N-cube days XI (Göteborg, 2019)

On Friday and Saturday, 15-16 November 2019, we will organize the N-cube days at Chalmers University of Technology and University of Gothenburg in Sweden. The workshop is funded by Längmanska kulturfonden and Vetenskapsrådet.

If you intend to come, please send an email to one of the organizers, see below for contact info. Please let us know by November 1st if you plan to come to the conference dinner on Friday evening and inform us of any dietary restrictions. We will be able to support the majority of the dinner costs, but might, due to budgetary restrictions, ask for a minor contribution (about 100 SEK or roughly 10 euro) to be paid at the venue.

We might have spare funding for junior participants from the Nordic countries, please indicate in your communication with us if you are interested in such support.


Confirmed speakers are:

  • Jean-Benoît Bost (Université d'Orsay)
  • Tim Dokchitser (University of Bristol)
  • Linda Frey (University of Copenhagen)
  • Lars Halvard Halle (University of Copenhagen)
  • Özlem Imamoglu (ETH, Zürich)
  • Fredrik Strömberg (University of Nottingham)
  • Joni Teräväinen (Oxford University)
  • Lola Thompson (Oberlin College/MPI Bonn)

Schedule (Pdf)

13.00 - 13.30 Registration
13.30 - 13.35
13.35 - 14.25 Jean-Benoît Bost
14.35 - 15.25 Lola Thompson

16.10 - 17.00
Fredrik Strömberg
17.10 - 18.00 Tim Dokchitser

Dinner at Heaven 23, at 20h00.

Leave from Math department at 19h20.

Leave from Panorama at 19h40.

09.00 - 09.50
Joni Teräväinen
10.00 - 10.50
Linda Frey

11.20 - 12.10
Özlem Imamoglu
12.20 - 13.10
Lars Halvard Halle


   Jean-Benoît Bost
        Arithmetic mod-affine schemes

        This talk will introduce some counterparts of affine schemes in the framework of Arakelov geometry. Their study relies on a formalism of ”nuclear quasi-coherent sheaves on arithmetic curves”, based on non-trivial estimates on the theta functions associated to Euclidean lattices and to their infinite dimensional generalizations. This formalism allows one to develop foundational results in Arakelov geometry in a manner much closer to the classical geometry of schemes than the classical approaches to Arakelov geometry, notably by avoiding properness or regularity assumptions and by permitting to transfer cohomological techniques. It also admits various «concrete applications » to Diophantine geometry, which I plan to discuss. This is joint work with François Charles.

    Lola Thompson
        Counting quaternion algebras, with applications to spectral geometry

        We discuss how classical techniques from analytic number theory can be used to count quaternion algebras over number fields subject to various constraints. Because of the correspondence between maximal subfields of quaternion algebras and geodesics on arithmetic hyperbolic manifolds, these counts have interesting applications to the field of spectral geometry. We will conclude by describing how the breakthrough work of Maynard and Tao on bounded gaps between primes can be useful in a geometric setting. This talk is based on joint work with B. Linowitz, D. B. McReynolds, and P. Pollack.

    Fredrik Strömberg
        Noncongruence subgroups and Maass forms

        I will present recent theoretical and computational results regarding spectral theory and Maass waveforms for non-congruence subgroups of the modular group. In particular I will discuss spectral counting functions and Weyl laws and also present a new interpretation of old- and newforms which naturally extends the classical notions for congruence subgroups.

    Tim Dokchitser
        Models of curves

        I would like to explain how to construct regular models and study invariants of families of curves using Newton polygons. Basically, for ‘generic’ families C_t: f_t(x,y) = 0 this gives criteria for the reduction of C, and describes its differentials, regular model, and etale cohomology. For elliptic curves this essentially recovers Tate’s algorithm.

    Joni Teräväinen
        Chowla's conjecture at almost all scales

        An unsolved conjecture of Chowla states that the Möbius function should not correlate with its own shifts. This can be viewed as a conjecture about the randomness of the Möbius function. In the last few years, there has been a lot of progress on Chowla's conjecture. Nearly all of the previously obtained results have concerned correlations that are weighted logarithmically, so one wonders whether it is possible to get rid of these weights. We show that one can indeed remove logarithmic weights from previously known results on Chowla's conjecture, provided that one restricts to almost all scales in a suitable sense. This is joint work with Terry Tao.

    Linda Frey
        Invariants of Hyperelliptic Curves of Genus Two with Complex Multiplication

        Elliptic curves (genus one) can be classified by the j-invariant about which we know a lot. A result from 2018 of Bilu, Habegger and Kühne states that there are no j-invariants of elliptic curves with complex multiplication that are algebraic units. In the genus two case it gets more complicated. We have a tuple of three invariants which almost classify the genus two curves. We call them Igusa invariants. But not much is known about of the curve has complex multiplication whether the Igusa invariants are algebraic integers or even units. We will compare the two cases (genus one and two), state some conjectures and outline some approaches.

    Özlem Imamoglu
        On class number formulas

        Dirichlet’s class number formula for binary quadratic forms is well known. In a mostly  forgotten paper Hurwitz gave another infinite series representation for the class number of positive definite quadratic forms. In this talk I will give a proof of Hurwitz’s formula and show how it can be generalized to indefinite case.

    Lars Halvard Halle
        Arithmetic Geometry of Crauder-Morrison Models for K3 Surfaces

        Kodaira's classification of degenerate fibers in elliptic fibrations is a very useful tool in the study of elliptic curves, with a wealth of applications both in geometry and in number theory. In the context of  K3 surfaces, there exists a partial classification of degenerate fibers, due to Crauder and Morrison. In this talk, I will explain how Crauder and Morrison's theory, when applicable, can be used to investigate some natural questions and invariants, such as: existence of logarithmic good reduction, the index, the motivic zeta function and the monodromy.


The organizers are

We are available for further inquiries at the above email addresses.


Travel information

Gothenburg Landvetter Airport (airport code GOT) is close to Gothenburg. You can come from the airport to the city:

  • By taxi. There should be a fixed price around 500 SEK.
  • By airport bus and public transportation
    • The station for Flygbussen is next to the airport exit. You can purchase tickets on the bus. The bus brings you to the city. The first stop (Korsvägen) is the closest one to Panorama hotel.
    • Public transportation in Gothenburg is decent. You can look up your further itinerary on the Västtrafik website.

Conference venue

The conference will take place in the math building on the campus of Chalmers University of Technology, Chalmers tvärgata 3.

Talks take place in the lecture hall Pascal in the math building, room number H2022. A map is available - you can safely ignore the Swedish text on the linked webpage.