[Turkmath:245] Ankara-Istanbul Algebraic Geometry and Number Theory Meetings - Spring schedule

[Alp Bassa]

Değerli Liste Üyeleri,

Türkiye'de cebirsel geometri ve sayılar kuramı alanlarında çalışan
araştırmacıları bir araya getirmek amacıyla oluşturulan Ankara-Istanbul
Cebirsel Geometri-Sayılar Kuramı Toplantıları'nın bahar dönemi programını
aşağıda bulabilirsiniz. Bu dönemin ilk toplantısı 28 Şubat'ta Ankara'da
gerçekleşecek. Her akademik dönem aylık toplantılar planlanmaktadır.
Etkinlikler ile ilgili daha ayrıntılı bilgiye şuradan ulaşabilirsiniz:

http://web0.boun.edu.tr/alp.bassa/ankaraistanbul/

Dönem içinde etkinliklerle ilgili duyuruları e-mail yolu ile almak
istiyorsanız lütfen benimle irtibata geçin: alp.bassa at gmail.com

Saygılarımla
Alp Bassa

Ankara-Istanbul Algebraic Geometry and Number Theory Meetings, Spring 2015

Dates:
28 February 2015 (Saturday), Ankara
11 April 2015 (Saturday), Istanbul
9 May 2015 (Saturday), Ankara
31 May 2015 (Sunday), Izmir*

(* Tentative)


Speakers and Titles:

Lecture series 1:  Universal Teichmuller Space and the
Grothendieck-Teichmuller Group -  Ilhan Ikeda, Ayberk Zeytin

Lecture series 2: Minicourse on Vector Bundles on Projective Varieties -
Emre Coskun  **

Lecture series 3: Arithmetic Statistics - Kazim Buyukboduk, Ilhan Ikeda,
Ekin Ozman

(** This lecture series aims to provide potential participants of the
upcoming conference "ACM Bundles on Algebraic Varieties" to be held at
METU, 15-19 June, 2015, with the necessary background material)


Abstracts:

Universal Teichmuller Space and the Grothendieck-Teichmuller Group -  Ilhan
Ikeda, Ayberk Zeytin

This lecture series is comprised of two parts. The first part is about the
geometric and analytic properties of the universal Teichmuller space. Our
aim will be to define the universal Teichmuller space and try to explain
what makes this space universal. Then we will discuss its relationship with
arithmetic.

The, essentially independent, second part will be about arithmetic
properties of Grothendieck Teichmuller (GT) group. The first talk of this
part is related with the relationship between GT and other groups closely
related with the absolute Galois group. The second talk is on the
representation theory of GT.



Minicourse on Vector Bundles on Projective Varieties - Emre Coskun

In this lecture series, we will study vector bundles on projective
varieties. After the definitions and basic properties, we will cover Chern
classes, stability, and construction methods (elementary modifications,
Serre construction).



Arithmetic Statistics - Kazim Buyukboduk, Ilhan Ikeda, Ekin Ozman

Arithmetic Statistics: The question of finding all rational solutions to
Diophantine equations is one of the oldest and most central questions in
number theory. Such solutions correspond to solutions of polynomials in
rational numbers or, geometrically speaking,Q-rational points on the curve
described by that polynomial. It has proved highly fruitful to view such
problems not just from an algebraic perspective but also a geometric one. A
recent approach is to view a family of equations(or curves) all together
instead of studying them individually and asking questions about average
number of rational points of a family or distribution of such points among
the family. This new approach, sometimes called Arithmetic Statistics, has
been studied from different perspectives by many mathematicians including
Bhargava, Mazur, Poonen and Rubin. In this series of talks, we will start
with defining main objects of this study and then focus on introducing this
new approach following the approach of Mazur, Rubin and their collaborator
Klagsbrun.

The theme of "variation of arithmetic invariants in families" goes all the
way back to Gauss, who then inquired about the (*horizontal*) variation of
class numbers of quadratic fields. Although there are heuristics about the
statistics governing that, we still fall short of a definitive answer. In
contrast with this rather erratic behaviour in *horizontal* families,
Iwasawa proved a neat variational formula for the class numbers along
(*vertical*) Z_p towers, in effect abusing the "p-adic analytic variation"
of class groups. This lead Greenberg and Mazur (and many others) to a much
broader study of the p-adic analytic variation in various arithmetic
families, which was emphasized in the last lecture of the Fall Semester (on
Rigid Geometry and Langlands' program). The perspective we shall take this
semester is akin to the *horizontal* approach (which looks much harder,
from historical perspective), following the lead of Bhargava, Mazur, Poonen
and Rubin as indicated above, investigating the statistics of the
Mordell-Weil ranks of elliptic curves ranging in horizontal families.
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