Finiteness in SU(3)3 models

Finiteness of small factor analysis models

Abstract: We consider small factor analysis models with one or two factors. Fixing the number of factors, we prove a finiteness result about the covariance matrix parameter space when the size of the covariance matrix increases. According to this result, there exists a distinguished matrix size starting at which one can determine whether a given covariance matrix belongs to the parameter space ...

Finiteness and anomalies in ( 4 , 0 ) supersymmetric sigma models

Power-counting arguments based on extended superfields have been used to argue that two-dimensional supersymmetric sigma models with (4,0) supersym-metry are finite. This result is confirmed up to three loop order in perturbation theory by an explicit calculation using (1,0) superfields. In particular, it is shown that the finite counterterms which must be introduced into the theory in order to...

Finiteness and Dual Variables for Lorentzian Spin Foam Models

A finiteness theorem for Markov bases of hierarchical models

We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist of elements of Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We also compute these Markov and Graver co...

Geometric Diffeomorphism Finiteness in Low Dimensions and Homotopy Group Finiteness

Our main result asserts that for any given numbers C and D the class of simply connected closed smooth manifolds of dimension m < 7 which admit a Riemannian metric with sectional curvature bounded in absolute value by |K| ≤ C and diameter uniformly bounded from above by D contains only finitely many diffeomorphism types. Thus in these dimensions the lower positive bound on volume in Cheeger’s F...