Mattia Talpo

PIMS Postdoctoral Fellow
PIMS - SFU Site, Simon Fraser University
8888 University Drive
Burnaby BC V5A 1S6, Canada
Email: mtalpo(at)sfu(dot)ca
I am currently on the job market for tenure-track positions:
CV, teaching statement, research statement (without future plans)

About me

I am a PIMS postdoctoral fellow at Simon Fraser University in Burnaby, BC, Canada, working with Nathan Ilten. My main interests are in algebraic geometry, more specifically in moduli theory, often involving algebraic stacks and/or logarithmic geometry.

Previously I was a postdoctoral fellow at UBC for 2 years, and at the Max Planck institute for Mathematics of Bonn for 9 months. 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. Logarithmic Picard groups, chip firing, and the combinatorial rank, with T. Foster, D. Ranganathan and M. Ulirsch. To appear in Mathematische Zeitschrift, 15 pages, 2016.
  2. 2. On the motivic class of the classifying stack of G2 and the spin groups, with R. Pirisi. Published online in IMRN, DOI:10.1093/imrn/rnx208, 34 pages, 2017.
    (here is a poster by R. Pirisi about this work)
  3. 3. The motivic class of the classifying stack of the special orthogonal group with A. Vistoli. Published online in Bull. Lond. Math. Soc., DOI:10.1112/blms.12072, 6 pages, 2017.
  4. 4. The Kato-Nakayama space as a transcendental root stack with A. Vistoli. Published online in IMRN, DOI:10.1093/imrn/rnx079, 32 pages, 2017.
  5. 5. Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes, with D. Carchedi, S. Scherotzke and N. Sibilla. Geometry & Topology 21-5 (2017), 3093–3158.
  6. 6. Moduli of parabolic sheaves on a polarized logarithmic scheme. Trans. Amer. Math. Soc. 369 (2017), no. 5, 3483–3545.
  7. 7. 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.
  8. 8. 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. 9. Parabolic sheaves with real weights as sheaves on the Kato-Nakayama space. 33 pages, 2017, submitted.
  2. 10. A general formalism for logarithmic structures, with A. Vistoli. 13 pages, 2017, submitted.
  3. 11. On a logarithmic version of the derived McKay correspondence, with S. Scherotzke and N. Sibilla. 52 pages, 2016, submitted.
  4. 12. Infinite root stacks and quasi-coherent sheaves on logarithmic schemes, with A. Vistoli. 57 pages, 2014, submitted.

Conference proceedings:

  1. 13. Batyrev Mirror Symmetry, in the proceedings of the Superschool on derived categories and D-branes. 11 pages, 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

In fall 2017, I am teaching FAN X99 (foundations of analytical and quantitative reasoning), section D300. See Canvas for information about the course.


Past courses:

at UBC:

  1. summerT1 2016: MATH 200/253 (multivariable calculus), section 921
  2. summerT1 2015: MATH 200/253 (multivariable calculus), section 921
  3. winterT2 2014: MATH 105 (integral calculus for commerce and social sciences), section 206