Month: May 2017

Leavitt Path Algebras

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Tuğba Güroğlu, Celal Bayar University.
Date: 24th and 31st of May, and 7th of June, 2017, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: Let E denote a directed graph and K be a field. The Leavitt path algebra of E with coefficient in K, denoted by L_K(E), were introduced by G. Abrams and G. Aranda Pino in 2005 as a generalization of Leavitt algebras and then extended to arbitrary graphs in 2008. In this talk, we talk about Leavitt path algebras and determine Leavitt path algebras of some graphs. Then using graph-theoretic properties, we mention the some ring-theoretic properties of Leavitt path algebras.
References
[1] Abrams, G. and Aranda Pino, G., The Leavitt path algebra of a graph, J. Algebra, 293(2), 319-334, 2005.
[2] Abrams, G. and Aranda Pino, G., The Leavitt path algebras of arbitrary graphs, Houston J. Math., 34(2), 423-442, 2008.

Nonstandard Analysis and Primality Test

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Haydar Göral, Koç University.
Date: 17th of May, 2017, Wednesday, Time: 11:00 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this talk, we first define the height function and the Mahler measure from Diophantine geometry on the field of algebraic numbers. The height function measures the arithmetic complexity of an algebraic number and it has some nice properties. Then, we explain nonstandard analysis which we apply to find certain height bounds. Nonstandard analysis was originated in the 1960’s by the work of A. Robinson, which arose as a rigorous and exhaustive way of studying infinitesimal calculus. Combining the properties of the height function with ideas from model theory and nonstandard analysis, we explain how to obtain some uniform height bounds in the polynomial ring over the field of algebraic numbers. This enables us to test the primality of an ideal.