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Geometric Methods in Rep Theory Seminar – Mikhail Kapranov (IPMU)

September 8, 2023 @ 4:00 pm - 5:00 pm

N-spherical functors and categorification of Euler’s continuants

Abstract. Euler’s continuants are universal polynomials expressing the numerator and denominator of a finite continued fraction in terms of its entries. Remarkably, they make an appearance in the very foundations of category theory: in the formalism of adjoint functors. More precisely, they upgrade to natural complexes of functors built out of a given functor and its iterated adjoints. Requiring exactness of some of these complexes leads to the concept of an N-spherical functor which specializes to that of an ordinary spherical functor for N=4. Such functors describe N-periodic semi-orthogonal decompositions of (enhanced) triangulated categories. Like ordinary spherical functors, they give rise to interesting self-equivalences. Conceptually, they can be seen as categorification of certain irregular differential equations (polynomial Schroedinger) in the complex plane. Joint work with T. Dyckerhoff, V. Schechtman.

Geometric Methods in Representation Theory Seminar Website


September 8, 2023
4:00 pm - 5:00 pm
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