Nov. 2022

Intervenant : | Mikhail Kapranov |

Institution : | KAVLI IPMU Tokyo |

Heure : | 14h00 - 15h00 |

Lieu : | Salle 3L15 |

A functor $F=F_1$ between triangulated categories often has several iterated adjoints

$F_2=F_1^*, F_3=f_2^*, ..., F_n = F_{n-1}^*$. In this case one can form two complexes of functors

by successively applying the counits $F_i F_{i+1}\to Id$ or units $Id\to F_{i+1}F_i$. These complexes can

be seen as categorical lifting of:

-- Fibonacci numbers;

-- Chebyshev polynomials of the second kind;

-- Euler continuants, i.e., universal numerators or denominators of finite continued fractions with

entries being independent variables.

Requiring the totalizations of such complexes to be equivalences of categories or quasi-isomorphic to zero leads

to a generalization of the concept of a spherical functor. Such generalized spherical functors describe periodic

semi-orthogonal decompositions of enhanced triangulated categories. Joint work in progress

with T. Dyckerhoff and V. Schechtman.