algebra

Counting from Left to Right

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Noyan Er, Dokuz Eylül University.
Date: 27th of February, 2019, Wednesday. Time: 09:30-10:30
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: This will the the beginning of a series of sporadic talks related to some classical methods bridging Ring Theory and Representation Theory, which will feature some well known results due to Eisenbud and Griffith.

Topological Equivalences of E∞ DGAs

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Haldun Özgür Bayındır, The University of Haifa.
Date: 6th of February, 2019, Thursday. Time: 11:00 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In algebraic topology we often encounter chain complexes with extra multiplicative structure. For example, the cochain complex of a topological space has what is called the E∞-algebra structure which comes from the cup product. In this talk I present an idea for studying such chain complexes, E∞ differential graded algebras (E∞ DGAs), using stable homotopy theory. Namely, I discuss new equivalences between E∞ DGAS that are defined using commutative ring spectra.We say E∞ DGAs are E∞ topologically equivalent when the corresponding commutative ring spectra are equivalent. Quasi-isomorphic E∞ DGAs are E∞ topologically equivalent. However, the examples I am going to present show that the opposite is not true; there are E∞ DGAs that are E∞ topologically equivalent but not quasi-isomorphic. This says that between E∞ DGAs, we have more equivalences than just the quasi-isomorphisms. I also discuss interaction of E∞ topological equivalences with the Dyer-Lashof operations and cases where E∞ topological equivalences and quasi-isomorphisms agree.

Annihilators of Cartier Quotients

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Mehmet Yeşil, The University of Sheffield.
Date: 12th of December, 2018, Thursday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: Let R be a commutative Noetherian ring of prime characteristic p, M be an R-module and e be a positive integer. Let f:R→R be the Frobenius homomorphism given by f(r)=r^p for all r in R whose e-th iteration is denoted by f^{e}. An e-th Cartier map on M is an additive map C:M→M such that rC(m)=C(r^{p^{e}}m) for all r in R and m in M. An R-module is called a Cartier module if it is equipped with a Cartier map. In the case that the Frobenius homomorphism is finite and M is a finitely generated R-module equipped with a surjective Cartier map, it is proved by M. Blickle and G. Böckle in [1] that the set of annihilators of Cartier quotients of M is a finite set of radical ideals consisting of intersections of the finitely many primes in it. In these talks, I will consider the case that R is a finite dimensional polynomial ring over a field of prime characteristic p, and I take a computational view of this finiteness result and drop the finiteness condition on the Frobenius homomorphism to give an alternative proof to the result.
References:
[1] M. Blickle and G. Böckle. Cartier modules: finiteness results.

Representation Theory of Artin Algebras

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Zübeyir Türkoğlu, Dokuz Eylül University.
Date: 5th of December, 2018, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this seminar, we will continue to talk about the transpose Tr. In general, Tr does not induce a functor from the mod(Λ) to the mod(Λ^{op}). But we do get a duality by replacing mod(Λ) with an appropriate category.

Representation Theory of Artin Algebras

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Zübeyir Türkoğlu, Dokuz Eylül University.
Date: 28th of November, 2018, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this seminar, we will talk about the transpose Tr. In general, Tr does not induce a functor from the mod(Λ) to the mod(Λ^{op}). But we do get a duality by replacing mod(Λ) with an appropriate category.

Representation Theory of Artin Algebras

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Meltem GÜLLÜSAÇ, Dokuz Eylül University.
Date: 14th of November, 2018, Wednesday, Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this seminar,  we will talk about a duality between finitely generated  Λ-modules and finitely generated   Λ^{op}-modules over an artin R-algebra Λ and we will prove the existence of enough injectives for finitely generated Λ-modules.