Jonas Bergström Docent, Stf prefekt

Present PhD-students
Sjoerd de Vries (link to his homepage)
Héloïse Mansat

Former PhD-students
Stefano Marseglia (link to his homepage)
Olof Bergvall (link to his homepage), together with Prof. Carel Faber

Present postdocs
Séverin Philip
Thomas Wennink

Former postdocs
Angelina Zheng
Valentijn Karemaker
Oliver Leigh
Alex Samuel Bamunoba

Links to seminars

The Algebra and geometry Seminar (KTH and SU)

Nordic number theory network

Links to webpages containing data

Here is a link to a github page containing results on the cohomology of moduli spaces of curves based on research from several different sources.

Here is a link to a webpage (together with Carel Faber, and Gerard van der Geer) containing traces of Hecke operators on spaces of Siegel modular forms of degree 2 and 3.

Erratum

There is an erratum to my articles here. pdf, 178 kB.

Preprints

28.
Periodicity of traces of Hecke operators modulo prime powers
Together with Sjoerd de Vries.
arXiv:2601.03029

27.
Abelian varieties over finite fields with commutative endomorphism algebra: theory and algorithms
(Accompanying Github-webpage.)
Together with Valentijn Karemaker, Stefano Marseglia.
arXiv:2409.08865

26.
Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions
(Accompanying Github-webpage.)
Together with Adrian Diaconu, Dan Petersen, Craig Westerland.
arXiv:2302.07664

Accepted for publication

25.
Appendix to: Traces of Hecke operators on Drinfeld modular forms for F_q[T]
Together with Sjoerd de Vries.
Main article by Sjoerd de Vries.
arXiv:2407.04555
Accepted for publication in Mathematika.

Publications

24.
Stable cohomology of moduli spaces of hyperelliptic curves on Hirzebruch surfaces
Together with Angelina Zheng.
Pure and Applied Mathematics Quarterly, 21 (5), (2025), 1893-1930.
arXiv:2312.14800

23.
Dimension formulas for spaces of vector-valued Siegel modular forms of degree two and level two
(Accompanying Github-webpage.)
Together with Fabien Cléry.
Publicacions Matemàtiques, 69 (2), (2025), 367-388.
arXiv:2309.04388

22.
Refinements of Katz-Sarnak theory for the number of points on curves over finite fields
Together with Everett W. Howe, Elisa Lorenzo García, Christophe Ritzenthaler.
Canadian Journal of Mathematics, 77 (2), (2025), 400-425.
arXiv:2303.17825

21.
Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves
Together with Carel Faber, Sam Payne.
Annals of Mathematics, 199 (3), (2024), 1323-1365.
arXiv:2206.07759

20.
Lower bounds on the maximal number of rational points on curves over finite fields
Together with Everett W. Howe, Elisa Lorenzo García, Christophe Ritzenthaler.
Mathematical Proceedings of the Cambridge Philosophical Society, 176 (1), (2024), 213-238.
arXiv:2204.08551

19.
Cohomology of moduli spaces via a result of Chenevier and Lannes
(Accompanying Github-webpage.)
Together with Carel Faber.
Épijournal de Géométrie Algébrique, Volume 7 (2023), Article no. 20.
arXiv:2207.05130

18.
Polarizations of abelian varieties over finite fields via canonical liftings
(Accompanying Github-webpage.)
Together with Valentijn Karemaker, Stefano Marseglia.
International Mathematics Research Notices, 4, (2023), 3194-3248.
arXiv:2101.05531

17.
Picard modular forms and the cohomology of local systems on a Picard modular surface
Together with Gerard van der Geer.
Commentarii Mathematici Helvetici, 97 (2), (2022), 305-381.
arXiv:2012.07673

16.
Appendix to: On the Brauer group of bielliptic surfaces
Together with Sofia Tirabassi.
Main article by Eugenia Ferrari, Sofia Tirabassi, Magnus Vodrup.
Documenta Mathematica, 27, (2022), 383-425.
arXiv:1910.12537

15.
A search for c-Wieferich primes
Together with Alex Samuel Bamunoba.
International Journal of Number Theory, 17 (7), (2021), 1599–1616.
arXiv:2011.11727

14.
The equivariant Euler characteristic of A_3[2]
Together with Olof Bergvall.
Annali della Scuola Normale Superiore di Pisa, 20 (4), (2020), 1345-1357.
arxiv:1804.09628

13.
GL2xGSp2 L-values and Hecke eigenvalue congruences
Together with Neil Dummigan, David Farmer and Sally Koutsoliotas
Journal de Théorie des Nombres de Bordeaux, 31 (3), (2019), 751-775.
arXiv:1910.14128

12.
Hirzebruch L-polynomials and multiple zeta values
Together with Alexander Berglund.
Mathematische Annalen, 372 (1-2), (2018), 125–137
arXiv:1708.05547

11.
Eisenstein congruences for SO(4,3), SO(4,4), spinor and triple product L-values
Together with Neil Dummigan and Thomas Mégarbané (with an appendix by Tomoyoshi Ibukiyama and Hidenori Katsurada).
Experimental Mathematics, 27 (2), (2018), 230-250.
arXiv:1605.00819

10.
Eisenstein congruences for split reductive groups
Together with Neil Dummigan.
Selecta Mathematica, 22 (3), (2016), 1073-1115.
arXiv:1502.07827

9.
On the cohomology of the Losev-Manin moduli space
Together with Satoshi Minabe.
Manuscripta Mathematica, 144 (1-2),  (2014), 241-252.
arXiv:1108.0338

8.
Siegel modular forms of degree three and the cohomology of local systems
Together with Carel Faber and Gerard van der Geer.
Selecta Mathematica, 20 (1), (2014), 83-124.
arXiv:1108.3731
See also the erratum pdf, 178 kB..

7.
On the cohomology of moduli spaces of (weighted) stable rational curves
Together with Satoshi Minabe.
Mathematische Zeitschrift, 275 (3-4), (2013), 1095-1108.
arXiv:1111.6438

6.
Inversion of series and the cohomology of the moduli spaces M^{delta}_{0,n}
Together with Francis Brown.
In `Motives, quantum field theory, and pseudodifferential operators'.
Clay Math. Proc. 12, (2010), 119-126, Amer. Math. Soc., Providence.
arXiv:0910.0120

5.
Equivariant counts of points of the moduli spaces of pointed hyperelliptic curves
Documenta Mathematica, 14, (2009), 259-296.
arXiv:math/0611813
See also the erratum pdf, 178 kB..

4.
Siegel modular forms of genus 2 and level 2: cohomological computations and conjectures
Together with Carel Faber and Gerard van der Geer.
International Mathematics Research Notices, 100, (2008).
arXiv:0803.0917
See also the erratum pdf, 178 kB..

3.
The Euler characteristic of local systems on the moduli of curves and abelian varieties of genus three
Together with Gerard van der Geer.
Journal of Topology, 1 (3), (2008), 651-662.
arXiv:0705.0293

2.
Cohomology of moduli spaces of curves of genus three via point counts
Journal für die reine und angewandte Mathematik, 622, (2008), 155-187.
arXiv:math/0611815

1.
The rational cohomology of Mbar_4
Together with Orsola Tommasi.
Mathematische Annalen, 338,  (2007), 207-239.
arXiv:math/0506502