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Basu
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#	Item
311	REFINED BOUNDS ON THE NUMBER OF CONNECTED COMPONENTS OF SIGN CONDITIONS ON A VARIETY SAL BARONE AND SAUGATA BASU Abstract. Let R be a real closed field, P, Q ⊂ R[X1 , . . . , Xk ] finite subsets of polynomials, with th Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-11-06 10:09:22 Algebraic geometry Commutative algebra Field extension Algebraic variety Algebraically closed field Zariski topology Betti number Puiseux series Algebraic closure Abstract algebra Algebra Field theory
312	A COMPLEXITY THEORY OF CONSTRUCTIBLE FUNCTIONS AND SHEAVES SAUGATA BASU Abstract. In this paper we introduce analogues of the discrete complexity classes VP and VNP of sequences of functions in the Blum-Shub-Smale model. Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2013-10-06 09:48:25 Algebraic topology Structural complexity theory Field theory Time hierarchy theorem Constructible sheaf Algebraic geometry Sheaf Constructible function Constructible universe Abstract algebra Mathematics Algebra
313	Divide and conquer roadmap for algebraic sets Saugata Basu Marie-Françoise roy Department of Mathematics Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2013-05-22 00:58:23 Algebraic geometry Algebraic variety Field extension Algebraic curve Field Algebraic extension Algebraic independence Abstract algebra Algebra Field theory
314	TRIANGULATIONS OF MONOTONE FAMILIES I: TWO-DIMENSIONAL FAMILIES arXiv:1402.0460v1 [math.AG] 3 Feb[removed]SAUGATA BASU, ANDREI GABRIELOV, AND NICOLAI VOROBJOV Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2014-02-04 22:57:25 Order theory Algebraic topology Convex analysis Topological spaces CW complex Homotopy theory Convex function Monotonic function Continuous function Mathematical analysis Mathematics Topology
315	ON THE BETTI NUMBERS OF SIGN CONDITIONS SAUGATA BASU, RICHARD POLLACK, AND MARIE-FRANC ¸ OISE ROY Abstract. Let R be a real closed field and let Q and P be finite subsets of R[XV1 , . . . , Xk ] such that the set P has Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:45 Orbifold Algebraic geometry Algebraic variety Μ operator
316	COMPUTING THE BETTI NUMBERS OF SEMI-ALGEBRAIC SETS DEFINED BY PARTLY QUADRATIC SYSTEMS OF POLYNOMIALS SAUGATA BASU, DMITRII V. PASECHNIK, AND MARIE-FRANC ¸ OISE ROY Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:26 Algebraic geometry Betti number Polynomial Semialgebraic set Ordinal number Probability theory Transcendental number Probability space Mathematics Abstract algebra Real algebraic geometry
317	Contemporary Mathematics Algorithmic Semi-algebraic Geometry and Topology – Recent Progress and Open Problems Saugata Basu Abstract. We give a survey of algorithms for computing topological invariants of semi-algebrai Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:06 Real algebraic geometry Equations Algebraic geometry Semialgebraic set Algebraic variety Betti number Sheaf Algebraic topology Topology Abstract algebra Mathematics Algebra
318	POLYNOMIAL HIERARCHY, BETTI NUMBERS AND A REAL ANALOGUE OF TODA’S THEOREM SAUGATA BASU AND THIERRY ZELL 1. Brief Description Toda proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the cl Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:35:58 Field theory Algebraic geometry Polynomial Field extension Field Computational complexity theory Betti number Finite field Number Abstract algebra Mathematics Algebra
319	Computing the First Few Betti Numbers of Semi-algebraic Sets in Single Exponential Time Saugata Basu 1 Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:07 Group theory Algebraic topology Mathematical structures Algebraic geometry Betti number Spectral sequence Singular homology Field Structure Algebra Abstract algebra Mathematics
320	A BABY STEP-GIANT STEP ROADMAP ALGORITHM FOR GENERAL ALGEBRAIC SETS ´ SCHOST S. BASU, M-F. ROY, M. SAFEY EL DIN, AND E. Abstract. Let R be a real closed field and D ⊂ R an ordered domain. We give an algorithm that tak Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2012-01-30 23:55:12 Field theory Algebraic geometry Scheme theory Commutative algebra Algebraic curve Algebraic variety Field extension Real algebraic geometry Semialgebraic set Abstract algebra Algebra General topology

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