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Autumn Semester 2014

Date / Time Speaker Title Location
3 October 2014
14:15-15:15 		Will Sawin
Princeton University
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Number Theory Seminar

Title A Tannakian category and a horizontal equidistribution conjecture for exponential sums
Speaker, Affiliation Will Sawin, Princeton University
Date, Time 3 October 2014, 14:15-15:15
Location HG G 43
Abstract We describe a group that plays a role in the horizontal equidistribution of Gauss sums, Kloosterman sums, Salie sums, etc. similar to the role that the Sato-Tate group plays in the distribution of traces of Frobenius in Galois representations. Using this we make a general equidistribution conjecture for exponential sums. The conjecture agrees with known results in some cases and numerical evidence in other cases.
A Tannakian category and a horizontal equidistribution conjecture for exponential sumsread_more
HG G 43
10 October 2014
14:15-15:15 		Chantal David
Concordia University, Montreal
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Number Theory Seminar

Title The distribution of elliptic curves over prime finite fields
Speaker, Affiliation Chantal David, Concordia University, Montreal
Date, Time 10 October 2014, 14:15-15:15
Location HG G 43
The distribution of elliptic curves over prime finite fields
HG G 43
17 October 2014
14:15-15:15 		Ariyan Javanpeykar
Universität Mainz
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Number Theory Seminar

Title Arakelov invariants, Belyi degree, Shafarevich conjecture
Speaker, Affiliation Ariyan Javanpeykar, Universität Mainz
Date, Time 17 October 2014, 14:15-15:15
Location HG G 43
Abstract Let X be a curve over a number field. We study invariants of X such as the Belyi degree d(X) and the stable Faltings height h(X). Our main result is an explicit inequality relating these invariants: h(X) <10^9 d(X)^6. As a first application of this inequality we prove the 2011 conjecture of Edixhoven-de Jong-Schepers on the Faltings height of a cover of curves. Then we discuss applications to Szpiro's small points conjecture and the effective Shafarevich conjecture. In fact, in a joint work with Rafael von Kaenel, we prove these conjectures for cyclic covers of the projective line. Moreover, we explain how von Kaenel uses the above theorem and certain modularity results to prove the effective Shafarevich conjecture for abelian varieties of product GL_2-type.
Arakelov invariants, Belyi degree, Shafarevich conjectureread_more
HG G 43
31 October 2014
14:15-15:15 		Prof. Dr. Javier Fresan
ETH Zurich, Switzerland
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Number Theory Seminar

Title Periods of connections and a conjecture of Gross-Deligne
Speaker, Affiliation Prof. Dr. Javier Fresan, ETH Zurich, Switzerland
Date, Time 31 October 2014, 14:15-15:15
Location HG G 43
Abstract Motivated by a new approach to the Chowla-Selberg formula, Gross and Deligne conjectured at the end of the 70s that periods of geometric Hodge structures with multiplication by an abelian number field are always products of special values of the gamma function, with exponents determined by the Hodge decomposition. I will explain a proof of an alternating variant of this conjecture for the cohomology groups of smooth, projective varieties with an automorphism of finite order. The main ingredient will be a global-to-local formula for periods of flat vector bundles due to Saito and Terasoma.
Periods of connections and a conjecture of Gross-Deligneread_more
HG G 43
7 November 2014
14:15-15:15 		Giuseppe Ancona
Universität Essen
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Number Theory Seminar

Title On the Chow group and the motive of a commutative algebraic group
Speaker, Affiliation Giuseppe Ancona, Universität Essen
Date, Time 7 November 2014, 14:15-15:15
Location HG G 43
Abstract A classical result of Beauville shows that the action of the multiplication by n on the Chow group of an abelian variety is semisimple with a finite number of explicit eigenvalues. This result was used by Deninger and Murre to show that the Chow motive of an abelian variety has a canonical Künneth decomposition. We will show that these two results generalize to commutative algebraic groups (e.g. to semiabelian varieties). The proof is different and also the logic dependency changes: we will directly work with the motive (in the language of Voevodsky) and then deduce the result on Chow groups. In this talk we will recall the generalities on Voevodsky's motives and we will motivate their construction by explaining some arithmetic and geometric applications. This is a joint work with Steven Enright-Ward and Annette Huber.
On the Chow group and the motive of a commutative algebraic groupread_more
HG G 43
14 November 2014
14:15-15:15 		Jürg Kramer
Humboldt Universität zu Berlin
Details

Number Theory Seminar

Title Sup-norm bounds of automorphic forms
Speaker, Affiliation Jürg Kramer, Humboldt Universität zu Berlin
Date, Time 14 November 2014, 14:15-15:15
Location HG G 43
Abstract In our talk, we will present sup-norm bounds of modular forms of even weight on average for any Fuchsian subgroup of the first kind. In particular, we will address uniformity of the bounds with regard to the weight and the subgroups in question. If time permits, we will also address work in progress on sup-norm bounds of Maass wave forms.
Sup-norm bounds of automorphic formsread_more
HG G 43
21 November 2014
14:15-15:15 		Eva Bayer
EPF Lausanne
Details

Number Theory Seminar

Title Embeddings of maximal tori in classical groups and explicit Brauer-Manin obstruction
Speaker, Affiliation Eva Bayer, EPF Lausanne
Date, Time 21 November 2014, 14:15-15:15
Location HG G 43
Embeddings of maximal tori in classical groups and explicit Brauer-Manin obstruction
HG G 43
28 November 2014
14:15-15:15 		Gerard Freixas i Montplet
CNRS
Details

Number Theory Seminar

Title On the analytic class number formula for Selberg zeta functions
Speaker, Affiliation Gerard Freixas i Montplet, CNRS
Date, Time 28 November 2014, 14:15-15:15
Location HG G 43
Abstract As a byproduct of the trace formula, Selberg attached a zeta function to every fuchsian group. This functions has some analogies with the Riemann zeta function: meromorphic continuatio, prime (geodesic) number theorem, Riemann hypothesis, etc. However, to the knowledge of the speaker, there is a missing element in this list: the analytic class number formula. In this talk I will consider this question, as a particular application of a generalized Riemann-Roch formula in Arakelov geometry. In particular I will provide the example of PSL_2(Z), that also suggests the kind of arithmetic information these mysterious zeta functions carry. A part of this talk will be based on work in progress with Anna von Pippich.
On the analytic class number formula for Selberg zeta functionsread_more
HG G 43
5 December 2014
14:15-15:15 		Abhishek Saha
Bristol University
Details

Number Theory Seminar

Title Nearly holomorphic modular forms and lowest weight representations
Speaker, Affiliation Abhishek Saha, Bristol University
Date, Time 5 December 2014, 14:15-15:15
Location HG G 43
Abstract Nearly holomorphic modular forms are a generalization of holomorphic modular forms and were first introduced by Shimura. They have been important for studying arithmetic properties of special L-values of automorphic representations. I will describe these objects from the representation-theoretic point of view for classical (degree 1) modular forms and degree 2 Siegel modular forms. In particular, I will describe a structure theorem which roughly says that all vector-valued nearly holomorphic Siegel modular forms of degree 2 (with some low weight exceptions) can be built up from vector-valued holomorphic Siegel modular forms via explicit weight raising operators. This theorem generalizes known results due to Shimura in the classical (degree 1) case, and is joint work with Ameya Pitale and Ralf Schmidt. Along the way, we will see a detailed picture of all the lowest weight representations of Sp(4, R), with descriptions of the possible K-types, multiplicities, and relevant differential operators.
Nearly holomorphic modular forms and lowest weight representationsread_more
HG G 43

Organisers: Özlem Imamoglu, Peter Simon Jossen, Emmanuel Kowalski, Paul Nelson, Richard Pink, Evelina Viada, Gisbert Wüstholz

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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