Mattia Talpo

PIMS Postdoctoral Fellow
PIMS - SFU Site, Simon Fraser University
TASC 2, Room 8515
8888 University Drive
Burnaby, BC, V5A 1S6
Canada

Email: mtalpo(at)sfu(dot)ca

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, mainly regarding moduli theory and using algebraic stacks, and with a focus on logarithmic geometry and parabolic sheaves.

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. On the motivic class of the classifying stack of G2 and the spin groups (with R. Pirisi), to appear in IMRN.
  2. 2. 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).
  3. 3. The Kato-Nakayama space as a transcendental root stack (with A. Vistoli) , published online in IMRN, (DOI:10.1093/imrn/rnx079).
  4. 4. 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.
  5. 5. Moduli of parabolic sheaves on a polarized logarithmic scheme, Trans. Amer. Math. Soc. 369 (2017), no. 5, 3483–3545.
  6. 6. 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.
  7. 7. 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. 8. Parabolic sheaves with real weights as sheaves on the Kato-Nakayama space, submitted.
  2. 9. A general formalism for logarithmic structures (with A. Vistoli), submitted.
  3. 10. On a logarithmic version of the derived McKay correspondence (with S. Scherotzke and N. Sibilla) , submitted.
  4. 11. Logarithmic Picard groups, chip firing, and the combinatorial rank (with T. Foster, D. Ranganathan and M. Ulirsch), submitted.
  5. 12. Infinite root stacks and quasi-coherent sheaves on logarithmic schemes (with A. Vistoli), submitted.

Conference proceedings:

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

Other material:

Notes and slides of talks, posters:

  1. PhD thesis defense "Infinite root stacks of logarithmic schemes and moduli of parabolic sheaves" (Feb 27th 2014)
  2. Milano - Seminario di natale 2014 "Root stacks of logarithmic schemes and moduli of parabolic sheaves" (Dec 16th 2014)
  3. Brown STAGS 2015 "Log geometry (with a slight view towards tropical geometry) and root stacks" (Apr 17th 2015)
  4. Caltech Nov 2015 "Logarithmic geometry and some applications" (Nov 16th 2015)
  5. (Infinite) root stacks of log schemes for WAGS, Oct 2015

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