# Istanbul Summer School in Algebraic Geometry Istanbul Center for Mathematical Sciences June 17-21, 2013

Speakers:

Lawrence Ein (U. Illinois at Chicago)
Joe Harris (Harvard University)
Mihnea Popa (U. Illinois at Chicago)

İlhan İkeda (Yeditepe University)
Hurşit Önsiper (Middle East Technical University)
Ali Sinan Sertöz (Bilkent University)
Betül Tanbay (Bosphorus University)
Meral Tosun (Galatasaray University)
Muhammed Uludağ (Galatasaray University)

Organizing Committee:

Kürşat Aker
Arzu Boysal (Bosphorus University)
İzzet Coşkun (U. Illinois at Chicago)
Ferit Öztürk (Bosphorus University)
Sinan Ünver (Koç University)

Registration: Registration is free and open to everyone. If you are planning to attend, please register by April 1, 2013 by filling out the registration form here. Please indicate whether you would like to attend the preparatory lectures the preceding week.

Funding: The summer school is open to everyone who registers. Unfortunately, there is no funding for the school, so anyone wishing to attend must pay for their own transportation and accommodation.

The preparatory lectures on June 12-13-14 will take place in the Istanbul Center for Mathematical Sciences. Due to the large number of participants, the lectures on June 17-21 will take place in room TB 310 (Anderson Hall--Faculy of Arts and Sciences).

Schedule:
Mon   Jun 17       9:30-10:45 Joe Harris         11:00-12:15 Mihnea Popa
Tue   Jun 18       9:30-10:45 Lawrence Ein     11:00-12:15 Joe Harris
Wed   Jun 19       9:30-10:45 Mihnea Popa     11:00-12:15 Lawrence Ein
Thu   Jun 20       9:30-10:45 Joe Harris           11:00-12:15 Mihnea Popa
Fri     Jun 21       9:30 -10:45 Lawrence Ein     11:00-12:15 Joe Harris

Titles and abstracts:

Joe Harris, Moduli space of curves

We'll discuss what parameter spaces and moduli spaces are, with examples (in particular, the distinction between fine moduli spaces and coarse ones). We'll talk about modular compactifications, and the significance of the valuative criterion in this context, focussing primarily on the Deligne-Mumford moduli space of stable curves $\overline M_g$. After some preliminaries on the geometry of stable curves, we'll describe the divisor theory of the Deligne-Mumford space and its relation to the global geometry of $\overline M_g$.

Lawrence Ein, Singularities and adjoint linear systems Lecture Notes

We'll discuss some basic results on surface singularities and adjoint linear systems on smooth surfaces.

Mihnea Popa, Generic vanishing theorems and applications. Lecture Notes

Classical vanishing theorems like Kodaira-Akizuki-Nakano vanishing have myriads of applications in algebraic geometry. These theorems require various strong versions of positivity for line bundles on algebraic varieties. After recalling them, together with a few consequences, I will explain a line of research which was started in the 80's with the aim of producing vanishing theorems under much weaker positivity hypotheses, on varieties with non-zero first Betti number. This goes under the name of generic vanishing theory. I will present its main results and applications, and briefly mention towards the end how this line of research has been given new impetus in the last few years years due to recent developments such areas as Hodge theory and derived categories.

Here is a list of registered participants. We will update this list every few weeks. Participants

The week preceding the workshop, there will be preparatory lectures given by İzzet Coşkun (U. Illinois at Chicago) on Curves and their equations, Sinan Ünver (Koç University) on Abelian varieties and Jacobians. We hope that these lectures will prepare beginning graduate students for the main lectures. The schedule for these lectures is as follows:
Wed (Jun 12), Thu (Jun 13), Fri (Jun 14)     10-12 Izzet Coskun     1:30-3:30 Sinan Unver