[Turkmath:8777] Fwd: Istanbul Number Theory Meetings VII: February 16th (This Saturday!)

[KAZIM Büyükboduk]

Dear Colleagues,

This is a reminder for the 7th Istanbul Number Theory Meetings, which will
take place on February 16th (tomorrow!) at IMBM (Boğaziçi Ü.). Please find
the poster for the meeting attached to this message.

We will have a full-day long talks by four speakers:
Hakan Ayral (YTÜ), Merve Durmuş (Yeditepe Ü.), Muhammed Uludağ (Galatasaray
Ü.) and Ayberk Zeytin (Galatasaray Ü.).
We thank our speakers for agreeing to talk at the meeting and IMBM for
hosting us.

Below you may find the information regarding the schedule, location of
the talks
and their titles and abstracts. It would be a great pleasure to meet many
of the interested colleagues tomorrow!

Best Regards,

Kazim Buyukboduk


Istanbul Number Theory Meetings - 7

Speakers: Hakan Ayral (YTÜ), Merve Durmuş (Yeditepe Ü.), Muhammed Uludağ
(Galatasaray Ü.), Ayberk Zeytin (Galatasaray Ü.).

Date and Schedule: February 16th, 2013 (Saturday)

10.30 - 10.50 Merve Durmuş
11.15 - 12.15 Muhammed Uludağ
13.45 - 14.45 Ayberk Zeytin
15.00 - 16.00 Hakan Ayral.

Location: IMBM (Boğaziçi Üniversitesi Kampüsü)

Titles and Abstracts:

(Merve Durmuş)

Title: Subgroups of the infinite dihedral group and graphs

Abstract: In this talk we will show how one constructs a unique graph to
every subgroup of the infinite dihedral group, which may be thought of as
the toy case of the modular group to be described in the next talk.

-------

(Muhammed Uludağ)

Title: Binary quadratic forms as dessins

Abstract: Since it encodes the Euclidean algorithm, the modular group is a
very fundamental object in mathematics. It acts by conjugation on an
infinite bipartite planar tree, which we call the Farey tree. The orbits
are graphs with one cycle which we call çarks. We show that each çark
represents naturally the class of an indefinite binary quadratic form, and
every such class can be represented this way. Given a çark, if we specify
an edge together with an orientation of its cycle, then this determines an
indefinite binary quadratic form belonging to the class represented by the
çark, and every such form can be represented this way. This work is funded
by TUBITAK110T690 and GSU12.504.001 grants.

(Joint work with M. Durmuş and A. Zeytin)

--------

(Ayberk Zeytin)

Title: Thompson's Groups and the Modular Group

Abstract: In this talk after defining Thompson's groups F and T via
universal Teichmuller theory, we will describe a new point of view on the
Thompson's groups (F and T) using the modular group. Then we will discuss
the category of carks, a category whose objects are indefinite binary
quadratic forms and morphisms are flips.

(this is joint work with M.Uludağ.)

------

(Hakan Ayral)

Title : Automated Theorem Proving Systems

Abstract: Automated theorem proving is formal proving of mathematical
theorems by computer programs with little or no user intervention.
A formal proof is a proof in which every single logical inference has been
checked back to the fundamental axioms of mathematics; first serious
attempt to formalize mathematics in terms of symbolic logical inferences
was by Russel and Whitehead in their Principia Mathematica, written with a
purpose to derive some of the mathematical expressions of number theory.
In a consistent axiomatic system, the validity of a theorem can be
expressed as the satisfiability of a logic formula which reduces to a set
of propositional satisfiability problems. The problem of deciding the
satisfiability of a formula (SAT-problem) varies from trivial to
impossible; for the case of propositional logic, the problem is decidable
but Co-NP-complete.
First-order theorem proving is one of the most mature subfields of
automated theorem proving as first order logic is expressive enough to
allow the specification of arbitrary problems, and a number of sound and
complete calculi have been developed, enabling fully automated systems.
As part of the talk we will present some of the widely known automated
theorem proving softwares and browse through formalizations of some trivial
facts (2+2=4, primality of 3) and some non-trivial proofs.
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