[Turkmath:464] Lectures on Abelian Varieties with Complex Multiplication

[Ekin Ozman]

Değerli liste üyeleri,

4 Mayıs, 6 Mayıs ve 7 Mayıs tarihlerinde İstanbul Matematiksel Bilimler
Merkezinde "Abelian Varieties with Complex Multiplication" konusunda bir
dizi konuşma verilecektir.
Konuşmalar ile ilgili detaylı bilgileri aşağıda ve ekteki etkinlik efişinde
bulabilirsiniz. İlgilenen herkesi bekliyoruz.

İyi çalışmalar.

-- 
Ekin Özman

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Dear colleagues,

You are cordially invited to the lecture series on Abelian Varieties with
Complex Multiplication which will take place at IMBM on May 4,6 and 7. The
details of the lectures are as below and also in the attachment.

Best regards,
-- 
Ekin Özman



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Lectures on Abelian Varieties with Complex Multiplication at IMBM



In this series of lectures our main scope is to introduce the subject and
mention come recent results about CM abelian varieties and their reduction.
There will be a series of 3 talks during the week of May 4. The time and
details of each lecture is as below. The lectures should be accesible to
students.

May 4,Monday, 13:00,  IMBM Seminar Room, Bogazici University South Campus

Speaker: Ekin Ozman, Boğaziçi University
Title: Abelian Varieties and Complex Multiplication
Abstract: This talk will be about the basics of Abelian Varieties and
complex multiplication(CM). After defining these terms, we will continue
with the discussion of good and bad reduction of CM abelian varieties. The
talk should be accessible to students and will introduce the notions needed
in the following talks of E. Garcia and R. Newton.



May 6, Wednesday, 13:00, IMBM Seminar Room, Bogazici University South Campus

Speaker: Elisa Lorenzo Garcia, Leiden University
Title: A Gross-Zagier formula and some generalizations.
Abstract: The aim of this talk is to introduce the original results of
Gross and Zagier about the factorization of products of differences of
singular moduli. We will also describe some generalizations to the problem
for CM curves of genus 2 due to the work of Goren, Lauter and Viray. These
results motivate the partial generalizations for genus 3 that R. Newton
will explain in the following talk.

May 7, Thursday, 13:00,  IMBM Seminar Room, Bogazici University South Campus

Speaker: Rachel Newton, Max Planck Institute for Mathematics, Bonn
Title: Bad reduction of genus 3 curves with complex multiplication.
Abstract: If we take a polynomial defining a curve and reduce its
coefficients modulo a prime, what happens to the curve? There are two kinds
of behaviour: either the curve remains irreducible, or it breaks down into
multiple components. We call the latter case 'bad reduction'.
Cryptographers need a supply of curves with good reduction in order to
build secure encryption algorithms. Complex multiplication (or CM) is an
additional structure which allowed Goren and Lauter to give a bound on the
primes of bad reduction for curves of genus 2 with CM. I will describe a
partial generalisation of this work to curves of genus 3 with CM. This is
joint work with I. Bouw, J. Cooley, K. Lauter, E. Lorenzo Garcia, M. Manes
and E. Ozman.


-- 
Ekin Özman
Boğaziçi University
Department of Mathematics
34342 Bebek, Istanbul
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