## When & Where

##### Second Seminar

The second ERLASS seminar was postponed due to the ongoing Coronavirus outbreak. We apologise for the inconvenience.

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DATE

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December 18, 2020

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Time

#### 9:30-13:00 (London)

## Programme

##### Timetable

##### ONLINE MEETING

9.30-10.30 Nicole Raulf (Lille) Asymptotics of class numbers

10.45-11.45 Christopher Frei (Graz) Constructing abelian extensions with prescribed norm

12.00-13.00 Polyxeni Spilioti (Aarhus) A prime geodesic theorem for SL_3(Z)

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Abstracts:

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Frei: Let K be a number field, S a finite set of elements of K, and

G a finite abelian group. We explain how to construct explicitly a

normal extension L of K with Galois group G, such that all elements of S are norms of elements of L. The construction is based on class field theory and a recent formulation of Tateâ€™s criterion for the validity of the Hasse norm principle. This is joint work with Rodolphe Richard (UCL).

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Raulf: We present results of the asymptotic behaviour of class numbers in the situation that the class numbers are ordered by the size of the regulator. We also will discuss the methods that

can be used to obtain these results.

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Spilioti:

In this talk, we will present a prime geodesic theorem for the group SL_3(Z). This is an arithmetic prime geodesic theorem for a higher rank locally symmetric space. Depending on the time, we will present a formulation of this theorem that involves class numbers.

This is a joint work with A. Deitmar and Y. Gon.

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##### Preliminary list of

##### participants

Christopher Frei

Nicole Raulf

Polyxeni Spilioti

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Stephanie Chan;

Jonathan Chapman;

FÃ©licien Comtat;

Tim Davis;

Chris Daw;

Natalie Evans;

Reynold Fregoli;

Michael Kural;

Steve Lester;

AndrÃ© Macedo;

Simon Myerson;

Rachel Newton;

Yiannis Petridis;

Ian Petrow;

Efthymios Sofos;

Ashwin Swaminathan;

Marios Voskou;

Martin Widmer;

Han Wu;

(to be updated)

## Organisers, Link & Sponsors

##### ERLASS organisers

##### Local organisers

Steve Lester (King's College London);

Rachel Newton (Reading);

Yiannis Petridis (UCL);

Martin Widmer (Royal Holloway);

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Yiannis Petridis (i.petridis@ucl.ac.uk)

Ian Petrow (i.petrow@ucl.ac.uk)

##### Sponsors

The ERLASS is funded by an LMS scheme-3 grant (31902).

## Zoom Link: https://ucl.zoom.us/j/96690024849?pwd=TzZhRlRHYlNPbWNlUGpDTlBLM3NKUT09

## â€‹

## Password: the first 10 decimal digits of the number with 17 digits ending at

## 515 that is one of the 3 numbers with sum of cubes equal to the Answer to the Ultimate Question of Life, the Universe, and Everything

## (or ask the host)

Meeting ID

966 9002 4849