Montserrat Teixidor i Bigas explained

Montserrat Teixidor i Bigas
Birth Date:	February 25, 1958
Birth Place:	Barcelona, Spain
Discipline:	Mathematics
Education:	University of Barcelona (BSc, PhD)
Sub Discipline:	Linear systems Algebraic curves Pure mathematics
Doctoral Advisor:	Gerard Eryk Welters
Workplaces:	University of Liverpool Radcliffe College Tufts University
Thesis Title:	Geometry of linear systems on algebraic curves

Montserrat Teixidor i Bigas (born February 25, 1958) is a Spanish-American academic who is a professor of mathematics at Tufts University in Medford, Massachusetts.^[1] She specializes in algebraic geometry, especially Moduli of Vector Bundles on curves.^[2]

Education

Teixidor i Bigas was born in Barcelona in 1958. She earned a bachelor's degree and PhD from the University of Barcelona, where she wrote her dissertation, "Geometry of linear systems on algebraic curves", under the supervision of Gerard Eryk Welters.^{[3] [4]}

Career

She worked in the department of pure mathematics at the University of Liverpool, where she wrote "The divisor of curves with a vanishing theta-null",^[5] for Compositio Mathematica in 1988.

In 1997, she proved Lange's conjecture for the generic curve, with Barbara Russo, which states that "If

0 <s\le n'(n - n')(g -1 ) , then there exist stable vector bundles with s _{n'} (E) = s ." They also clarified 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]

She took up an appointment as an Associate Professor of Mathematics at Tufts University, and has been on the faculty of Tufts since 1989. She has been a reviewer for several journals, including the Bulletin of the American Mathematical Society, the Duke Mathematical Journal, and the journal of algebraic geometry. She has held visiting positions at Brown University and the University of Cambridge.^[7] She was also a co-organizer of the Clay Institute's workgroup on Vector Bundles on Curves.^[8]

In 2004, she spent a year at Radcliffe College as a Vera M. Schuyler Fellow, devoting her time to study of "the interplay between the geometry of curves and the equations defining them."^[9]

Selected publications

• Montserrat Teixidor i Bigas, "Brill-Noether theory for vector bundles," Duke Math. J. Volume 62, Number 2 (1991), 385-400.^[10]
• Montserrat Teixidor i Bigas Curves in Grassmannians, Proc. Amer. Math. Soc. 126 (1998), no. 6, 1597–1603^[11]
• Montserrat Teixidor i Bigas "Green's conjecture for the generic

r -gonal curve of genus g\ge 3 r -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.^[12]
• 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)^[13]
• Montserrat Teixidor i Bigas, Vector bundles on reducible curves and applications, Clay Mathematics Proceedings (2011)^[14]
• Tawanda Gwena, Montserrat Teixidor i Bigas, Maps between moduli spaces of vector bundles and the base locus of the theta divisor^[15]
• Brian Osserman, Montserrat Teixidor i Bigas Linked alternating forms and linked symplectic Grassmannians, Int. Math. Res. Not. IMRN 2014, no. 3, 720–744.^[16]

Notes and References

1. Web site: Montserrat Teixidor i Bigas Tufts University - Graduate Programs. asegrad.tufts.edu. 2019-05-07.
2. http://math.tufts.edu/people/facultyTeixidor.htm People Montserrat Teixidor i Bigas
3. http://genealogy.math.ndsu.nodak.edu/id.php?id=95650 Mathematics Genealogy Project
4. Web site: Montserrat Teixidor i Bigas. 2021-01-10. webhosting.math.tufts.edu.
5. http://archive.numdam.org/ARCHIVE/CM/CM_1988__66_1/CM_1988__66_1_15_0/CM_1988__66_1_15_0.pdf The divisor of curves with a vanishing theta-null
6. http://adsabs.harvard.edu/abs/1997alg.geom..5019T On Lange's Conjecture
7. Web site: Montserrat Teixidor i Bigas. 2012-03-16. Radcliffe Institute for Advanced Study at Harvard University. en. 2019-05-07.
8. http://sites.tufts.edu/poincare/meet-the-team/montserrat-teixidor-i-bigas/ Montserrat Teixidor-i-Bigas
9. http://www.radcliffe.harvard.edu/people/montserrat-teixidor-i-bigas FELLOW Montserrat Teixidor i Bigas
10. http://projecteuclid.org/euclid.dmj/1077296363 Brill-Noether theory for vector bundles, Duke Math. J. (1991)
11. https://www.ams.org/journals/proc/1998-126-06/S0002-9939-98-04475-X/S0002-9939-98-04475-X.pdf Curves in Grassmannians, PAMS, 126 (1998), no. 6, 1597–1603
12. http://www.worldscientific.com/doi/abs/10.1142/S0129167X08004777 Existence of coherent systems, IJM, 19 (2008), no. 4, 449–454.
13. http://ebooks.cambridge.org/chapter.jsf?bid=CBO9781139107037&cid=CBO9781139107037A012, Moduli spaces and vector bundles, London Math. Soc. Lecture Note Ser., 359, Cambridge (2009)
14. http://www.math.ucdavis.edu/~osserman/math/montserrat-Clay.pdf Vector bundles on reducible curves and applications, Clay Mathematics Proceedings (2011)
15. https://arxiv.org/abs/0706.3953 Maps between moduli spaces of vector bundles and the base locus of the theta divisor
16. https://archive.today/20130410042106/http://libra.msra.cn/Publication/27615582/linked-alternating-forms-and-linked-symplectic-grassmannians Linked alternating forms and linked symplectic Grassmannians, IMRN (2014), no. 3, 720–744.