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Sofia Tirabassi

About me

I will be hiring a PhD student in 2024!

 

Since January 1st 2019 I am an associate professor at the Department of Mathematics  of Stockholm University. I earned my docentship in May 2021.

 
Since January 1st 2024 I am the leader of the project project Generic Vanishing and characterization of semiabelian varieties, funded by the VR. Under the Fall 2024 I will also be hosting Rita Pardini who will be a Guest Professor at the department of Mathematics, funded by the Alice och Knut Wallenberg Foundation. For more information about these projects see the projects tab below.
 
I was the pricipal Investigator of the project "Derived Categories in Positive Characteristic" funded by the KAW fundation under the scheme "International Postdoctoral Scholarship" between 2021 and 2023.  I was the manager of the project The Aritmetic of the derived Categories funded by the Research Council of Norway under the scheme "Young Research Talents" for the years 2017-2021.
 
Before coming to Stockholm, I was an associate professor at the University of Bergen,  a Postdoctoral Research Assistant Professor at the Mathematics Department of University of Utah (Salt Lake City (UT), USA), and a Marie Curie Fellow at the Faculty of Mathematics, Informatics and Mechanics, University of Warsaw. This fellowship was awarded by "The ERCIM Alain Bensoussan Fellowship Programme" and was supported by the Marie Curie Co-funding of Regional, National and International Programmes (COFUND) of the European Commission.

In February 2012, I completed my Ph.D. in Mathematics at the Università degli studi Roma TRE with a thesis entitled Syzygies, Pluricanonical Maps and the Birational Geometry of Irregular Varieties, written under the supervision of Prof. G. Pareschi (Università degli studi di Roma "Tor Vergata").

Before entering in the Ph.D. program of the Università degli Studi Roma TRE, I was a student at the University of Bologna where I completed both my B.Sc. in Mathematics (2006) and M.Sc. in Mathematics (2008).
 

 

 

 

Teaching

In the academic year 2024/20205 I am going to teach various courses at different levels: 

  • Teacher and examiner for MM3001- Mathematical methods for economic analysisis ( outsorced by the faculty of Economics) 

  • Teacher and examiner for MM7045- Galois Theory ( Master program in Mathematics) 

  • Teacher and examiner and  Huvudlärare for MM5023 Matematik III - Combinatorics (Advanced bachelor level). 

  • Teacher and examiner for MM5021- Matematik III - Abstract Algebra ((Advanced bachelor level). 

  • Examiner for bachelor and master theses (including thesis in teacher-programs) 

  • Huvudlärare for MM7052-Topology 

I have also received funds from the Faculty of Science to develop a Master level course in Algebraic geometry (my specific field of expertise). 

 

Research

My primary field of interest is the study of Algebraic Geometry whcih is about the study of geometric object with an algebraic soul. An example of such objects are zero loci of polynomial, like a circle of radious 1, which is the locus of points in the plane satisfying the equation

x^2+y^2-1=0.

One of my main tools are the so called cohomological methods, and currently, I have  two ongoing research directions.

On one side, I  study derived categories and derived invariants of algebraic varieties defined over fields of positive characteristic.  This was the main topic of my Wallenberg International Postdoc Project.

On the other side,  I am  working on finding an effective birational characterization of semiabelian varieties.  This is the main focus of my VR grants and the Wallenberg visiting professor project.

Research projects

Generic vanishing and characterization of semi-abelian varieties

This is a project in algebraic geometry, the branch of mathematics which studies geometric objects arising from algebraic ones, such as solutions of polynomial equations. The proposal revolves around a central theme within algebraic geometry: the classification problem.

Three figures: a sphere, a torus (donut shape) and one like two donuts glued together like an 8.
Unknown properties of abstract geometric objects

This is a project in algebraic geometry, the branch of mathematics which is concerned with the study of geometric objects that can be described through polynomial equations. These are called (algebraic) varieties.

Research

Publications

A selection from Stockholm University publication database

  • Effective characterization of quasi-abelian surfaces

    2023. Margarida Mendes Lopes, Rita Pardini, Sofia Tirabassi. Forum of Mathematics, Sigma 11

    Article

    Let V be a smooth quasi-projective complex surface such that the first three logarithmic plurigenera 𝑃1 (𝑉), 𝑃2 (𝑉)and 𝑃3 (𝑉) are equal to 1 and the logarithmic irregularity 𝑞(𝑉) is equal to 2. We prove that the quasi-Albanesemorphism 𝑎𝑉 : 𝑉 → 𝐴(𝑉) is birational and there exists a finite set S such that 𝑎𝑉 is proper over 𝐴(𝑉) \ 𝑆, thusgiving a sharp effective version of a classical result of Iitaka [12].

    Read more about Effective characterization of quasi-abelian surfaces

  • A footnote to a theorem of Kawamata

    2023. Margarida Mendes Lopes, Rita Pardini, Sofia Tirabassi. Mathematische Nachrichten 296 (10), 4739-4744

    Article

    Kawamata has shown that the quasi-Albanese map of a quasi-projective variety with log-irregularity equal to the dimension and log-Kodaira dimension 0 is birational. In this note, we show that under these hypotheses the quasi-Albanese map is proper in codimension 1 as conjectured by Iitaka. 

    Read more about A footnote to a theorem of Kawamata

  • Fourier-Mukai partners of Enriques and bielliptic surfaces in positive characteristic

    2021. Katrina Honigs, Max Lieblich, Sofia Tirabassi. Mathematical Research Letters 28 (1), 65-91

    Article

    We prove that a twisted Enriques (respectively, untwisted bielliptic) surface over an algebraically closed field of positive characteristic at least 3 (respectively, at least 5) has no non-trivial Fourier-Mukai partners.

    Read more about Fourier-Mukai partners of Enriques and bielliptic surfaces in positive characteristic

  • On the Brauer group of bielliptic surfaces (with an appendix by Jonas Bergström and Sofia Tirabassi)

    2022. Eugenia Ferrari (et al.). Documenta Mathematica 27, 383-425

    Article

    We provide explicit generators of the torsion of the second cohomology of bielliptic surfaces, and we use this to study the pullback map between the Brauer group of a bielliptic surface and that of its canonical cover.

    Read more about On the Brauer group of bielliptic surfaces (with an appendix by Jonas Bergström and Sofia Tirabassi)

  • Theta-regularity and log-canonical threshold

    2020. Morten Øygarden, Sofia Tirabassi. Mathematica Scandinavica 126 (1), 73-81

    Article

    We show that an inequality, proven by Küronya-Pintye, which governs the behavior of the log-canonical threshold of an ideal over Pn and that of its Castelnuovo-Mumford regularity, can be applied to the setting of principally polarized abelian varieties by substituting the Castelnuovo-Mumford regularity with Θ-regularity of Pareschi-Popa.

    Read more about Theta-regularity and log-canonical threshold

  • Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic

    2020. Katrina Honigs, Luigi Lombardi, Sofia Tirabassi. Mathematische Zeitschrift 295, 727-749

    Article

    We prove that any Fourier–Mukai partner of an abelian surface over an algebraically closed field of positive characteristic is isomorphic to a moduli space of Gieseker-stable sheaves. We apply this fact to show that the set of Fourier–Mukai partners of a canonical cover of a hyperelliptic or Enriques surface over an algebraically closed field of characteristic greater than three is trivial. These results extend earlier results of Bridgeland–Maciocia and Sosna to positive characteristic.

    Read more about Derived equivalences of canonical covers of hyperelliptic and Enriques surfaces in positive characteristic

  • ON ORDINARY ENRIQUES SURFACES IN POSITIVE CHARACTERISTIC

    2020. Roberto Laface, Sofia Tirabassi. Nagoya mathematical journal

    Article

    We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.

    Read more about ON ORDINARY ENRIQUES SURFACES IN POSITIVE CHARACTERISTIC

  • GV-subschemes and their embeddings in principally polarizedabelian varieties

    2015. Luigi Lombardi, Sofia Tirabassi. Mathematische Nachrichten 288 (11-12), 1405-1412

    Article

    We prove that any embedding of a GV -subscheme in a principally polarized abelian variety does not factorthrough any nontrivial isogeny. As an application, we present a new proof of a theorem of Clemens–Griffithsidentifying the intermediate Jacobian of a smooth cubic threefold to the Albanese variety of its Fano surface oflines.

    Read more about GV-subschemes and their embeddings in principally polarizedabelian varieties

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