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.
On the Geometric background of Drinfeld and Sokolov's equations of KdV-type,
in preparation.
Hamiltonian structures and integrable evolutions of twisted gons in RPn, with J.P. Wang, in preparation.
Discrete moving frames and applications,
with Elizabeth Mansfield and Jing Ping Wang, submitted. discrete-moving-frame.pdf
An integrable flow for starlike curves in centroaffine space, with A. Calini and T. Ivey, in preparation.
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
On generalizations of the pentagram map: discretizations of AGD flows,
submitted. pentagrammap1.pdf
Geometric Poisson brackets on Grassmannians and the
conformal sphere, with Mike Eastwood, accepted for publication in the Proceeding of the Royal Society of Edinburg Grassmannian-Conformal.pdf
Moving frames, Geometric Poisson brackets and the KdV-Schwarzian evolution of pure spinors, accepted for publication at the Annales de l'Institut Fourier. O2n-spinors.pdf
Poisson structures for Geometric curve flows in semi-simple homogeneous spaces,
with Peter Olver, Regular and Chaotic Dynamics 15 (2010) 532-550. psgs.pdf
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
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
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
Hamiltonian evolutions of curves in classical affine geometries,
Phys. D 238 (2009), no. 1, 100-115, affine-geometries.pdf.
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
Geometric Hamiltonian structures on
flat semisimple homogeneous
manifolds,
the Asian Journal of Mathematics, v. 12, 1, (2008) 1-33. gbracket.ps
Transvection and differential invariants
of parametrized curves,
with Jan Sanders, Journal of Lie Theory, v. 18, #1, (2008) pp 93-123.
Geometric realizations of Bi-Hamiltonian completely integrable systems, Symmetry, Integrability
and Geometry: Methods and Applications, 4 (2008), 034, 23 pages; arXiv:0803.3866.
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.
On completely integrable
geometric evolutions of curves of Lagrangian planes,
Proceedings of the Royal Society of
Edinburg, 137A (2007), 111--131.
Poisson geometry of differential invariants of curves in
some nonsemisimple homogenous spaces, Proc. Amer. Math. Soc. 134 (2006) 779-791.
Poisson brackets associated to the Conformal geometry of curves,
Trans. Amer. Math. Soc. 357 (2005) 2799-2827.
Poisson brackets associated to invariant evolutions of Riemannian curves
,
Pacific Journal of Mathematics, 215 (2) (2004) 357-380.
On Relative and Absolute Differential invariants
of conformal curves,
Journal of Lie Theory, 13 (2003) 213-245.
On Integrable systems in 3--dimensional Riemannian Geometry
, with J. Sanders and J.P. Wang,
J. Nonlinear Sci. V. 12, pp. 143--167 (2002)
KdV Hamiltonian systems and differential invariants in projective
and conformal geometries,
Contemporary Mathematics, AMS, V. 285 pp:29-38 (2001).
Corrigenda to Conformal analogue of the ADG bracket
in two dimensions
,
J.Phy.A: Math Gen 33(2000) 8601.
Conformal analogue of the ADG bracket
in two dimensions
, J. Phy.A: Math Gen 33 (2000) 4689--4707.
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).
The Theory of differential invariants and KdV Hamiltonian evolutions
, Bull. Soc. math. France, 127, pp 363--391, 1999.
Differential Invariants for Parametrized Projective
Surfaces
, with Peter Olver, Communications in Analysis and Geometry, V. 7, no 4,
807--839, 1999.
Invariant Differential Equations and the
Adler-Gel'fand-Dikii bracket
, with A. Lopez and R. Heredero, J. Math. Phy. 38, 5720--5738, (1997).
The Second Hamiltonian Structure for the Periodic
Toda Lattice
, Proceedings of the Royal Math Soc of Edinburg,
127 A , 547-566, 1997.
Transverse sections for the Second Hamiltonian
KdV structure
, The Journal of Geometrical Analysis, V.8, #3, 385--407 (1998).
On the Poisson geometry of the Adler-Gel'fand-Dikii
brackets
, The Journal of Geometrical Analysis,
v. 6-2 , 207-232, 1996.
Poisson Geometry of Adler-Gel'fand-Dikii Manifolds
, Proc. of the Cornelius Lanczos International Centenary Conference,
Ed. Brown, Chu and Ellison, SIAM 1994.
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).
A Transverse structure for the Lie-Poisson bracket
on the dual of the
Virasoro algebra
, Pacific Journal of Mathematics
163-1 , 43-72 (1994).
A symplectic realization for a nonlinearizable Poisson
structure on
$sl(2, \R)^{\ast}$
, with J. Conn, preprint.
Modelos matem\' aticos no lineales con umbral
en la Teor\' \i a de Epidemias
, Proceedings of the CNEDA, Santander, Spain 1985.
Los modelos SIS and SIRS en la Teoria de Epidemias
, Proceedings of the Jornadas Hispano-Lusas de Matem\` aticas,
Badajoz, Spain 1986.
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.
I am organizing the conference "Symmetries of Differential
Equations: Frames, Invariants and Applications" together with Willard Miller,
Niky Kamran and Guillermo Sapiro. The conference is in honor of the 60th birthday of Peter Olver.
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.
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 a member of the steering committee in charge of the AWM mentor network.
I am the mother of a twelve and a seventeen years old, wife and we take care of a house. How we manage to do everything is beyond my understanding.