### Ankara-Istanbul AGNT - X

Below you can find details of the second meeting of Fall 2015 term.

**Date:**14th of November, 2015, Saturday

**Place:** Istanbul Center for Mathematical
Sciences (IMBM), Bogazici University South Campus (Campus map)

How to get to
IMBM

#### 14:30 - 15:30 The Tchebotarev Density Theorem (Mehpare Bilhan - METU)

Notes taken by Özlem Beyarslan of the talk
by Mehpare Bilhan on the first meeting.

Notes taken by Alp Bassa of the talk by
Mehpare Bilhan on the first meeting.

A nice
paper by Stevenhagen and Lenstra on "Chebotarëv and his density theorem",
published in the Mathematical Intelligencer.

#### 16:00 - 17:00 Seiberg-Witten invariants of 4-manifolds (Çağrı
Karakurt - Boğaziçi University)

**Abstract:** Donaldson proved his celebrated
diagonalization theorem by studying the solutions Yang-Mills equation.
Since then gauge theory has been an extremely important tool for
understanding the topology of 4-manifolds. With the advent of
Seiberg-Witten equations, which significantly simplified and extended the
use of gauge theory, the field of 4-manifolds has experienced a period of
phenomenal growth and development. This lecture will be on the
construction and properties of the smooth 4-manifold invariants which are
extracted from the moduli space of solutions of Seiberg-Witten
equations.

- A review paper by Bayram Tekin on Seiberg-Witten
theory written in 1997 (untouched since then)

**17:30 - 18:30 Combinatorics of Schubert Polynomials (Olcay
Coşkun - Boğaziçi University)**

**Abstract: **Schubert polynomials are polynomial
representatives of Schubert cycles in the cohomology ring of flag
varieties. Due to their nature, it is possible to describe these
polynomials in a purely combinatorial way. In this second part of the
series, we introduce Schubert polynomials algebraically, and discuss some
combinatorial descriptions of them.
- Notes taken by Özlem Beyarslan of the talk
by Özer Öztürk on the first meeting.
- Notes taken by Alp Bassa of the talk by Özer
Öztürk on the first meeting.