## Will Troiani (LIPN and Melbourne (Australia)), Computation in logic as the splitting of idempotents in algebraic geometry; two models of multiplicative linear logic

### Schedule

- March 30, 2023, 15:15 - 16:15

### Abstract

A hypersurface f = 0 in complex affine space is singular if and only
if there exists a non-contractible matrix factorization (to be defined in the
talk). Matrix factorisations are organised into a bicategory where composition
is defined via a two-step process, first an infinite model of the composite is
described, and then a terminating procedure is followed to extract a *finite*
presentation. Is this terminating procedure a semantics of cut-elimination?
By considering simple cases, Daniel Murfet and myself have uncovered two
models of multiplicative linear logic, one in the space of coordinate rings
where cut-elimination corresponds to the celebrated Buchberger Algorithm, and
the other in the space of Quantum Error Correction Codes, where
cut-elimination corresponds to quantum error correction. The general picture
has led Murfet and myself to postulate that the splitting of idempotents has
*fundamental relevance* to the theory of computation. This talk defends this
proposition.