Montserrat Teixidor i Bigas

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 , which states that "If ${\displaystyle 0<s\leq n'(n-n')(g-1)}$, then there exist stable vector bundles with ${\displaystyle s_{n'}(E)=s}$." They also clarified what happens in the interval ${\displaystyle n'(n-n')(g-1)<s\leq n'(n-n')g}$ 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 . 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 ${\displaystyle r}$-gonal curve of genus ${\displaystyle g\geq 3r-7}$," 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.^[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]

References[]