Martina Iannella

I am a postdoctoral researcher at the Institute of Discrete Mathematics and Geometry at TU Wien.

I received my PhD in October 2023 from the University of Udine, under the supervision of Alberto Marcone and co-supervision of Vincenzo Dimonte.

My research areas are Mathematical Logic and Set Theory. My research focuses on descriptive set theory, large cardinals and generalized descriptive set theory.

Preprints

• Borel classification of simplicial complexes and non-compact 2- and 3-manifolds
  Joint with Vadim Weinstein
  Submitted, 2026 (arXiv copy).
• Alexander's conjecture for infinite simplicial complexes
  Joint with Vadim Weinstein
  Submitted, 2026 (arXiv copy).
• The complexity of wellordered- and scattered-convex embeddability
  Joint with Juan P. Aguilera
  Submitted, 2025.

Publications

• Piecewise convex embeddability on linear orders
  Joint with Alberto Marcone, Luca Motto Ros, and Vadim Weinstein
  Annals of Pure and Applied Logic (arXiv copy, journal copy).
• Convex embeddability and knot theory
  Joint with Alberto Marcone, Luca Motto Ros, and Vadim Weinstein
  Transactions of the American Mathematical Society (arXiv copy, journal copy).
• Descriptive properties of I2-embeddings
  Joint with Vincenzo Dimonte and Philipp Lücke
  The Journal of Symbolic Logic (arXiv copy, journal copy).
• A one-page proof of a theorem of Beleznay
  Joint with Juan P. Aguilera
  Bulletin of Symbolic Logic (journal copy).

In preparation

• Laver algebras and their embeddings
  Joint with Juan P. Aguilera.

Selected Talks

• Borel classification of simplicial complexes and classes of non-compact manifolds, XXIX Incontro di Logica AILA 2026, Roma (Italy), 16 September 2026
• A descriptive set-theoretic perspective on classification: Borel reducibility and blurry duality, 17th Young Set Theory Workshop, Barcelona (Spain), 31 August 2026
• On Laver algebras and their embeddings, Conference: Infinitary Proof Theory, BIRS, Oaxaca (Mexico), 15 August 2025
• Classification of 3-manifolds, Arctic Set Theory Workshop 7, Kilpisjärvi (Finland), 18 February 2025
• Classification of 3-manifolds, Séminaire Général de Logique, Université de Paris Cité, Paris (France), 9 December 2024
• Descriptive consequences of rank-into-rank axioms, Conference: 120 Years of Choice, University of Leeds, Leeds (UK), 10 July 2024
• Piecewise convex embeddability on linear orders, STUK 12: Set Theory in the UK, University College London (online), 15 February 2024

Prizes and Grants

• FWF ESPRIT Grant
  for the project “Laver tables and large cardinals”, Grant DOI: 10.55776/ESP1625325 (2025-2028).
• AILA-UMI “Franco Montagna” Prize 2025
  for the best doctoral thesis in mathematical logic and its applications of the years 2022-2024.