Türkiye'deki Matematiksel Etkinlikler
23 Ocak 2014, 16:00 ![]() Mimar Sinan Güzel Sanatlar Üniversitesi Matematik Bölümü SeminerleriZariski Topology of an Abstract Groups Dikran Dikranjan
This topology was implicitly introduced by A. Markov in 1944
and later explicitly introduced by R. Bryant, under the name
verbal topology. In the last ten years a wealth of new papers
appeared, where this topology is given the name Zariski topology
for its striking similarity with the Zariski topology studied in
algebraic geometry. Actually, one of the main direction of
research on this topic (pursued by Baumslag, Myasnikov and
Remeslennikov) has as principal objective the development of a
counterpart of Algebraic Geometry in abstract groups.
This cycle of lectures will be dedicated to another direction,
namely the one undertaken by Markov himself towards the solution
of one of his problems: the existence of non-discrete Hausdroff
group topologies on the infinite groups. To this end one can make
use of another topology, introduced again implicitly by Markov.
This topology was explicitly introduced by Dikranjan and
Shakhmatov under the name Markov topology. In these terms,
Markov's problem can be formulated as follows: is the Markov
topology of an infinite group always non-discrete. It is easy to
see that the Markov topology is finer than the Zariski topology.
Markov showed that they coincide for countable groups and asked if
this is always the case. The first infinite group with discrete
Markov topology was built by Shelah in 1980 under the assumption
of the Continuum Hypothesis. Shortly afterwards Ol'shankij gave an
example of a countable group with discrete Zariski topology.
Finally, some attention will be dedicated to a recently relevant
progress in this line obtained by Ol'shankij and his school, in
building groups with preassigned properties of the Zariski
topology.
Cebirsel Geometri İngilizce Mimar Sinan University, Department of Mathematics admin 20.03.2020 |
Akademik biriminizin ya da çalışma grubunuzun ülkemizde gerçekleşen etkinliklerini, ilan etmek istediğiniz burs, ödül, akademik iş imkanlarını veya konuk ettiğiniz matematikçileri basit bir veri girişi ile kolayca turkmath.org sitesinde ücretsiz duyurabilirsiniz. Sisteme giriş yapmak için gerekli bilgileri almak ya da görüş ve önerilerinizi bildirmek için iletişime geçmekten çekinmeyiniz. Katkı verenler listesi için tıklayınız.
Özkan Değer ozkandeger@gmail.com
31. Journees Arithmetiques Konferansı Organizasyon Komitesi
Web sitesinin masraflarının karşılanması ve hizmetine devam edebilmesi için siz de bağış yapmak, sponsor olmak veya reklam vermek için lütfen iletişime geçiniz.