Abstract: Determinants of elliptic operators were introduced by Ray and
Singer in 1974. The notion was partially motivated by trying to
understand an analytical counterpart of the combinatorial torsion,
and it was also motivated by physics. Probably, Schwinger was the first
person who used determinants, without calling them determinants.
The regularization procedure that is used for defining determinants
leads to anomalies. For example, the determinant of the product
does not necessarily equal the product of determinants.
In the talk, I will discuss the general notion of the determinant,
different regularization procedures, and the anomalies.
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