- REAL SCHUBERT CALCULUS: POLYNOMIAL SYSTEMS AND A CONJECTURE OF SHAPIRO AND SHAPIRO
- IDENTITIES OF STRUCTURE CONSTANTS FOR SCHUBERT POLYNOMIALS AND ORDERS ON S n
- A PIERI-TYPE FORMULA FOR THE K-THEORY OF A FLAG CRISTIAN LENART AND FRANK SOTTILE
- Manuscript, October 7, 2009 ArXiV.org/0907.1847 FRONTIERS OF REALITY IN SCHUBERT CALCULUS
- COMBINATORIAL HOPF ALGEBRAS AND GENERALIZED DEHNSOMMERVILLE RELATIONS
- (FORMULAS OF BRION, LAWRENCE, AND VARCHENKO ON RATIONAL GENERATING FUNCTIONS FOR CONES)
- Algebraic Geometry in Algebraic Statistics and Geometric Modeling
- Mathematical Research Letters, to appear, March 2005 QUIVER COEFFICIENTS ARE SCHUBERT
- INTERSECTION THEORY ON SPHERICAL VARIETIES R. MacPherson
- ELEMENTARY TRANSVERSALITY IN THE SCHUBERT CALCULUS IN ANY CHARACTERISTIC
- 2 October 2007 arXiv:0706.3745 BOUNDS ON THE NUMBER OF REAL SOLUTIONS TO
- Topics in Algebraic Geometry and Geometric Modeling, Contemp. Math., 334, 2003. Toric ideals, real toric varieties,
- Extended abstract, submitted to MEGA 05 EXPERIMENTATION AND CONJECTURES IN THE REAL
- Draft of February 15, 2011 ORIENTABILITY OF REAL TORIC VARIETIES
- US Participation in workshop: Enumeration and bounds in real algebraic geometry
- Version of 1 June 2005. math.CO/0501359 IRRATIONAL PROOFS FOR THREE THEOREMS OF STANLEY
- Proc. DIMACS workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, to appear.
- GROTHENDIECK POLYNOMIALS VIA PERMUTATION PATTERNS AND CHAINS IN THE BRUHAT ORDER
- STRUCTURE OF THE MALVENUTO-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS
- 2 January 2008 arXiv:0710.4607 GALOIS GROUPS OF SCHUBERT PROBLEMS
- 21 July 2008 math.AG/0801.2611 J. Alg. Geom., to appear GENERAL ISOTROPIC FLAGS ARE GENERAL
- Contemporary Mathematics Experimentation at the Frontiers of Reality
- 18 September 2007 ArXiV:0706.3745 GALE DUALITY FOR COMPLETE INTERSECTIONS
- Tableau Switching: Algorithms and Applications Georgia Benkart
- 2 February 2008 arXiv:0801.2554 BETTI NUMBER BOUNDS FOR FEWNOMIAL HYPERSURFACES
- Proposal for IMA Participating Institutions Graduate Student Summer Program
- STRUCTURE OF THE LODAYRONCO HOPF ALGEBRA OF TREES
- 18 September 2007 ArXiV:0706.3745 GALE DUALITY FOR COMPLETE INTERSECTIONS
- Jeux de tableaux Tom Roby 1 , Frank Sottile ?2 , Je rey Stroomer 3 , and Julian West ??4
- 27 February 2006 THE HORN RECURSION FOR SCHUR P AND Q FUNCTIONS
- Applicable Algebraic Geometry: Real Solutions, Applications, and Combinatorics
- arXiv:math.AG/0706.2116 4 February 2009 LINEAR PRECISION FOR PARAMETRIC PATCHES
- RAMAN SANYAL, FRANK SOTTILE, AND BERND STURMFELS Abstract. An orbitope is the convex hull of an orbit of a compact group acting linearly
- December 2008 PolicyPerspective
- PROPOSAL: SIAM ACTIVITY GROUP ON ALGEBRAIC GEOMETRY We propose to create a SIAM Activity Group on the topic of Algebraic Geometry. While
- Bounds for real solutions to polynomial equations
- Mss. ArXiV.org/1106.0096 THE PHASE LIMIT SET OF A VARIETY
- 4 October 2010 THE SECANT CONJECTURE IN THE REAL SCHUBERT CALCULUS
- June 25, 2011 DENSE FEWNOMIALS
- Toric degenerations of Bezier patches Luis David Garcia-Puente
- Mss., 22 January 2010, ArXiv.org/1001.4125 SOLVING SCHUBERT PROBLEMS WITH
- Proc AMS, to appear. 3 May 2008. A LITTLEWOOD-RICHARDSON RULE FOR GRASSMANNIAN
- (FORMULAS OF BRION, LAWRENCE, AND VARCHENKO ON RATIONAL GENERATING FUNCTIONS FOR CONES)
- POLYNOMIAL SYSTEMS WITH FEW REAL ZEROES BENO^IT BERTRAND, FREDERIC BIHAN, AND FRANK SOTTILE
- Gale duality for complete intersections Frank Sottile
- 27 February 2006 THE HORN RECURSION FOR SCHUR P-AND Q-FUNCTIONS
- Emissary, (MSRI Newsletter) Fall 2004. TROPICAL INTERPOLATION
- Contemporary Schubert Calculus and Schubert Geometry Frank Sottile
- alphaCertified Jonathan D. Hauenstein
- Discrete and Applicable Algebraic Geometry Frank Sottile
- Applicable Algebraic Geometry IMA Summer Program 2007
- GROTHENDIECK POLYNOMIALS VIA PERMUTATION PATTERNS AND CHAINS IN THE BRUHAT ORDER
- 11 May 2005. Advances in Mathematics, to appear. LOWER BOUNDS FOR REAL SOLUTIONS TO SPARSE POLYNOMIAL
- COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
- FEWNOMIAL BOUNDS FOR COMPLETELY MIXED POLYNOMIAL FREDERIC BIHAN AND FRANK SOTTILE
- Manuscript of 20 December 2007, revised 18 March 2008 CONVEX HULLS OF ORBITS AND ORIENTATIONS OF A MOVING
- REAL HESSIAN CURVES ADRIANA ORTIZ-RODRIGUEZ AND FRANK SOTTILE
- Manuscript math.AG/0507377 EXPERIMENTATION AND CONJECTURES IN THE REAL
- AN INTRODUCTION TO MAPLE CHRISTOPHER J HILLAR
- ENUMERATIVE GEOMETRY FOR THE REAL GRASSMANNIAN OF LINES IN PROJECTIVE SPACE
- math.AG/0701667 To appear in the IMA volume on Algorithms in Algebraic Geometry, 22 May 2007 ON THE SHARPNESS OF THE FEWNOMIAL BOUND AND THE
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- Manuscript, 31 August 2007. math.AG/0607669 THE RECURSIVE NATURE OF
- Discr. Comput. Geom., to appear. 20 March 2003 COMMON TRANSVERSALS AND TANGENTS TO
- POLYNOMIAL SYSTEMS WITH FEW REAL ZEROES BENO IT BERTRAND, FR
- PIERI-TYPE FORMULAS FOR MAXIMAL ISOTROPIC GRASSMANNIANS VIA TRIPLE INTERSECTIONS
- ArXiv.org/0812.1275 to appear in Proceedings of Mathematical methods of Curves and Surfacecs, 4 March 2009 SOME GEOMETRICAL ASPECTS OF CONTROL POINTS
- STRUCTURE OF THE MALVENUTOREUTENAUER HOPF ALGEBRA OF PERMUTATIONS
- ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY
- Manuscript, 31 August 2007. math.AG/0607669 THE RECURSIVE NATURE OF
- Real Enumerative Geometry and Effective Algebraic Equivalence 2
- APPENDICES FOR SCHUBERT POLYNOMIALS, THE BRUHAT ORDER,
- UNIVERSITY OF TORONTO Department of Mathematics
- Emissary, (MSRI Newsletter) Fall 2004. TROPICAL INTERPOLATION
- Computing Monodromy via Parallel Homotopy Continuation
- Manuscript of 20 December 2007, revised 18 March 2008 CONVEX HULLS OF ORBITS AND ORIENTATIONS OF A MOVING
- 6 September 2004 THE ENVELOPE OF LINES MEETING A FIXED LINE AND
- Gale duality for complete intersections Frank Sottile
- Contemporary Mathematics Rational Curves on Grassmannians
- 30 November 2006. math.AG/0602161 THE EQUIVARIANT CHOW RINGS OF QUOT SCHEMES
- New Hopf Structures on Binary Trees Stefan Forcey,1
- Advances in Geometry, to appear. 20 June 2005. CREMONA CONVEXITY, FRAME CONVEXITY,
- 11 May 2005. Advances in Mathematics, to appear. LOWER BOUNDS FOR REAL SOLUTIONS TO SPARSE POLYNOMIAL
- On the number of line tangents to four triangles in threedimensional Herv e Br onnimann + Olivier Devillers # Sylvain Lazard Frank Sottile
- 30 November 2006. math.AG/0602161 THE EQUIVARIANT CHOW RINGS OF QUOT SCHEMES
- APPENDICES TO EXPLICIT ENUMERATIVE GEOMETRY FOR THE REAL
- math.AG/0701667 To appear in the IMA volume on Algorithms in Algebraic Geometry, 22 May 2007 ON THE SHARPNESS OF THE FEWNOMIAL BOUND AND THE
- Version of 1 June 2005. math.CO/0501359 IRRATIONAL PROOFS FOR THREE THEOREMS OF STANLEY
- Mathematical Sciences Scientific Computing Research Environments (SCREMS)
- STRUCTURE OF THE MALVENUTO-REUTENAUER HOPF ALGEBRA OF PERMUTATIONS
- Some Remarks on Real and Complex Output Feedback
- PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- REAL SCHUBERT CALCULUS: POLYNOMIAL SYSTEMS AND A CONJECTURE OF SHAPIRO AND SHAPIRO
- Report on the MSRI semester on Topological Aspects of Real Algebraic Goemetry, Spring 2004.
- Proceedings of Symposia in Pure Mathematics Enumerative geometry for real varieties
- Shifted Quasi-Symmetric Functions and the Hopf algebra of peak functions ?
- SOME REAL AND UNREAL ENUMERATIVE GEOMETRY FOR FLAG MANIFOLDS
- FRONTIERS OF REALITY IN SCHUBERT CALCULUS FRANK SOTTILE
- STRUCTURE OF THE LODAY-RONCO HOPF ALGEBRA OF TREES
- 19 June 2008 ArXiv.org:0806.3230 LINEAR PRECISION FOR TORIC SURFACE PATCHES
- HOPF ALGEBRAS AND EDGELABELED POSETS NANTEL BERGERON AND FRANK SOTTILE
- May 20, 2004 REAL kFLATS TANGENT TO QUADRICS IN R n
- A SAGBI BASIS FOR THE QUANTUM GRASSMANNIAN FRANK SOTTILE AND BERND STURMFELS
- Manuscript. 18 May 2006 REAL HESSIAN CURVES
- MAXIMALLY INFLECTED REAL RATIONAL CURVES VIATCHESLAV KHARLAMOV AND FRANK SOTTILE
- Draft of June 22, 2010 HOPF STRUCTURES ON THE MULTIPLIHEDRA
- 19 June 2009 ArXiv.org:0806.3230 LINEAR PRECISION FOR TORIC SURFACE PATCHES
- 31 May 2011 ALGORITHM XXX: ALPHACERTIFIED: CERTIFYING SOLUTIONS
- Advances in Geometry, to appear. 20 June 2005. CREMONA CONVEXITY, FRAME CONVEXITY,
- TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- TRANSVERSALS TO LINE SEGMENTS IN R 3 ONNIMANN, H. EVERETT, S. LAZARD, F. SOTTILE, AND S. WHITESIDES
- PIERI'S FORMULA VIA EXPLICIT RATIONAL EQUIVALENCE FRANK SOTTILE
- Form 101, Part II Research Proposal
- Manuscript math.AG/0507377 EXPERIMENTATION AND CONJECTURES IN THE REAL
- JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY
- Manuscript, April 2007. math.MG/0610407 LINE PROBLEMS IN NONLINEAR COMPUTATIONAL GEOMETRY
- PIERI'S FORMULA FOR FLAG MANIFOLDS AND SCHUBERT POLYNOMIALS
- A STRAIGHTENING LAW FOR THE DRINFEL'D LAGRANGIAN GRASSMANNIAN
- math.AG/0609544, To appear in Moscow Math. Journal. 24 November 2006 NEW FEWNOMIAL UPPER BOUNDS FROM
- Topics in Algebraic Geometry and Geometric Modeling, Contemp. Math., 334, 2003. Toric ideals, real toric varieties,
- "! $# %$&%'!(0)123"4%657 8 9A@CBEDAFHGPIRQTSUBV9XWYGPBA`aSUBAb ca9dBAePfXgh`aBAePWiQpcqDrDs@CSVI
- GALOIS GROUPS OF SCHUBERT PROBLEMS VIA HOMOTOPY COMPUTATION
- AN EXCURSION FROM ENUMERATIVE GEOMETRY TO SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS
- math.AG/0609544, To appear in Moscow Math. Journal. 24 November 2006 NEW FEWNOMIAL UPPER BOUNDS FROM
- SHIFTED QUASI-SYMMETRIC FUNCTIONS AND THE HOPF ALGEBRA OF PEAK FUNCTIONS
- COMPLEMENTARY ALGORITHMS FOR TABLEAUX TOM ROBY, FRANK SOTTILE, JEFF STROOMER, AND JULIAN WEST
- PIERITYPE FORMULAS FOR MAXIMAL ISOTROPIC GRASSMANNIANS VIA TRIPLE INTERSECTIONS
- COCOMMUTATIVE HOPF ALGEBRAS OF PERMUTATIONS AND TREES
- A GEOMETRIC APPROACH TO THE COMBINATORICS OF SCHUBERT POLYNOMIALS
- 21 July 2008 math.AG/0801.2611 J. Alg. Geom., to appear GENERAL ISOTROPIC FLAGS ARE GENERAL
- Real Solutions to Equations From Geometry Frank Sottile
- Proc AMS, to appear. 3 May 2008. A LITTLEWOODRICHARDSON RULE FOR GRASSMANNIAN
- Contemporary Mathematics Rational Curves on Grassmannians
- NON-COMMUTATIVE PIERI OPERATORS ON POSETS NANTEL BERGERON, STEFAN MYKYTIUK, FRANK SOTTILE,
- Manuscript, April 2007. math.MG/0610407 LINE PROBLEMS IN NONLINEAR COMPUTATIONAL GEOMETRY
- SKEW LITTLEWOODRICHARDSON RULES FROM HOPF ALGEBRAS
- J. Symbolic Computation (1998) 26, 767{788 Article No. sy980239
- Manuscript of 21 February 2005. LINE TANGENTS TO FOUR TRIANGLES
- Four Entries for Kluwer Encyclopaedia of Mathematics
- Conics from the configuration of Figure 1 in x4 of ``Enumerative geometry for real varieties''.
- 2 October 2007 arXiv:0706.3745 BOUNDS ON THE NUMBER OF REAL SOLUTIONS TO
- On the number of line tangents to four triangles in three-dimensional Herve Bronnimann
- Summer School on Applicable Algebraic Geometry: Additional Funding
- Computing Monodromy via Parallel Homotopy Continuation
- ArXiv.org/0812.1275 to appear in Proceedings of Mathematical methods of Curves and Surfacecs, 4 March 2009 SOME GEOMETRICAL ASPECTS OF CONTROL POINTS
- arXiv:1003.5141, 26 March 2010 ARITHMETIC TORIC VARIETIES
- math.AG/0105180, Trans. Amer. Math. Soc, to appear, 2002 LINES TANGENT TO 2n 2 SPHERES IN R n
- 2 February 2008 arXiv:0801.2554 BETTI NUMBER BOUNDS FOR FEWNOMIAL HYPERSURFACES
- arXiv:math.AG/0706.2116 4 February 2009 LINEAR PRECISION FOR PARAMETRIC PATCHES
- A MONOID FOR THE GRASSMANIANN BRUHAT ORDER NANTEL BERGERON AND FRANK SOTTILE
- SCHUBERT POLYNOMIALS, THE BRUHAT ORDER, AND THE GEOMETRY OF FLAG MANIFOLDS
- Mathematical Research Letters, to appear, March 2005 QUIVER COEFFICIENTS ARE SCHUBERT
- PHYLOGENETIC TORIC VARIETIES ON GRAPHS WERONIKA JULIA BUCZYNSKA
- KHOVANSKII-ROLLE CONTINUATION FOR REAL SOLUTIONS DANIEL J. BATES AND FRANK SOTTILE
- 6 September 2004 THE ENVELOPE OF LINES MEETING A FIXED LINE AND
- Injectivity of 2D Toric Bezier Patches Frank Sottile
- FPSAC 2011, Reykjavik, Iceland DMTCS proc. (subm.), by the authors, 112 Cofree compositions of coalgebras
- TORIC DEGENERATIONS OF BEZIER PATCHES: EXTENDED LUIS DAVID GARCIA-PUENTE, FRANK SOTTILE, AND CHUNGANG ZHU
- Draft of September 6, 2011 ALGORITHM XXX: ALPHACERTIFIED: CERTIFYING SOLUTIONS
- Numerical real algebraic geometry Frank Sottile
- alphaCertified Jonathan D. Hauenstein
- Draft of October 19, 2011 NON-ARCHIMEDEAN COAMOEBAE
- Certifying solutions to square systems of polynomial-exponential equations
- Applications and Combinatorics in Algebraic Geometry
- Mss. arXiv.org/1111.3501November 15, 2011 STATIC SKEW-SYMMETRIC OUTPUT FEEDBACK CONTROL
- Mss., January 31, 2012 DISCRIMINANT COAMOEBAS THROUGH HOMOLOGY
