Mattia Talpo

Studio II-16 exDMA
Dipartimento di Matematica
Università di Pisa
via Buonarroti 1/c
56127 Pisa, Italy

Phone: +39 050 2213831
Email: mattia.talpo(at)unipi(dot)it

About me


I am an Associate Professor in the Department of Mathematics of the University of Pisa. My main interests are in algebraic geometry, more specifically in moduli theory, often involving algebraic stacks and/or logarithmic geometry.

Previously I have been a postdoctoral fellow at Imperial College London, at Simon Fraser University and the University of British Columbia in Vancouver, and at the Max Planck institute for Mathematics in Bonn. I received my PhD from the Scuola Normale Superiore of Pisa, supervised by Angelo Vistoli.

Here are my full CV and my Google Scholar profile.

Research


My research is in algebraic geometry, mostly regarding moduli theory. The techniques that I employ often involve the use of algebraic stacks and logarithmic geometry.

Log geometry (not this kind) is a variant of algebraic geometry where the objects of study are algebraic varieties with an "extra structure" (a sheaf of monoids that keeps track of additional "regular functions" of interest), that typically encodes either a "boundary" on the variety, or some infinitesimal information about a family, of which the variety is a fiber. It was initially developed in the work of Fontaine-Illusie and Kato for problems related to arithmetic geometry, but afterwards gained popularity in moduli theory (and beyond) as well, mostly as a powerful tool for controlling degerations of smooth things.


Publications:

  1. 1. Betti realization of varieties defined by formal Laurent series, with P. Achinger. Geom. Topol. 25 (2021), no. 4, 1919-1978.
  2. 2. Parabolic semi-orthogonal decompositions and Kummer flat invariants of log schemes, with S. Scherotzke and N. Sibilla. Doc. Math. 25 (2020), 955-1009.
  3. 3. Gluing semi-orthogonal decompositions, with S. Scherotzke and N. Sibilla. J. Algebra 559 (2020), 1-32.
  4. 4. Holonomic and perverse logarithmic D-modules, with C. Koppensteiner. Adv. Math. 346 (2019), 510–545.
  5. 5. Parabolic sheaves with real weights as sheaves on the Kato-Nakayama space. Adv. Math. 336 (2018), 97-148.
  6. 6. On a logarithmic version of the derived McKay correspondence, with S. Scherotzke and N. Sibilla. Compos. Math. 154 (2018), no. 12, 2534-85.
  7. 7. Infinite root stacks and quasi-coherent sheaves on logarithmic schemes, with A. Vistoli. Proc. Lond. Math. Soc. 117 (2018), no. 5, 1187–1243.
  8. 8. Logarithmic Picard groups, chip firing, and the combinatorial rank, with T. Foster, D. Ranganathan and M. Ulirsch. Math. Z. 291 (2019), no. 1-2, 313-327.
  9. 9. A general formalism for logarithmic structures, with A. Vistoli. Boll. Unione Mat. Ital. 11 (2018), no. 4, 489–502.
  10. 10. On the motivic class of the classifying stack of G2 and the spin groups, with R. Pirisi. Int. Math. Res. Not. 2019, no. 10, 3265–3298.
    (here is a poster by R. Pirisi about this work)
  11. 11. The motivic class of the classifying stack of the special orthogonal group with A. Vistoli. Bull. Lond. Math. Soc. 49 (2017), no. 5, 818-823.
  12. 12. The Kato-Nakayama space as a transcendental root stack with A. Vistoli. Int. Math. Res. Not. 2018, no. 19, 6145–6176.
  13. 13. Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes, with D. Carchedi, S. Scherotzke and N. Sibilla. Geom. Topol. 21-5 (2017), no. 5, 3093–3158.
  14. 14. Moduli of parabolic sheaves on a polarized logarithmic scheme. Trans. Amer. Math. Soc. 369 (2017), no. 5, 3483–3545.
  15. 15. Stacks of uniform cyclic covers of curves and their Picard groups, with F. Poma and F. Tonini. Algebr. Geom. 2 (2015), no. 1, 91–122.
  16. 16. Deformation theory from the point of view of fibered categories, with A. Vistoli. Handbook of moduli, Vol. III, 281–397,  Adv. Lect. Math. (ALM), 26, Int. Press, Somerville, MA, 2013.

Preprints:

  1. 17. On the profinite homotopy type of log schemes, with D. Carchedi, S. Scherotzke and N. Sibilla. 2019, submitted.

Conference proceedings:

  1. 18. Batyrev Mirror Symmetry. Proceedings of the Superschool on derived categories and D-branes, 2017.

Other material:

Some notes and slides of talks, posters (warning: the notes are informal, are often missing references and attributions, and could contain mistakes/inaccuracies):

  1. Infinite root stacks of logarithmic schemes and moduli of parabolic sheaves (slides) - PhD defense (Feb 2014)
  2. Root stacks of logarithmic schemes and moduli of parabolic sheaves (slides) - Milano, Seminario di natale 2014 (Dec 2014)
  3. Log geometry (with a slight view towards tropical geometry) and root stacks (slides) - Brown STAGS 2015 (Apr 2015)
  4. (Infinite) root stacks of log schemes (poster) for WAGS, Oct 2015
  5. Logarithmic geometry and some applications (notes) - Caltech (Nov 2015)
  6. Kato-Nakayama spaces vs infinite root stacks (notes) - Boulder (Dec 2015)
  7. Parabolic sheaves, root stacks and the Kato-Nakayama space (slides) - Ontario (Feb 2016)
  8. Grothendieck rings of varieties and stacks (notes) - SFU (Jan 2017)
  9. Divisor theory on tropical and log smooth curves (notes) - Liverpool (Apr 2017)

Theses:

  1. PhD thesis: Infinite root stacks of logarithmic schemes and moduli of parabolic sheaves
  2. for the "Laurea specialistica" (Master's thesis): Deformation theory - slides (in Italian)
  3. for the "Laurea triennale" (Bachelor's thesis): Classi caratteristiche di fibrati vettoriali (in Italian) - slides (in Italian)

Teaching


Nel 2024 insegno

  1. Analisi Matematica (corso C) a Informatica, link alla pagina del corso su classroom
  2. Geometria 2 a Matematica (insieme a R. Frigerio e T. Szamuely), link alla pagina del corso su elearning
  3. Geometria algebrica F (varietà toriche) a Matematica

Events


Past

  1. Youngish Researchers Meeting in Algebra and Geometry 2023 - 20-22 settembre 2023, Roma Tre
  2. Young Researchers Meeting in Algebra and Geometry 2022 - 28-30 settembre 2022, SISSA
  3. Geometry and arithmetic of moduli spaces - 18-22 luglio 2022, Unipi
  4. Ricercatori in Algebra e Geometria 2020 - 30 settembre / 1 ottobre 2021, SNS Pisa

Future

  1. Youngish Researchers Meeting in Algebra and Geometry 2024 - 25-27 settembre 2024, Unimi
  2. Enumerative Geometry and Geometric Representation Theory - 23 giugno-4 luglio 2025, Unipi