differential Invariance and Hamiltonian systems , "Poisson Geometry", Banach center, Warsaw, Poland August 1998.

  • Using Geometry to solve some analysis problems , St Thomas University, StPaul, Minnesota April 1998.

  • Differential Invariants and KdV evolutions ,Geometry seminar, U. of Wisconsin, Madison October 1997.

  • The Geometer sketchpad , Mathematics and computers seminar, U. of Wisconsin, Madison October 1997.

  • Normal forms for differential equations with periodic coefficients , Mathematics dept., Ohio State University, Columbus, Ohio February 1997.

  • Normal forms and the Second KdV Poisson structure , Mathematics Colloquium, Georgia State University, Atlanta, February 1997.

  • Invariant differential equations and the Second Adler-Gel'fand-Dikii bracket, Geometric analysis seminar, U of Minnesota, Minneapolis, February 1997.

  • Normal forms and the Geometry of infinite dimensional manifolds, The Noetherian Ring (a seminar for women graduate students), Madison, September 1996.

  • Invariant Differential Equations and the Adler-Gelfand-Dikii bracket , Geometry-Algebra seminar, CPT, Lumini, Marseille, France June 1996.

  • Invariant Differential Equations and the Second KdV Hamiltonian Structure, Theoretical Physics seminar, Departamento de Fisica Teorica, Physics Department, U. Complutense, Madrid, Spain June 1996.

  • Differential Invariants and the Second Hamiltonian KdV Structure, joint Theoretical Physics-Applied Math seminar, Mathematics department, Instituto Tecnico Superior, Lisbon, Portugal December 1995.

  • Poisson Geometry of Adler-Gel'fand-Dikii manifolds , Cornelius Lanczos International Centenary Conference, Raleigh NC, December 1993.

  • Normal forms for nth order scalar differential operators with periodic coefficients, Geometric analysis seminar, U Minnesota, Minneapolis Spring 1993.

  • Poisson Geometry of Kac-Moody algebras and their associated Adler-Gelfand-Dikii brackets , Joint Symplectic Geometry seminar Stanford-Berkeley-Davis-Santa Cruz, UC Berkeley, Winter 1992.

  • Transverse structures in infinite dimensions , Geometry and Topology seminar, UC Davis, winter 1992.

  • Transverse structure on the dual of the Virasoro algebra (I and II), given on January and February 1990 at the Math Physics joint seminar IMA-School of Mathematics, University of Minnesota.

  • Several talks at the Graduate Math-Physics seminar, during 1990 and 1991 at the School of Mathematics, University of Minnesota.
    • Last modified: September 2020 by Gloria Mari Beffa
    maribeff(at)math.wisc.edu