Research Interests

Algebraic Geometry, Symplectic Geometry, Mathematical Physics

Events 

Upcoming events

• Geometry, Higher Structures, and Physics, ICMS Edinburgh, UK, 8-12 December 2025. 

• IX School and Workshop on Lie Theory, State University of Maringá, Brazil, 24-28 November 2025. 

• MathAmSud 24-MATH-12 Workshop in Geometry and Physics, UNSAAC Cusco, Peru, 20-24 October 2025. 

• Algebraic Geometry session, XXXIII Congreso de Matemática Capricórnio, Antofagasta, Chile, 6-8 August 2025. 

Past Events

Publications

1. Intrinsic Mirrors for Minimal Adjoint Orbits and Categories of Singularities, to appear in Eur. J. Math. (2025)

2. Intrinsic Mirrors for Minimal Adjoint Orbits (ICM G&T 2022), ZAG Handbook of Modern Algebraic Geometry,  CRC Press  (2025) n.77

3. Some contributions of Edoardo Ballico to Moduli spaces and their applications, Boll. Un. Mat. Ital. 18 (2025) 1-12

4. Hyperelliptically fibred surfaces with nodes, with E Ballico, B Suzuki, Ann. Univ. Ferrara 70  (2024) (pdf) 

5. Lagrangian skeleta, collars and duality, with E. Ballico, F. Rubilar,  B. Suzuki,  Springer Proc. Math. Stat. 409 (2023) (pdf)

6. The Katzarkov-Kontsevich-Pantev conjecture for minimal adjoint orbits, with E. Ballico, F. Rubilar,  L. San Martin, Eur. J. Math.  9  (2023) (pdf)

7. Morse functions and Real Lagrangian Thimbles on Adjoint Orbits, with L. A. B. San Martin,  J.Topol. Anal. 15 (2023) (pdf) 

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

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

10. The Kuranishi map for vector bundles on certain products of curves, with E. Ballico, F. Rubilar, B. Suzuki, Top. Appl. 312 (2022) (pdf) 

11. 25 open questions about Vector Bundles and their Moduli,  with E. Ballico, F. Rubilar, Proyecciones 41 (2022) (pdf)

12. Curvature grafted by instantons, with B. Suzuki, Indian J. Phys. 95   (2021)  (pdf)

13.  20 open questions about deformations of compactifiable manifolds, with E. Ballico, F. Rubilar, Sao Paulo J. Math.  Sci. 15 (2021) (pdf)

14. Invariant generalized complex structures on maximal flag manifolds, with F. Valencia, C. Varea, J. Geom. Phys. 163 (pdf)

15. Infinite dimensional families of Calabi-Yau threefolds and moduli of vector bundles, with E. Ballico, B. Suzuki, J. Pure  App. Algebra 225  (pdf).

16. Deformations of noncompact Calabi-Yau manifolds, families and diamonds, with F. Rubilar, Contemp. Math.  766 (2021) (pdf)

17. Infinitesimally tight Lagrangian orbits, with L. A. B. San Martin, F. Valencia, Mathematische Zeitschrift  297 (2021)  (pdf ) 

18. Classical deformations of local surfaces and their moduli of instantons, with S. Barmeier, J. Pure App. Algebra 223 (2019) (pdf) 

19. Aplicações da teoria de Lie à geometria simplética, with C. Bassani,  Boletim da Soc. Parana. Mat. 39 (2018)  (pdf)

20. Deformations of noncompact Calabi-Yau threefolds, with T. Köppe, F. Rubilar, B. Suzuki,  Rev. Colomb.  Mat. 52  (2018)  (pdf)

21. A Lie theoretical construction of a Landau–Ginzburg models without projective mirrors, with E. Ballico, S. Barmeier, L. Grama, L. A. B. San Martin, Manuscripta Math. 158 (2018) (pdf)

22. Compactifications of adjoint orbits and their Hodge diamonds, with E. Ballico, B. Callander,  J. Algebra Appl. 16  (2018)  (pdf) 

23. Some Landau-Ginzburg models viewed as rational maps, with E. Ballico, L. Grama, L. A. B. San Martin, Indag. Math. 28 (2017)  (pdf)

24. Topological string partition function on generalised conifolds, with A. Torres-Gomez, B. Suzuki, C. A. B. Varea, J. Math. Phys. 58 (2017) (pdf)

25. Symplectic Lefschetz fibrations from a Lie theoretical viewpoint, with B. Callander, L. Grama, L. A. B. San Martin,  Proc. Langlands, TQFT & MS. (2018) (pdf) 

26. Adjoint orbits of semi-simple Lie groups and Lagrangian submanifolds, with L. Grama, L. A. B. San Martin, Proc. Edinb. Math. Soc. (2) 60 (2017) (pdf) 

27. Symplectic Lefschetz fibrations on adjoint orbits,  with L. Grama, L. A. B. San Martin, Forum Math. 28 (2016) (pdf) 

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

29. Moduli Stacks of Bundles on Local Surfaces, with O. Ben-Bassat, Homological Mirror Symmetry and Tropical Geometry, LNM UMI  (2014)  (pdf) 

30. Isomorphisms of moduli spaces, with C. Casorrán Amilburu, S. Barmeier, B. Callander,  Mat. Contemporânea 41 (2012)  (pdf)

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

32. On the geometry of moduli spaces of anti-self-dual connections, with E. Ballico, C. Eyral, Top. Appl. 159 (2012)  (pdf)

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

34. Sheaves on singular varieties, with T. Köppe. J. Singularities 2 (2010)  (pdf)

35. The Nekrasov conjecture for toric surfaces, with Melissa Liu. Comm. Math. Phys. 293 (2010) (pdf)

36. Local moduli of holomorphic bundles, with E. Ballico, T. Köppe, J. Pure Appl. Algebra 213 (2009) (pdf)

37. Vector bundles near negative curves: moduli and local Euler characteristic, with E. Ballico, T. Köppe, Comm. Algebra 37  (2009) (pdf)

38. Smoothing of rational m-ropes, with E. Ballico, T. Köppe, Cent. Eur. J. Math. 7 (2009) (pdf)

39. The Atiyah-Jones conjecture for rational surfaces, Advances Math. 218 (2008) (pdf)

40. Local holomorphic Euler characteristic and instanton decay, with T. Köppe,  P. Majumdar, Pure Appl. Math. Q. 4  (2008) (pdf)

41. Multiplicity of complex hypersurface singularities, Rouché satellites and Zariski's problem, with C. Eyral., C. R. Math. 344 (2007) (pdf)

42. Three applications of instanton numbers, with P. Ontaneda, Comm. Math. Phys. 270 (2007) (pdf)

43. Computing Instanton numbers of curve singularities, with I. Swanson, J. Symbolic Computation 40 (2005) (pdf)

44. Vector bundles on a three dimensional neighborhood of a ruled surface, with E. Ballico, J. Pure Appl. Algebra 195 (2005) (pdf)

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

46. Vector bundles on a neighborhood of a curve in a surface and elementary transformations, with E. Ballico, Forum Math. 15 (2003) (pdf)

47. Numerical invariants for bundles on blow-ups, with E. Ballico. Proc. Amer. Math. Soc. 130  (2002) (pdf)

48. Two applications of instanton numbers. Isaac Newton Inst. Preprint NI02022 HDG, 1–15 (2002)

49. Holomorphic vector bundles on holomorphically convex complex surfaces, with E. Ballico. Matematiche (Catania) 55 (2001)

50. Chern classes of bundles on blown-up surfaces. Comm. Algebra 28  (2000) (pdf)

51. Vector bundles on a formal neighborhood of a curve in a surface, with E. Ballico, Rocky Mountain J. Math. 30 (2000)

52. Holomorphic and algebraic vector bundles on 0-convex algebraic surfaces, with E. Ballico, Proc. Indian Acad. Sci. 109  (1999)

53. On the topology of holomorphic bundles. Bol. Soc. Parana. Mat. 18  (1998)

54. Rank two bundles on the blow-up of C2. J. Algebra 199  (1998) (pdf)

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

56. Holomorphic bundles on O(-k) are algebraic. Comm. Algebra 25  (1997) (pdf)

57. GAGA para variedades não compactas. Anais Acad. Bras. Ciencias 69  (1997)

58. Fibrados Holomorficos sobre blow-ups. XXX Anniversary P.U.C. Peru, Pro - Math. 10 (1996)

59. Ph.D. Thesis: Holomorphic rank two vector bundles on blow-ups. The University of New Mexico (1995)

60. Masters Thesis: Three topological invariant cardinals. Universidade Estadual de Campinas, Brazil (1989)

Minicourses 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

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".

Research Students

• PhD students appear at  Genealogy 

• Former students

Networks

• Network in Geometry and Lie Theory

• Network on Symmetries in Geometry and Physics

Past networks

Personal interests

Swimming, Dancing, Comedy