My (former) academic page

In early 2019 I left academia for a job in the industry in the Stockholm area, where I live with my family. I currently focus on machine learning techniques in the field of medical imaging for cancer treatment. Although now I’m busy with other things, I’m still very happy to talk about math, so don’t hesitate to reach out.

I do research in computational discrete geometry. I use algorithms, AI and computer assisted proofs to answer questions in pure mathematics coming from combinatorics, commutative algebra and algebraic geometry.

News

I wrote a paper! Comments are welcome.

Publications

  • G. Balletti, A. Kasprzyk and B. Nill: On the maximum dual volume of a canonical Fano polytope, Forum of Mathematics, Sigma 10 (2022), e109 [arXiv].
  • G. Balletti: Enumeration of lattice polytopes by their volume, Discrete & Computational Geometry 65 (2021) 1087–1122 [arXiv].
  • G. Balletti, M. Panizzut, B. Sturmfels: K3 Polytopes and their Quartic Surfaces, Advances in Geometry 21-1 (2021), 85–98 [arXiv].
  • G. Balletti, C. Borger: Families of lattice polytopes of mixed degree one, Journal of Combinatorial Theory Series A 173 (2020) [arXiv].
  • G. Balletti, C. Borger: Families of 3-dimensional polytopes of mixed degree one, Proceedings of the Summer Workshop on Lattice Polytopes, Osaka, Japan, 23 July – 10 August 2018, 72–84 (2019).
  • G. Balletti, T. Hibi, M. Meyer and A. Tsuchiya: Laplacian simplices associated to digraphs, Arkiv för Matematik 56 (2018), 243–264 [arXiv].
  • G. Balletti, A. Higashitani: Universal inequalities in Ehrhart Theory, Israel Journal of Mathematics 227 (2018), 843–859 [arXiv].
  • G. Balletti, Connectivity through bounds for the Castelnuovo-Mumford regularity, Journal of Combinatorial Theory Series A 147 (2017), 46–54 [arXiv].

Preprints

  • G. Balletti: A genetic algorithm to search the space of Ehrhart h∗-vectors (2023), [arXiv].
  • G. Balletti, A. Kasprzyk: Three-dimensional lattice polytopes with two interior lattice points (2016), [arXiv].

Datasets

  • G. Balletti: Dataset of small lattice polytopes (2020) [doi].
  • G. Balletti, A. Kasprzyk, B. Nill, Benjamin: Supporting data for “On the maximum dual volume of a canonical Fano polytope” (2016) [doi].

Other

  • G. Balletti, Classifications, volume bounds and universal Ehrhart inequalities of lattice polytopes, Doctoral thesis (2018)
  • G. Balletti, Classifications and volume bounds of lattice polytopes, Licentiate thesis (2017)

Past activities and places where we could have met

  • 2018
    • 22 October, 2018 - Thesis defense
    • 1-7 October, 2018 - Nottingham, England - Research visit to Alexander Kasprzyk
    • July 23 to August 10, 2018 - Osaka, Japan - Summer Workshop on Lattice Polytopes
    • 20-24 May 2018 - Sendai, Japan - Invited speaker at “The Japanese Conference on Combinatorics and its Applications (JCCA 2018)”
    • 19-23 February 2018 - Sweden, Stockholm - Workshop on Combinatorics, polytopes, and complexity at Institut Mittag-Leffler
    • February 12 to March 4, 2018 - Christopher Borger (OvGU) visiting in Stockholm
    • January-April 2018 - Stockholm, Sweden - “Tropical Geometry, Amoebas and Polytopes” program at Institut Mittag-Leffler
    • 10-13 January 2018 - San Diego, USA - “Combinatorial Commutative Algebra and Polytopes” at the JMM
  • 2017
    • September-October 2017 - Magdeburg, Germany - Research visit at OvGU
    • 17-23 September 2017 - Oberwolfach, Germany - Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications
    • 14-16 September 2017 - Magdeburg, Germany - Interactions with Lattice Polytopes
    • 3-9 September 2017 - Lukecin, Poland - 40th Autumn School in Algebraic Geometry - Binomial Ideals
    • 14-27 August 2017 - Stockholm, Sweden - Stockholm Master Class in Tropical Geometry
    • 10 - 14 July 2017 - Osaka, Japan - The Prospects for Commutative Algebra
    • June-July 2017 - Osaka, Japan - Research visit at Hibi’s research group
    • 10 June 2017 - Berlin, Germany - Polynomials and Polytopes
    • 22-23 May 2017 - Stockholm, Sweden - Mini-Conference for PhD-Students in Mathematics
    • 15-19 May 2017 - Berlin, Germany - Research visit at TU
    • 15 May 2017 - Berlin, Germany - Talk at “Monday Lectures and Colloquia”
    • 11-12 May 2017 - Berlin, Germany - Computing in Tropical Geometry
    • 9 May 2017 - Magdeburg, Germany - Talk at Institut für Algebra und Geometrie seminar
    • 3 May 2017 - Stockholm, Sweden - Talk at KTH combinatorics seminar
    • 8 March - Stockholm, Sweden - Licentiate dissertation
    • 10-28 January 2017 - Osaka, Japan - Workshop on Convex Polytopes for Graduate Students
  • 2016
    • 12-15 December - Berlin, Germany - Einstein Workshop on Lattice Polytopes
    • 8-9 December - Chemnitz, Germany - Saxonian Geometry Day 2016
    • November-December - Magdeburg, Germany - Research visit to Benjamin Nill (OvGU)
    • 9 November - Stockholm, Sweden - Talk - KTH combinatorics seminar
    • 26 October - Genoa, Italy - Talk - Algebra&Geometry seminar
    • 25-28 July - Magdeburg, Germany - Research visit to Benjamin Nill (OvGU)
    • 18-22 July - Berlin, Germany - 7th European Congress of Mathematics
    • 13-24 June - Medellin, Colombia - Encuentro Colombiano de Combinatoria ECCO 2016
    • 13 May - Leicester, England - Invited talk (East Midlands Seminar in Geometry)
    • 9-20 May - Nottingham, England - Research visit to Alexander Kasprzyk (University of Nottingham)
    • March - Magdeburg, Germany - Research visit to Benjamin Nill (OvGU)
  • 2015
    • November-December - Magdeburg, Germany - Research visit to Benjamin Nill (OvGU)
    • 7-10 October - Osnabrück, Germany - Combinatorial and Experimental Methods in Commutative Algebra and Related Fields
    • 29 June-10 July - Berlin, Germany - Convex geometry - discrete and computational
    • 22-26 June - Budapest, Hungary - Intuitive Geometry, László Fejes Tóth Centennial
    • 8-20 June - London, England - Research visit to Alexander Kasprzyk (Imperial College)
    • 1-5 June - Edinburgh, Scotland - Minimal free resolutions, Betti numbers, and combinatorics
    • 9-13 February - Genoa, Italy - HTCA – Homology: Theoretical and Computational Aspects