
Intercity Number Theory SeminarMarch 16, Utrecht. Location: Buys Ballotgebouw 161 (Princetonplein 5, 3584 CC Utrecht).
Note: at the moment the main entrance of the BBG is closed and you will need to enter the Buys Ballotgebouw via the Koningsbergergebouw (Budapestlaan 4ab, 3584 CD Utrecht)12:3013:00  tea break,  13:0013:50  Masha Vlasenko (Warsaw), Dwork crystals and related congruences Abstract. In the talk I will describe a realization of the padic cohomology of an affine toric hypersurface
which originates in Dwork's work and give an explicit description of the unitroot subcrystal
based on certain congruences for the coeficients of powers of a Laurent polynomial.
This is joint work with Frits Beukers.  14:0014:50  Diego Izquierdo (Paris), On a conjecture of Kato and Kuzumaki Abstract. In 1986, Kato and Kuzumaki stated a set of conjectures which aimed at giving a Diophantine characterization of the cohomological dimension of fields in terms of Milnor Ktheory and of points in projective hypersurfaces of small degree. The conjectures are known to be wrong in full generality, but they remain open for various fields that usually appear in number theory or in algebraic geometry. In this talk, I will present several results related to the conjectures of Kato and Kuzumaki for global fields and for some function fields.  15:0015:30  tea break,  15:3016:20  Sara Checolli (Grenoble), On some arithmetic properties of Mahler functions Abstract. Mahler functions are power series f(x) with complex
coefficients for which there exist a natural number n and an integer
l ≥ 2 such that
f(x),f(x^{l}),ldots,f(x^{ln1}),f(x^{ln}) are linearly
dependent over C(x). The study of these functions and of the
transcendence of their values at algebraic points was initiated by
Mahler around the 30's and then developed by many authors.
In this talk we will investigate some arithmetic aspects of Mahler
functions. In particular, when f(x) satisfies the equation
f(x)=p(x)f(x^{l}) with p(x) a polynomial with integer
coefficients, we will see how certain properties of f(x) mirrors on
the polynomial p(x), also in connection with the theory of automatic
sequences. If time allows, we will also discuss some analogies with
E and G functions. This is a joint work with Julien Roques.  16:3017:20  Jakub Byszewski (Kraków), Sparse generalised polynomials and automatic sequences Abstract. We investigate generalised polynomials (i.e., polynomiallike expressions involving the use of the floor function) which take the value 0 on all integers except for a set of density 0. By a theorem of BergelsonLeibman, generalised polynomials can be completely described in terms of dynamics on nilmanifolds. Our main result is that the set of integers where a sparse generalised polynomial takes nonzero value cannot be combinatorially rich (specifically, cannot contain a translate of an IP set). We study some explicit constructions and give some evidence for the claim that generalised polynomial sets of exponential growth have interesting arithmetic behaviour. In particular, we show that the characteristic functions of the Fibonacci and Tribonacci numbers are given by generalised polynomials. Finally, we show that any sufficiently sparse {0,1}valued sequence is given by a generalised polynomial. We apply these results to a question on automatic sequences. This is joint work with Jakub Konieczny. 

BelgianDutch Algebraic Geometry SeminarMarch 23, Leiden. See website. 
Intercity Number Theory SeminarApril 20, Groningen. Bernoulliborg, room 165, start at 11:45.11:4512:45  Maarten Derickx (Groningen), Torsion subgroups of rational elliptic curves over infinite extensions of Q. Abstract. Recently there has been much interest in studying the torsion subgroups of elliptic curves baseextended to infinite extensions of Q. In this talk, given a finite group G, we will study what happens with the torsion of an elliptic curve E over Q when changing base to the compositum of all number fields with Galois group G. This is done by studying a group theoretic condition called generalized Gtype, which is a necessary condition for a number field with Galois group H to be contained in that compositum. In general, group theory allows one to reduce the original problem to the question of finding rational points on finitely many modular curves. This method is illustrated by completely determining which torsion structures occur for elliptic curves defined over Q and basechanged to the compositum of all fields whose Galois group is of generalized A4type.  13:3014:30  Pınar Kılıçer (Oldenburg), On primes dividing the invariants of Picard curves Abstract. The jinvariants of elliptic curves with complex
multiplication (CM) are algebraic integers. For invariants of genus g
= 2 or 3, this is not the case, though suitably chosen invariants do
have smooth denominators in many cases. Bounds on the primes in these
denominators have been given for g=2 (GorenLauter) and some cases of
g=3. For Picard curves of genus 3, we give a new approach based not on
bad reduction of curves but on a very explicit type of good reduction.
This approach simultaneously yields much sharper bounds and a
simplification of the proof. This is joint work with Marco Streng and
Elisa Lorenzo García.  14:4515:45  Harm Voskuil (Amsterdam), Mumford curves in positive characteristic. Abstract. Mumford curves can be defined as quotients of an open analytical subspace of the projective line over a complete nonarchimedean field by the action of a free discontinuous group. We consider Mumford curves in positive characteristic that have many automorphisms.Then the free group Δ defining the Mumford curve X is contained as a normal subgroup in a finite amalgam Γ of finite groups. The automorphism group Aut(X) is the quotient Γ/Delta. We describe the amalgams Γ that occur and obtain a formula for the upper bound of the order of the automorphism group in terms of the genus of the Mumford curve (assuming that the genus is >1). Furthermore, all the Mumford curves that realise this upper bound are described in terms of the corresponding amalgam Γ and the automorphism group Γ/Δ is determined. (This is joint work with Marius van der Put).  16:0017:00  Florian Hess (Oldenburg), Explicit isomorphisms and fields of definition and moduli of curves Abstract. We define some isomorphism invariants of pointed curves and
discuss a constructive approach to compute fields of definition and
fields of moduli of curves. These invariants generalise the well known
jinvariant of elliptic curves in a different direction than for
example the Igusa invariants of hyperelliptic curves. 

Intercity Number Theory SeminarJune 22, Leiden. This is the last day of the workshop Effective Methods for Diophantine Problems. All talks will be in the Havingazaal of the Gorlaeus Building, located on the first floor of what's indicated by LMUY on this map and the detailed map on the last page of that document. Note that you can not get there through the main entrance of the Gorlaeus Lecture Hall, indicated by (4) on the map. 
BelgianDutch Algebraic Geometry seminarSeptember 20, Nijmegen. This is a twoday event: September 20 and 21. See the website, also for (free) required registration. 
AachenBonnKoelnLilleSiegen seminar on automorphic formsNovember 23, Utrecht. Location: Minnaert Building, room 20113:1514:15  Peter Bruin (Leiden), On explicit computations with modular Galois representations Abstract. I will explain a compact way of encoding representations of the absolute Galois group of a field K on finite Abelian groups as dual pairs of finite Kalgebras. These are in principle equivalent to finite commutative group schemes or Hopf algebras, but are easier to compute and to store. I will show how to compute these objects and to work with them, with a focus on representations attached to modular forms over finite fields. Work is ongoing to include such representations in the LFunctions and Modular Forms Database.  14:1515:15  Alexandru Ciolan (Köln), Asymptotics and inequalities for partitions into squares Abstract. In this talk we show that the number of partitions into squares with an even number of parts is asymptotically equal to that of partitions into squares with an odd number of parts. We further prove that, for n large enough, the two quantities are different and which of the two is bigger depends on the parity of n. This solves a recent conjecture formulated by Bringmann and Mahlburg (2012).  15:4516:45  JanWillem van Ittersum (Utrecht), A symmetric BlochOkounkov theorem Abstract. Bloch and Okounkov showed that the generating series associated to a wide class of functions on partitions of integers are quasimodular forms. We consider a different class of functions on partitions. In this class the functions are symmetric in the parts and multiplicities of the parts of the partitions. We show that the associated generating series are quasimodular forms as well.  16:4517:45  Annalena Wernz (Aachen), On Hermitian modular forms  Theta series and Maass spaces Abstract. It is well known (Cohen, Resnikoff 1978 and Hentschel, Nebe 2009) that Hermitian theta series of an even unimodular theta lattice of rank k belong to [U(2,2;O_{K}),k] where U(2,2;O_{K}) is the full Hermitian modular group of degree 2. In this talk, we consider the normalizer U^{*}(2,2;O_{K}) of U(2,2;O_{K}) in the special unitary group SU(2,2;C) and examine the behavior of Hermitian theta series under its action. Furthermore, we consider the Hermitian Maaß spaces S(k,O_{K}) and M(k,O_{K}) introduced by Sugano (1985) and Krieg (1991) respectively. In an approach which is similar to the paramodular case (Heim, Krieg 2018), we prove that a Maaß form in the Sugano sense is an element of Krieg's Maaß space if and only if it is a modular form with respect to U^{*}(2,2;O_{K}). 

Intercity Seminar Number TheoryDecember 7, Eindhoven. In Metaforum 14 (6e verdieping); PhD defense Guus Bollen in Senaatszaal of Auditorium.11:4512:30  Wieb Bosma (Nijmegen), Enumerating selfcomplementary graphs Abstract. Graphs that are isomorphic to their complement are among
the objects to which Polya's counting method has been most
successfully applied. We will discuss methods for counting and
enumerating selfcomplementary graphs (both ordinary and
directed, with and without particular structure) on small
numbers of points, and interaction between the two.
On the way we will also encounter some interesting
properties and problems of these graphs.  13:1514:00  Winfried Hochstättler (Hagen), The Varchenko Determinant of an Oriented Matroid Abstract. The Varchenko matrix M of a hyperplane arrangement is a symmetric square
matrix indexed by the full dimensional regions of the arrangement, where
M_{ij} equals the product of the hyperplanes seperating the cells i and j.
Varchenko proved 1993 that the determinant of this matrix has a nice
factorization. Using a proof strategy suggested by Denham and Henlon in
1999 we show that the same factorization works in the abstract setting
of oriented matroids. For that purpose we show that every Tconvex
region of the set of topes, considered as a subcomplex of the Edelman
poset, has a contractible order complex, which might be of independent
interest.  14:1515:00  Dustin Cartwright (Tennessee), Onedimensional groups and algebraic matroids Abstract. I will talk about a construction of algebraic matroids from modules over
endomorphism rings of 1dimensional algebraic groups, which generalizes
both linear and monomial realizations of matroids. The algebraic matroid
constructed in this way coincides with a linear matroid over the
endomorphism ring. I will explain how this relationship also extends to
the Lindström valuation and the Frobenius flock of the algebraic
matroid. This is joint work with Jan Draisma and Guus Bollen.  16:0017:00  Guus Bollen (Eindhoven), PhD defense 

Intercity Number Theory SeminarDecember 18, Leiden. In Snellius 412; PhD defense Erik Visse in the Academiegebouw in the center of Leiden.10:0011:00  Erik Visse (Leiden), PhD defense  13:4514:45  Rachel Newton (Reading), Number fields with prescribed norms Abstract. Let G be a finite abelian group, let k be a number field, and let x be an element of k. We count Galois extensions K/k with Galois group G such that x is a norm from K/k. In particular, we show that such extensions always exist. This is joint work with Christopher Frei and Daniel Loughran.  15:0016:00  Daniel Loughran (Manchester), Integral points on Markoff surfaces Abstract. Integral solutions to Markofftype equations of the form x^{2} + y^{2} + z^{2}  xyz = m were studied by Ghosh and Sarnak. In this talk we explain how to reinterpret their work using the BrauerManin obstruction, and quantify the number of such surfaces which fail the integral Hasse principle. This is joint work with Vlad Mitankin.  16:1517:15  Efthymios Sofos (Bonn), The size of the primes p for which a Diophantine equation is not soluble modulo p Abstract. The set of the primes p for which a variety over the rational numbers has no padic point plays a fundamental role in arithmetic geometry. This set is deterministic, however, we prove that if we choose a typical variety from a family then the set has random behaviour. We furthermore prove that this behaviour is modelled by a random walk in Brownian motion. This has several consequences, the main one being the description of the finer properties of the distribution of the primes in this set via the FeynmanKac formula. 


