Scientific seminar “On the inversions of the Melrose invariant”

Scientific seminar “On the inversions of the Melrose invariant”

The event passed
12 Oct 2021
Location
Online
About the event

Speaker

Zhuikov Konstantin N., RUDN, Moscow

Topic: On the inversions of the Melrose invariant.

The concept of the ????η-invariant was introduced in the famous work of Atiyah, Pathodi, and Singer for elliptic self-adjoint pseudodifferential operators (PDOs) on a closed manifold. It is by definition a spectral invariant, participates in many index formulas, and has many applications. An important generalization of the η-invariant was given by Melrose. Namely, it was proposed to consider the families ???? (????) of PDOs with a real parameter ????, and the η-invariant of the family was defined as a special regularization of the rotation number.

We will give the definition of the η-invariant for families of the form of linear combinations of PDOs with a parameter and periodic coefficients on a smooth closed manifold, and establish the basic properties of the ????-invariant. Then we will give the definition of the η-invariant of the PDO on the line with coefficients periodic at infinity.

The report will describe the results obtained in joint work with A.Yu. Savin.

Online

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