Posted in

Speaker:

Mikhail Kapranov
Affiliation:

Kavli IPMU
Date:

Tue, 08/03/2022 - 11:00 - 12:00
Parent event:

Algebra, Geometry and Physics: a mathematical mosaic Various contractions of the composition of a string of iterated adjoint functors form

a diagram whose shape is known in computer science as the "Fibonacci cube".

Such diagrams can be seen as categorical lifts of Euler continuants, the universal numerators

and denominators of finite continued fractions whose entries are independent variables.

Vanishing (exactness) of the totalization of the (N-1)st Fibonacci cube defines the concept

of an N-spherical functor, with usual spherical functors appearing

for N=4. They are related to N-periodic semi-orthogonal decompositions in triangulated categories.

Joint work in progress with T. Dyckerhoff and V. Schechtman.

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