Montserrat Teixidor i Bigas

Montserrat Teixidor i Bigas is Full Professor in the Department of Mathematics at Tufts University in Medford, MA. Teixidor earned her PhD at Universitat de Barcelona in Spain in 1986, her dissertation being "Geometry of linear systems on algebraic curves." Her doctoral advisor was Gerard Eryk Welters.^[1]

She worked in the Department of Pure Mathematics at the University of Liverpool, UK, where in 1988 she produced "The divisor of curves with a vanishing theta-null",^[2] which was published in Compositio Mathematica. She took up an appointment as an Associate Professor of Mathematics at Tufts University, and has been on the faculty of Tufts since 1989. Her area of expertise is Algebraic Geometry and especially Moduli of Vector Bundles on Curves.^[3] She was also a co-organizer of the Clay Institute's workgroup on Vector Bundles on Curves.^[4] Between 2004 and 2005 she spent a year at Radcliffe College, Harvard as a Vera M. Schuyler Fellow, devoting her time to study of "the interplay between the geometry of curves and the equations defining them."^[5] In addition she worked with Barbara Russo to prove Lange's conjecture, which states that "If 0<s\le n'(n-n')(g-1), then there exist stable vector bundles with s_n'(E)=s." Teixidor and Russo prove this result for the generic curve. They also clarify what happens in the interval n'(n-n')(g-1)<s\le n'(n-n')g using a degeneration argument to a reducible curve.^[6]

Poincaré Institute

She is the most senior of three Principal Investigators for the Poincaré Institute, which was launched in 2011 with funding from the NSF, which announced : receiving $9,550,799, Tufts University (Medford) for the project, entitled "The Poincare Institute: A Partnership for Mathematics Education", which is under the direction of Montserrat Teixidor-i-Bigas.^[7] The goal of the Institute is to improve the teaching and learning of mathematics through the various stages of high school. The project rests on the premise that to improve students' learning one needs to broaden and deepen teachers' understanding of mathematics, of how children think and learn, and of mathematics knowledge required for teaching. The Poincaré Institute offers an interdisciplinary, research-based model for introducing a deeper, integrated approach to mathematics in districts where minority and under-privileged students typically underperform. Part of the reason for the concentration on highschool mathematics, and teachers of high school maths, is that, according to Teixidor, "There is substantial evidence that precollege mathematical education in the United States is far from optimal."^[8] Programs developed by the Institute are directed at both teachers and students in an effort to address this matter.

Key articles

• Montserrat Teixidor i Bigas, "Brill-Noether theory for vector bundles," Duke Math. J. Volume 62, Number 2 (1991), 385-400.^[9]
• Montserrat Teixidor i Bigas Curves in Grassmannians, Proc. Amer. Math. Soc. 126 (1998), no. 6, 1597–1603^[10]
• Montserrat Teixidor i Bigas "Green's conjecture for the generic r-gonal curve of genus g≥3r−7," Duke Math. J. 111 (2002), no. 2, 195–222.
• Montserrat Teixidor i Bigas Existence of coherent systems, Internat. J. Math. 19 (2008), no. 4, 449–454.^[11]
• Ivona Grzegorczyk, Montserrat Teixidor i Bigas, Brill-Noether theory for stable vector bundles, Moduli spaces and vector bundles, 29–50, London Math. Soc. Lecture Note Ser., 359, CUP, Cambridge (2009)^[12]
• Montserrat Teixidor i Bigas, Vector bundles on reducible curves and applications, Clay Mathematics Proceedings (2011) ^[13]
• Tawanda Gwena, Montserrat Teixidor i Bigas, Maps between moduli spaces of vector bundles and the base locus of the theta divisor^[14]
• Brian Osserman, Montserrat Teixidor i Bigas Linked alternating forms and linked symplectic Grassmannians, Int. Math. Res. Not. IMRN 2014, no. 3, 720–744.^[15]

References

1. Mathematics Genealogy Project
2. The divisor of curves with a vanishing theta-null
3. People Montserrat Teixidor i Bigas
4. Montserrat Teixidor-i-Bigas
5. FELLOW Montserrat Teixidor i Bigas
6. On Lange's Conjecture
7. Kerry Announces Massachusetts To Receive Additional $28 Million In Science Investments
8. Prime factors in Middle School Math
9. Brill-Noether theory for vector bundles, Duke Math. J. (1991)
10. Curves in Grassmannians, PAMS, 126 (1998), no. 6, 1597–1603
11. Existence of coherent systems, IJM, 19 (2008), no. 4, 449–454.
12. Moduli spaces and vector bundles, London Math. Soc. Lecture Note Ser., 359, Cambridge (2009)
13. Vector bundles on reducible curves and applications, Clay Mathematics Proceedings (2011)
14. Maps between moduli spaces of vector bundles and the base locus of the theta divisor
15. Linked alternating forms and linked symplectic Grassmannians, IMRN (2014), no. 3, 720–744.