[Turkmath:5610] MSGSU Mathematics Seminars (11 May 2022, 15:00)

[İpek Tuvay]

Dear all,
You can see the information for this week's seminar in our department
below.
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*Time: *Wednesday, 11 May 2022, 15:00

*Speaker:* Rizos Sklinos (Chinese Academy of Sciences)

*Title: *Elementary theories of hyperbolic groups

*Abstract:* The discovery of non euclidean geometry in the early nineteenth
century had shaken the beliefs and conjectures of more than two thousand
years and changed the picture we had for mathematics, physics and even
philosophy. Lobachevsky and Bolyai independently around 1830 discovered
hyperbolic geometry. A notable distinguish feature of hyperbolic geometry
is its negative curvature in a way that the sum of angles of a triangle is
less than π. Gromov much later in 1987 introduced hyperbolic groups which
are groups acting “nicely” on hyperbolic spaces, or equivalently finitely
generated groups whose Cayley graphs are “negatively curved”. Main examples
are free groups and almost all surface groups. The fascinating subject of
hyperbolic groups touches on many mathematical disciplines such as
geometric group theory, low dimensional topology and combinatorial group
theory. It is connected to model theory through a question of Tarski.

Tarski asked around 1946 whether non abelian free groups have the same
first order theory. This question proved extremely hard to answer and only
after more than fifty years in 2001 Sela and Kharlampovich-Myasnikov
answered it positively. Both works are voluminous and have not been fully
absorbed yet. The great novelty of the methods and the depth of the needed
results have made it hard to streamline any of the proofs. Despite the
difficulties there is some considerable progress in the understanding of
the first-order theory of “the free group” and consequently first-order
theories of hyperbolic groups from the scopes of basic model theory,
Shelah’s classification theory and geometric stability. In this talk I will
survey what is known about these theories and what are the main open
questions.

*Link: *
https://teams.microsoft.com/l/meetup-join/19%3a1eaca84648fa440e94bc4d7382675247%40thread.tacv2/1651904725164?context=%7b%22Tid%22%3a%22ddd5afa6-82d7-4e0e-b457-3000f5a23749%22%2c%22Oid%22%3a%22b11f2b28-e233-4b68-b781-77d2029695cb%22%7d
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*For future talks please visit: *
https://researchseminars.org/seminar/MSGSUMath

Best,

İpek Tuvay
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