**PRESENTATION**

There
will be 3 back-to-back programs of fundamental importance for modern
mathematics, theoretical and mathematical physics:

1) Affine and Double Affine Hecke
Algebras, AHA (June 19-24),

2) The Langlands Program, the geometric
and arithmetic directions, LP (June 25 - July 1),

3) Conformal Field Theory and Matrix
Models, CFT-MM (July 2 - 14).

The
focus of the meeting is:

(a)
interaction among mathematicians, and between mathematicians and
physicists,

(b)
understanding the perspectives in these highly interdiscilplinary
directions,

(c)
accelerating the progress and finding new lines of development and
cooperation.

**Topics**

AHA, LP. The
main topics will be:

(a)
various aspects of the double affine Hecke algebras,

(b)
affine Hecke algebras, applications in algebra and analysis,

(c)
the geometric Langlands program, the latest developments,

(d)
the theory in finite characteristic, the p-adic Langlands program.

CFT-MM. The
major lines will be:

(a)
the theory of random matrix models and relations to conformal field
theory,

(b)
2D quantum gravity and the string theory (branes, Calabi-Yau manifolds),

(c)
the boundary and perturbed conformal field theories, AdS/CFT
correspondence,

(d)
mathematical aspects of integrable models and statistical mechanics.

**Main
directions of the meeting**

There
will be expository lectures and the advanced ones based on
the latest works. The coverage is not comprehensive, but the organizers
tried to give a systematic representation of quite a few topics.

The
subjects of the lectures are entirely up to the speakers and
will be determined right before the meeting. The overview reflects the
expectations of the organizers. There will be also seminars
to be decided on the spot.

The
speakers of the physics half will be asked to take into consideration
that quite a few participants will be mathematicians.

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