Elizabeth Gasparim

• CV UoE format
• Publications
• Poster
• Minicourse and Lectures
• Computational Algebraic Geometry
• Research Students
• Personal interests

Research Interests

Algebraic Geometry, Algebraic Topology, Mathematical Physics

Events

Seminars

• Topology Seminar, jointly organised with Andrew Ranicki

Past events

• First Latin Congress on Symmetries in Geometry and Physics (formerly known as the “First Cuban Congress”) and the Conference announcement (poster).

Publications

1. The Nekrasov conjecture for toric surfaces, with Melissa Liu, Comm. Math. Phy. 293 (2010), no.3, 661–700 (pdf)
2. Local moduli of holomorphic bundles, with E. Ballico and T. Köppe. J. Pure Appl. Algebra 213, 397–408 (2009). (pdf)
3. Vector bundles near negative curves: moduli and local Euler characteristic, with E. Ballico and T. Köppe. Comm. Algebra 37 no. 8, 2688–2713 (2009). (pdf)
4. Smoothing of rational m-ropes, with E. Ballico and T. Köppe, to appear in Cent. Eur. J. Math. (pdf)
5. The Atiyah-Jones conjecture for rational surfaces, Advances Math. 218, 1027–1050 (2008). (pdf)
6. Local holomorphic Euler characteristic and instanton decay, with T. Köppe and P. Majumdar. Pure Appl. Math. Q. 4, no. 2, Special Issue: In honor of Fedya Bogomolov, Part 1, 161–179 (2008). (pdf)
7. Multiplicity of complex hypersurface singularities, Rouché satellites and Zariski's problem, with C. Eyral. C. R. Math. Acad. Sci. Paris 344, no. 10, 631–634 (2007). (pdf)
8. Three applications of instanton numbers, with P. Ontaneda. Comm. Math. Phys. 270 (1), 1–12 (2007). (pdf)
9. Computing Instanton numbers of curve singularities, with I. Swanson. J. Symbolic Computation 40, no. 2, 965–978 (2005). (pdf)
10. Vector bundles on a three dimensional neighborhood of a ruled surface, with E. Ballico. J. Pure Appl. Algebra 195 no. 1, 7–19 (2005). (pdf)
11. The Atiyah-Jones conjecture for rational surfaces, with R. J. Milgram. MPIM Bonn preprint 2004-14 (2004).
12. Vector bundles on a neighborhood of a curve in a surface and elementary transformations, with E. Ballico. Forum Math. 15 no. 1, 115–122 (2003). (pdf)
13. Numerical invariants for bundles on blow-ups, with E. Ballico. Proc. Amer. Math. Soc. 130 no. 1, 23–32 (2002). (pdf)
14. Two applications of instanton numbers. Isaac Newton Inst. Preprint Series no. NI02022 HDG, 1–15 (2002).
15. Holomorphic vector bundles on holomorphically convex complex surfaces, with E. Ballico. Matematiche (Catania) 55 no. 1, 3–15 (2001).
16. Chern classes of bundles on blown-up surfaces. Comm. Algebra 28 no. 10, 4919–4926 (2000). (pdf)
17. Vector bundles on a formal neighborhood of a curve in a surface, with E. Ballico. Rocky Mountain J. Math. 30 no. 3, 795–814 (2000).
18. Holomorphic and algebraic vector bundles on 0-convex algebraic surfaces, with E. Ballico. Proc. Indian Acad. Sci. 109 no. 4, 353–358 (1999).
19. On the topology of holomorphic bundles. Bol. Soc. Parana. Mat. 18 no. 1.2, 1–7 (1998).
20. Rank two bundles on the blow-up of C². J. Algebra 199 no. 2, 581–590 (1998). (pdf)
21. Chern classes of bundles over rational surfaces. Instituto Politecnico di Torino Rapporto Interno 30 (1998).
22. Holomorphic bundles on O(-k) are algebraic. Comm. Algebra 25 no. 9, 3001–3009 (1997). (pdf)
23. GAGA para variedades não compactas. Anais Acad. Bras. Ciencias 69 no. 4 (1997).
24. Fibrados Holomorficos sobre blow-ups. XXX Anniversary P.U.C. Peru, Pro - Math. 10 no. 20 (1996).
25. Ph.D. Thesis: Holomorphic rank two vector bundles on blow-ups. The University of New Mexico (1995)
    Adviser: Charles P. Boyer
26. Masters Thesis: Three topological invariant cardinals. Universidade Estadual de Campinas, Brazil (1989)
    Adviser: Ofelia T. Alas (USP)

Minicourses, talks, and lecture notes

1. The Nekrasov conjecture for toric surfaces - (slides)
2. Constantin's lectures on Geometric Langlands, typed by me, University of Edinburgh (2007) (pdf)
3. A first lecture on sheaf cohomology, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998)
4. The classification of rational surfaces, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998), math-ph/9909010
5. Fibração de Hopf, uma interpretação geométrica, with P. Majumdar and P. Ontaneda, Summer Lectures, Recife, Brazil (1997)
6. Undergraduate topology lecture notes

Computational Algebraic Geometry

1. Macaulay 2 code used on the paper "Computing Instanton Numbers of Curve Singularities" (with I. Swanson) (2004)
2. Computing instanton invariants, by T. Köppe, contains the Macaulay 2 code used in "Local holomorphic Euler characteristic and instanton decay" and "Vector bundles near negative curves"
3. The Macaulay 2 website, this is the original source, by Grayson and Stillmann.

Research Students

• Jesus Martinez Garcia - PhD Edinburgh
• Thomas Köppe - PhD Edinburgh
• Megan Lockwood - undergradaute research NMSU 2006
• Samatha Kilroy - undergraduate research NMSU 2006
• Zac Harlow - undergraduate research NMSU 2006
• Pablo Gustavo Albuquerque Braz e Silva - postdoc - ICTP 2001
• Antonio Fernado Pereira de Souza - Master - UFPE 2000

Personal interests

Swimming, Dancing, Comedy, Wearing biquinis