Research Interests

Algebraic Geometry, Symplectic Geometry, Mathematical Physics

Events

Upcoming events

• Workshop on deformation theory II - ICTP Italy - September 2023.

Past Events

Publications

1. Lagrangian skeleta, collars and duality, with E. Ballico, F. Rubilar, and  B. Suzuki, in Birational  Geometry, Kahler-Einstein Metrics and Degenerations,  Springer Proc. Math. Stat. 409 (2023). (pdf)

2. Poisson structures on the conifold and local Calabi-Yau threefolds, with E. Ballico, T. Koppe and B. Suzuki,  Rep. Math. Phys.  90 n.3 (2022) 299-324. (pdf)

3. Quantizations of local surfaces and rebel instantons, with S. Barmeier, J. Noncommut. Geom. 16 (2022). (pdf)

4. The Kuranishi map for vector bundles on certain products of curves, with E. Ballico, F. Rubilar and B. Suzuki, Topology and its Applications 312 (2022) 108056. (pdf) 

5. 25 open questions about Vector Bundles and their Moduli,  with E. Ballico and F. Rubilar, Proyecciones 41 n.2 403 - 36. (pdf)

6. Curvature grafted by instantons, with B. Suzuki, Indian J. Phys. 95 n.8  (2021) 1631 -1638. (pdf)

7.  20 open questions about deformations of compactifiable manifolds, with E. Ballico and F. Rubilar, Sao Paulo J. Math.  Sci. 15 n.2 (2021) 661-681. (pdf)

8. Invariant generalized complex structures on maximal flag manifolds, with F. Valencia and C. Varea, (pdf)

9. Infinite dimensional families of Calabi-Yau threefolds and moduli of vector bundles, with E. Ballico and B. Suzuki, Journal of Pure and Applied Algebra 225 (4), 106554. (pdf).

10. Deformations of noncompact Calabi-Yau manifolds, families and diamonds, with F. Rubilar, arXiv:1908.09045. 

11. Infinitesimally tight Lagrangian orbits, with L. A. B. San Martin and F. Valencia, Mathematische Zeitschrift  297 (2021) 1877-1898. (pdf ) 

12. KKP conjecture for minimal adjoint orbits, with E. Ballico, L. A. B. San Martin and F. Rubilar, arXiv:1901.07939. 

13. Classical deformations of local surfaces and their moduli of instantons, with S. Barmeier, J. Pure and Applied Algebra. 223 n. 6, (2019), 2543-2561

14. Aplicações da teoria de Lie à geometria simplética, with C. Bassani, to appear in Boletim da Soc. Parana. Matemática.  (pdf) (pdf, alternative link)

15. Deformations of noncompact Calabi-Yau threefolds, with T. Köppe, F. Rubilar and B. Suzuki, Proc. VI Latin American Congress of Mathematicians, Rev. Colombiana de Matemáticas, 52 no. 1 (2018) 41-57. (pdf)

16. A Lie theoretical construction of a Landau–Ginzburg models without projective mirrors, with E. Ballico, S. Barmeier, L. Grama and L. A. B. San Martin, Manuscripta Math. (2018), 1–17. (arXiv:1610.06965)

17. Compactifications of adjoint orbits and their Hodge diamonds, with E. Ballico, and B. Callander,  J. Algebra Appl. 16  (2018) no 2.  (pdf) 

18. Some Landau-Ginzburg models viewed as rational maps, with E. Ballico, L. Grama and L. A. B. San Martin, Indag. Math. (N.S.) 28 (2017), no. 3, 615–628. 

19. Topological string partition function on generalised conifolds, with A. Torres-Gomez, B. Suzuki and C. A. B. Varea, J. Math. Phys. 58 (2017), no. 4, 042303, 12 pp. (pdf)

20. 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 (2017). (pdf) 

21. Adjoint orbits of semi-simple Lie groups and Lagrangean submanifolds, with L. Grama, and L. A. B. San Martin, Proc. Edinb. Math. Soc. (2) 60 (2017), no. 2, 361–385.  (pdf) 

22. Symplectic Lefschetz fibrations on adjoint orbits,  with L. Grama and L. A. B. San Martin, Forum Math. 28 (2016), no. 5, 967–979. (pdf) 

23. Self-duality for Landau--Ginzburg models, with B. Callander, R. Jenkins, and Lino M. Silva, J. Geom. Symmetry Phys. 35 (2014), 1–10. (pdf) 

24. 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) 

25. 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)

26. BPS counting on singular varieties, with T. Köppe, P. Majumdar and K. Ray, J. Phys. A: Math. Theor. 45 (2012) 265–401. (pdf)

27. 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)

28. Cohomology gaps for reflexive sheaves on threefolds, with E. Ballico, J. Geom. Symmetry Phys. 21 (2011) 29–39. (pdf)

29. Sheaves on singular varieties, with T. Köppe. J. Singularities 2 (2010) 56–66. Proceedings of Singularities in Aarhus, August 2009. (pdf)

30. The Nekrasov conjecture for toric surfaces, with Melissa Liu. Comm. Math. Phys. 293 (2010), no. 3, 661–700. (pdf)

31. Local moduli of holomorphic bundles, with E. Ballico and T. Köppe. J. Pure Appl. Algebra 213, 397–408 (2009). (pdf)

32. 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)

33. Smoothing of rational m-ropes, with E. Ballico and T. Köppe. Cent. Eur. J. Math. 7 no. 3, 623–628 (2009) (pdf)

34. The Atiyah-Jones conjecture for rational surfaces, Advances Math. 218, 1027–1050 (2008). (pdf)

35. 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)

36. 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)

37. Three applications of instanton numbers, with P. Ontaneda. Comm. Math. Phys. 270 (1), 1–12 (2007). (pdf)

38. Computing Instanton numbers of curve singularities, with I. Swanson. J. Symbolic Computation 40, no. 2, 965–978 (2005). (pdf)

39. 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)

40. The Atiyah-Jones conjecture for rational surfaces, with R. J. Milgram. MPIM Bonn preprint 2004-14 (2004).

41. 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)

42. Numerical invariants for bundles on blow-ups, with E. Ballico. Proc. Amer. Math. Soc. 130 no. 1, 23–32 (2002). (pdf)

43. Two applications of instanton numbers. Isaac Newton Inst. Preprint Series no. NI02022 HDG, 1–15 (2002).

44. Holomorphic vector bundles on holomorphically convex complex surfaces, with E. Ballico. Matematiche (Catania) 55 no. 1, 3–15 (2001).

45. Chern classes of bundles on blown-up surfaces. Comm. Algebra 28 no. 10, 4919–4926 (2000). (pdf)

46. 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).

47. Holomorphic and algebraic vector bundles on 0-convex algebraic surfaces, with E. Ballico. Proc. Indian Acad. Sci. 109 no. 4, 353–358 (1999).

48. On the topology of holomorphic bundles. Bol. Soc. Parana. Mat. 18 no. 1.2, 1–7 (1998).

49. Rank two bundles on the blow-up of C2. J. Algebra 199 no. 2, 581–590 (1998). (pdf)

50. Chern classes of bundles over rational surfaces. Instituto Politecnico di Torino Rapporto Interno 30 (1998).

51. Holomorphic bundles on O(-k) are algebraic. Comm. Algebra 25 no. 9, 3001–3009 (1997). (pdf)

52. GAGA para variedades não compactas. Anais Acad. Bras. Ciencias 69 no. 4 (1997).

53. Fibrados Holomorficos sobre blow-ups. XXX Anniversary P.U.C. Peru, Pro - Math. 10 no. 20 (1996).

54. Ph.D. Thesis: Holomorphic rank two vector bundles on blow-ups. The University of New Mexico (1995), Adviser: Charles P. Boyer.

55. Masters Thesis: Three topological invariant cardinals. Universidade Estadual de Campinas, Brazil (1989), Adviser: Ofelia T. Alas (USP).

Minicourses, talks, and lecture notes

1. Curso de Verão em Maringá 2015 (notas)

2. Hodge diamonds and adjoint orbits, with B. Callander (pdf) 

3. Variedades Tóricas (notes).

4. The Nekrasov conjecture for toric surfaces - (slides)

5. Constantin's lectures on Geometric Langlands, typed by me, University of Edinburgh (2007) (pdf)

6. A first lecture on sheaf cohomology, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998)(pdf)

7. The classification of rational surfaces, with P. Majumdar, The Institute of Mathematical Sciences Madras, India (1998), math-ph/9909010

8. Fibração de Hopf, uma interpretação geométrica, with P. Majumdar and P. Ontaneda, Summer Lectures, Recife, Brazil (1997)

9. Undergraduate topology lecture notes

10. Isomorphisms of Moduli Spaces

Computational Algebraic Geometry

1. Hodge diamonds and adjoint orbits, with B. Callander, explains the Macaulay2 code used in "Compactifications of Adjoint orbits and their Hodge diamonds". 

2. Toric Varieties: página do Marcelo, página do Michel. 

3. Macaulay 2 code used in the paper "Computing Instanton Numbers of Curve Singularities", with I. Swanson. 

4. 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".

5. The Macaulay 2 website, this is the original source, by Grayson and Stillmann.

Current Research Students

• Diego Lizana - Master

• Former students

Networks

• Institute for Geometry and Physics Miami-Cinvestav-Campinas

• Network on Symmetries in Geometry and Physics

Personal interests

Swimming, Dancing, Comedy