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### Sino-Russian algebra seminar

Dr. Egor Voronetsky and Dr. Raimund Preusser from St. Petersburg University, Russia, were invited by Associate Professor Zhang Zuhong of the School of Mathematics and Statistics of Beijing Institute of Technology to give a series of three lectures on a series of recent advances in unitary groups and algebraic K theory. Egor Voronetsky systematically reports his latest research findings: A new algebraic construction of the Odd Unitary Group covering all the classical canonical groups and Bak's Even Unitary Group and Petrov's Odd Unitary Group At the same time he considered K theory on this structure. Raimund Preusser will introduce the Sandwich classification on the classical-like group. Welcome to join us!

Lecture 1

SpeakerEgor Voronetsky, （PhD student of Nikolai Vavilov in Saint Petersburg University, Russia）

TitleNew Construction of Odd Unitary Group I

Abstract:

Unitary groups are a generalization of the classical groups GL(n, K), O(n, K), and Sp(n, K). They may be defined in terms of an involution ring with a form parameter. More recent and more general constructions of so-called odd unitary groups are due to V. Petrov and myself. Ultimately, the construction via new algebraic objects called odd form rings allow to describe, for example, all fppf twisted forms of the classical group schemes. In the talk I am going to give the details of these constructions.

Time 2021,10.13 18:30—20:30 Beijing Time

To Join Zoom Meeting:

https://zoom.us/j/83289582840?pwd=SFZkSDlrM0VyUXQxS1F6ZDJCSUZ0dz09

Meeting ID：832 8958 2840

Lecture 2

Speaker Raimund Preusser Postdoc at the St. Petersburg State University

TitleSandwich classification in classical-like groups revisited

Abstract

It follows from the Sandwich Classification Theorem for general linear groups that if $\sigma\in GL_n(R)$, where $R$ is a commutative ring and $n\geq 3$, then any elementary transvection $t_{kl}(\sigma_{ij})~(i\neq j,k\neq l)$ can be expressed as a product of $E_n(R)$-conjugates of $\sigma$ and $\sigma^{-1}$. This talk will be concerned with finding the optimal bound for the number of factors needed for such an expression. Analogues of this problem in other classical-like groups will also be discussed.

Time2021.10.20  18：30-19：30 Beijing Time

To Join Zoom Meeting:

https://us02web.zoom.us/j/81377121141?pwd=djJpUDdJeUZQd1VOdmk2b21wbVdXQT09

Meeting ID：813 7712 1141

Speaker：Egor Voronetsky, （PhD student of Nikolai Vavilov in Saint Petersburg University, Russia）

Title：New Construction of Odd Unitary Group II

Abstract:

Unitary groups are a generalization of the classical groups GL(n, K), O(n, K), and Sp(n, K). They may be defined in terms of an involution ring with a form parameter. More recent and more general constructions of so-called odd unitary groups are due to V. Petrov and myself. Ultimately, the construction via new algebraic objects called odd form rings allow to describe, for example, all fppf twisted forms of the classical group schemes. In the talk I am going to give the details of these constructions.

Lecture 3

SpeakerEgor Voronetsky, （PhD student of Nikolai Vavilov in Saint Petersburg University, Russia）

TitleNew Construction of Odd Unitary Group III

Abstract:

Unitary groups are a generalization of the classical groups GL(n, K), O(n, K), and Sp(n, K). They may be defined in terms of an involution ring with a form parameter. More recent and more general constructions of so-called odd unitary groups are due to V. Petrov and myself. Ultimately, the construction via new algebraic objects called odd form rings allow to describe, for example, all fppf twisted forms of the classical group schemes. In the talk I am going to give the details of these constructions.

Time: 2021.10.27 18：30-19：30 Beijing Time

To Join Zoom Meeting:

https://us02web.zoom.us/j/81810103842?pwd=WldZdVdCMlIrM2o5aHAxd01IRmRrZz09

Meeting ID818 1010 3842