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On October 21 at 7 pm Novosibirsk time (6 pm Omsk time, 3 pm Moscow time) the seminar #225 of  will take place. Arkadiy Tsurkov (Federal University of Rio Grande do Norte (UFRN) Natal, Brazil) will present his talk 鈥淎utomorphic equivalence in the classical varieties of linear algebras鈥�.

We consider some variety of universal algebras 螛 and the category 螛₀. Objects of this category are finitely generated free algebras of the variety 螛, morphisms of this category are homomorphisms of these algebras. 

After this we consider algebras H₁, H₂ 鈭� 螛. The automorphisms of the category 螛₀ are very important in the study of the question when these algebras have same algebraic geometry. In this talk we will consider as 螛 the classical varieties of linear algebras: 
1. Variety of all linear algebras, 
2. Variety of all commutative algebras, 
3. Variety of all power associative algebras, 
4. Variety of all alternative algebras, 
5. Variety of all associative algebras, 
6. Variety of all Jordan algebras, 
7. Arbitrary subvariety of the variety of all anticommutative algebras over the arbitrary field k of characteristic 0. 

The structure of the group of the all automorphisms of the category 螛₀ will be studied in all these cases. Also examples of algebras which are not geometric equivalent (the families of closed congruences are not coincides) but have the same algebraic geometry (exist a monotone bijection between these families) will be given in all these cases.

To join the seminar, connect to the Zoom meeting a few minutes prior to the beginning at  (or manually by entering the meeting ID 812 2079 3393 in the Zoom app).

Please pay attention to the following rules for conducting an Internet seminar:

• Please log in under your name and surname
• During the report, please turn off the microphone
• For the convenience of the presenter, it is recommended to submit your questions in the chat in advance