Algebraic Geometry, Algebraic Topology, Symplectic Geometry, Mathematical Physics
Professor • Universidad Católica del Norte, Antogafasta, Chile
Visiting Associate Professor • Stanford University
- 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).
- 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
- LG models as symplectic Lefschetz fibrations on adjoint orbits, with L. Grama and L. A. B. San Martin
- 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.
- 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.
- 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 m-ropes, with E. Ballico and
T. Köppe. Cent. Eur. J. Math. 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).
- 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).
- Vector bundles on a three dimensional neighborhood of a ruled surface,
with E. Ballico. J. Pure Appl. Algebra 195 no. 1, 7–19
- 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).
- 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 C2. J. Algebra
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
Adviser: Ofelia T. Alas (USP)
- 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),
- 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
- 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.
- Rollo Jenkins - posdoc
- Brian Callander - PhD - paper,
- Severin Barmeier- PhD - paper
- Carlos Bassani Varea - Master
- Bruno Suzuki - Master
- Michel Faleiros - undergraduate research
- Marcelo Maizman - undergraduate research
- Former students