Email: etgasparim@gmail.com
## Research InterestsAlgebraic Geometry, Algebraic Topology, Symplectic Geometry, Mathematical Physics ## Professor • Universidad Católica del Norte, Antogafasta, Chile## Visiting Associate Professor • Stanford University## Director of the Institute for Geometry and Physics Miami-Cinvestav-Antofagasta## Events## Seminars## Upcoming events- Conference on Homological Mirror Symmetry and Geometry - Miami January 2015
## Past events- V Latin American Conference on Lie Groups and Geometry - Petrolina/Juazeiro November 2014
- Fifth Conference of the IGPMCC : Playa del Carmen (Mexico)
- Fourth conference of the IGPMCC : Miami (USA)
- Third conference of the IGPMCC: Third Latin Congress, Maranhão (Brazil)
- Second conference of the IGPMCC: TQFT, Langlands and HMS (Mexico)
- First conference of the IGPMCC: Homological Mirror Symmetry (Miami)
- Second Latin Congress on Symmetries in Geometry and Physics, Curitiba (Brazil)
- Hodge Theoretic Reflexions on the String Landscape, Edinburgh (UK)
- First Latin Congress on Symmetries in Geometry and Physics (Cuba)
## Publications*Symplectic Lefschetz fibrations from a Lie theoretical viewpoint,*with B. Callander, L. Grama and L. A. B. San Martin, to appear in the Proc. Langlands, TQFT and Mirror Symmetry, Playa del Carmen, Mexico (2014). (pdf)*Compactifications of adjoint orbits and their Hodge diamonds,*with B. Callander (pdf)*Adjoint orbits of semi-simple Lie groups and Lagrangean submanifolds, with L. Grama and L. A. B. San Martin, to appear in the Proc. Edinburgh Math. Society (pdf)**LG models as symplectic Lefschetz fibrations on adjoint orbits, with L. Grama and L. A. B. San Martin (pdf)**Self-duality for Landau--Ginzburg models, with B. Callander, R. Jenkins, and Lino M. Silva, to appear in J. Geom. Symmetry Phys. (pdf)**Moduli Stacks of Bundles on Local Surfaces*, with O. Ben-Bassat, Homological Mirror Symmetry and Tropical Geometry (Cetraro, Italy, July 2-8, 2011) Lecture Notes in Mathematics UMI, Springer (2014) 1--32 (pdf)*Isomorphisms of moduli spaces*, with C. Casorrán Amilburu, S. Barmeier and B. Callander, Proceedings of the Second Latin Congress on Symmetries in Geometry and Physics, Matemática Contemporânea 41 (2012) 1–10. (pdf)*BPS counting on singular varieties*, with T. Köppe, P. Majumdar and K. Ray, J. Phys. A: Math. Theor. 45 (2012) 265–401. (pdf)*On the geometry of moduli spaces of anti-self-dual connections*, with E. Ballico and C. Eyral, Top. Appl. 159, n. 3, 15 (2012) 633–645. (pdf)*Cohomology gaps for reflexive sheaves on threefolds*, with E. Ballico, J. Geom. Symmetry Phys.**21**(2011) 29–39. (pdf)*Sheaves on singular varieties*, with T. Köppe. J. Singularities**2**(2010) 56–66. Proceedings of Singularities in Aarhus, August 2009. (pdf)*The Nekrasov conjecture for toric surfaces*, with Melissa Liu. Comm. Math. Phys.**293**(2010), no. 3, 661–700. (pdf)*Local moduli of holomorphic bundles*, with E. Ballico and T. Köppe. J. Pure Appl. Algebra**213**, 397–408 (2009). (pdf)*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)*Smoothing of rational*, with E. Ballico and T. Köppe. Cent. Eur. J. Math.`m`-ropes**7**no. 3, 623–628 (2009) (pdf)*The Atiyah-Jones conjecture for rational surfaces*, Advances Math.**218**, 1027–1050 (2008). (pdf)*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)*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)*Three applications of instanton numbers*, with P. Ontaneda. Comm. Math. Phys.**270**(1), 1–12 (2007). (pdf)*Computing Instanton numbers of curve singularities*, with I. Swanson. J. Symbolic Computation**40**, no. 2, 965–978 (2005). (pdf)*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)*The Atiyah-Jones conjecture for rational surfaces*, with R. J. Milgram. MPIM Bonn preprint 2004-14 (2004).*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)*Numerical invariants for bundles on blow-ups*, with E. Ballico. Proc. Amer. Math. Soc.**130**no. 1, 23–32 (2002). (pdf)*Two applications of instanton numbers*. Isaac Newton Inst. Preprint Series no. NI02022 HDG, 1–15 (2002).*Holomorphic vector bundles on holomorphically convex complex surfaces*, with E. Ballico. Matematiche (Catania)**55**no. 1, 3–15 (2001).*Chern classes of bundles on blown-up surfaces*. Comm. Algebra**28**no. 10, 4919–4926 (2000). (pdf)*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).*Holomorphic and algebraic vector bundles on 0-convex algebraic surfaces*, with E. Ballico. Proc. Indian Acad. Sci.**109**no. 4, 353–358 (1999).*On the topology of holomorphic bundles*. Bol. Soc. Parana. Mat.**18**no. 1.2, 1–7 (1998).*Rank two bundles on the blow-up of C*. J. Algebra^{2}**199**no. 2, 581–590 (1998). (pdf)*Chern classes of bundles over rational surfaces*. Instituto Politecnico di Torino Rapporto Interno 30 (1998).*Holomorphic bundles on O(-k) are algebraic*. Comm. Algebra**25**no. 9, 3001–3009 (1997). (pdf)*GAGA para variedades não compactas*. Anais Acad. Bras. Ciencias**69**no. 4 (1997).*Fibrados Holomorficos sobre blow-ups*. XXX Anniversary P.U.C. Peru, Pro - Math. 10 no. 20 (1996).- Ph.D. Thesis:
*Holomorphic rank two vector bundles on blow-ups.*The University of New Mexico (1995) Adviser: Charles P. Boyer - Masters Thesis:
*Three topological invariant cardinals.*Universidade Estadual de Campinas, Brazil (1989) Adviser: Ofelia T. Alas (USP)
## Minicourses, talks, and lecture notes- Curso de Verão em Maringá 2015 (notas)
*Hodge diamonds and adjoint orbits*, with B. Callander (pdf)- Variedades Tóricas (notes).
- The Nekrasov conjecture for toric surfaces - (slides)
- Constantin's lectures on Geometric Langlands, typed by me, University of Edinburgh (2007) (pdf)
- A first lecture on sheaf cohomology, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998)(pdf)
- The classification of rational surfaces, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998), math-ph/9909010
- Fibração de Hopf, uma interpretação geométrica, with P. Majumdar and P. Ontaneda, Summer Lectures, Recife, Brazil (1997)
- Undergraduate topology lecture notes
- Isomorphisms of Moduli Spaces
## Computational Algebraic Geometry- Hodge diamonds and adjoint orbits, with B. Callander, explains the Macaulay2 code used in "Compactifications of Adjoint orbits and their Hodge diamonds".
- Toric Varieties: página do Marcelo, página do Michel
*.* *Macaulay 2*code used in the paper "Computing Instanton Numbers of Curve Singularities", with I. Swanson.- 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". - The
*Macaulay 2*website, this is the original source, by Grayson and Stillmann.
## Current Research Students- Rollo Jenkins - posdoc
- Brian Callander - PhD - paper, Master thesis
- Severin Barmeier- PhD - paper
- Carlos Bassani Varea - Master
- Bruno Suzuki - Master
- Michel Faleiros - undergraduate research
- Marcelo Maizman - undergraduate research
- Former students
## Personal interests |