On Friday and Saturday, 1516 November 2019, we will organize the Ncube 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:
Friday  

13.00  13.30  Registration 
13.30  13.35 
Welcome 
13.35  14.25  JeanBenoît Bost 
14.35  15.25  Lola Thompson 
Fika 

16.10  17.00 
Fredrik Strömberg 
17.10  18.00  Tim Dokchitser 
Evening 
Dinner at Heaven 23, at 20h00. Leave from Math department at 19h20. Leave from Panorama at 19h40. 
Saturday  
09.00  09.50 
Joni Teräväinen 
10.00  10.50 
Linda Frey 
Fika  
11.20  12.10 
Özlem Imamoglu 
12.20  13.10 
Lars Halvard Halle 
JeanBenoît Bost
Arithmetic
modaffine schemes
This talk will introduce some
counterparts of affine schemes in the framework of Arakelov
geometry. Their
study relies on a formalism of ”nuclear quasicoherent sheaves
on arithmetic
curves”, based on nontrivial 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
noncongruence 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 jinvariant about which we know a lot. A
result from 2018 of
Bilu, Habegger and Kühne states that there are no jinvariants
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 CrauderMorrison 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.
Gothenburg Landvetter Airport (airport code GOT) is close to Gothenburg. You can come from the airport to the city:
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.