21 citations · 31 across the 11 of their papers we have counts for
5 papers · 1 filter
On the complexity of analyticity in semi-definite optimization
Saugata Basu, Ali Mohammad-Nezhad
It is well-known that the central path of semi-definite optimization, unlike linear optimization, has no analytic extension to in the absence of the strict complementarity c…
Random fields and the enumerative geometry of lines on real and complex hypersurfaces
Saugata Basu, Antonio Lerario, Erik Lundberg +1
We derive a formula expressing the average number of real lines on a random hypersurface of degree in in terms of the expected modulus of the…
Bounds on the individual Betti numbers of complex varieties, stability and algorithms
Saugata Basu, Cordian Riener
We prove graded bounds on the individual Betti numbers of affine and projective complex varieties. In particular, we give for each , explicit bounds on the -th Betti numb…
Algorithms in Real Algebraic Geometry: A Survey
Saugata Basu
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals…
Toric cubes are closed balls
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
We prove that toric cubes, which are images of under monomial maps, are the closures of graphs of monotone maps, and in particular semi-algebraically homeomorphic to clos…