Jonas Bergström
Teaching
Present PhD-students
Sjoerd de Vries (link to his homepage)
Former PhD-students
Stefano Marseglia (link to his homepage)
Olof Bergvall (link to his homepage), together with Prof. Carel Faber
Research
Webpage containing traces of Hecke operators on spaces of Siegel modular forms of degree 2 and 3
Together with Carel Faber, and Gerard van der Geer we have (with help by Gerrit Oomens) constructed a website containing dimensions and Hecke eigenvalues of spaces of Siegel modular forms of genus 3 and level 1, and of genus 2 and level 1 or 2. The website also contains Fourier coefficients for genus 2 and level 1 (and also level 1 with character).
Some links
The Algebra and geometry Seminar (KTH and SU)
The Stockholm Number Theory Seminar (KTH and SU)
Preprints
25.
Stable cohomology of moduli spaces of hyperelliptic curves on Hirzebruch surfaces
Together with Angelina Zheng.
arXiv:2312.14800
24.
Dimension formulas for spaces of vector-valued Siegel modular forms of degree two and level two
(Accompanying Github-webpage.)
Together with Fabien Cléry.
arXiv:2309.04388
23.
Hyperelliptic curves, the scanning map, and moments of families of quadratic L-functions
Together with Adrian Diaconu, Dan Petersen, Craig Westerland.
arxiv:2302.07664
Accepted for publication
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.
To appear in the "Canadian Journal of Mathematics".
arXiv:2303.17825
21.
Polynomial point counts and odd cohomology vanishing on moduli spaces of stable curves
Together with Carel Faber, Sam Payne.
To appear in "Annals of Mathematics".
arXiv:2206.07759
Publications
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
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
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
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
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