Research Talks: Frank Sottile

• Bounds for real solutions to equations from geometry, Discrete Structures in Geometry and Topology, ECM July 2008, abstract.
• Linear precision for parametric patches, Mathematical methods for curves and surfaces, 26 June 2008. abstract. text of talk
• Bounds for real solutions to polynomial systems, (4 lectures) Introductory workshop, semester on real and tropical algebraic geometry, CIB, EPFL, Lausanne, 21--25 January 2008. abstract.
• Frontiers of reality in the Schubert calculus, Workshop on Real, tropical, and complex enumerative geometry. Centre de recherches mathematiques. 21 June 2007. Some images from talk.
• New Fewnomial Upper Bounds from Gale Dual Polynomial Systems, IMA workshop on Algorithms in Algebraic Geometry. 18--22 September 2006. Abstract.
• Line problems in nonlinear computational geometry, Discrete and Computational Geometry: Twenty Years Later. Snowbird, Utah, 18-23 June 2006. Abstract.
• Lower bounds for real polynomial systems from sign-imbalanced posets, Saturday on Discrete Mathematics in Darmstadt, 26 November 2005. Abstract
• Shapiro Conjecture, at Workshop on Real Algebra, Quadratic Forms and Model Theory; Algorithms and Applications, 2--9 November, Centre Émile Borel, Institut Henri Poincaré, Paris. Abstract.
• Bounds for real solutions to sparse polynomial systems, 9 September 2005, Annual Network Meeting - RAAG2005, Abstract.
• The Horn recursion in the cominuscule Schubert calculus, 6 August 2005, Plenary talk, XVI Coloquio Latinoamericano de Álgebra, 1 - 9 August 2005, Colonia, Uruguay. Abstract.
• The Horn recursion in the Schubert calculus, at CombinaTexas, 25--26 February 2005, Texas State University-San Marcos. Abstract.
• The Horn recursion in the cominuscule Schubert calculus, at Trends in Topological Combinatorics, 14-16 February 2005, KTH Stockholm. Abstract.
• Real Solutions to Polynomial Systems and Enumerative Real Algebraic Geometry I, II, III, 7-9 January 2004. Introductory workshop, Topological Aspects of Real Algebraic Geometry, MSRI. .html slides.
• Real Solutions to Structured Equations, 1 April 2003. Commutative Algebra and Geometry, Banff International Research Station.
• Topology of Real Algebraic Curves, 21 September 2002. MSRI - Howard Workshop, Howard University, Washington, D.C.
• Solving Equations and Viro's Method, 22 September 2002. MSRI--Howard Workshop, Howard University, Washington, D.C.
• A tutorial on projective toric varieties, 30 July 2002. Workshop on Algebraic Geometry and Geometric Modeling, Vilnius, Lithuania. 29 July 2002 -- 2 August 2002. Text of talk (gzipped postscript).
• Common transversals and tangents, July 19, 2002, Symbolic Computational Algebra 2002, 15-19 July 2002. Ontario Research Centre for Computer Algebra, University of Western Ontario, London Ontario.   Abstract. Text of Talk.
• Topological lower bounds on the number of real solutions, 23 May 2002, Solving Systems of Polynomial Equations, Texas A&M University, 20-24 May 2002.   Abstract.
• Enumerative real algebraic geometry, 14 June 2001, Real Algebraic and Analytic Geometry 2001, Rennes, France. Abstract.
• A Gromov-Witten invariant in the real world, 28 April 2001, Invited Address, AMS Regional Meeting in Hoboken, NJ.   Abstract.
• Enumerative real algebraic geometry, 13 March 2001. Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, 12-16 March 2001, DIMACS. Abstract.   Outline.
• Reality in the Schubert calculus, 11 September 2000, RiP-Workshop "Perspectives in Topology of Real Algebraic Varieties", 11-15 September 2000, MFI Oberwolfach, Germany.
• Some real and unreal enumerative geometry, 21 June 2000, Effective Methods in Algebraic Geometry `00, Bath, England. Abstract.
• Some real and unreal conjectures in enumerative geometry, 12 June 2000, Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering, AMS-IMS-SIAM Joint Research Conference, Mt. Holyoke College, 11-15 June 2000. Abstract.
• Some real and unreal enumerative geometry for flag manifolds, 15 April 2000, Workshop in Algebraic Geometry in honor of William Fulton, University of Michigan, Ann Arbor. Abstract.
• A SAGBI basis for the quantum Grassmannian, 4 June 1999, COCOA VI, Villa Gualino, Torino, Italy. Abstract.
• Feedback control of linear systems and the real Schubert calculus, Solving Systems of Equations Workshop, 14-18 September 1998, MSRI, Berkeley. gzipped Postscript Slides, and gzipped .tar file. (A picture from the talk.)
• Pieri-type formulas for the classical groups, 4 April 1997, Schubert Varieties, 31 March - 5 April 1997, MFI Oberwolfach, Germany. Abstract.
• Real enumerative geometry for Grassmannians, 29 July 1995, Computational Geometry Seminar, AMS Summer Research Institute in Algebraic Geometry, Santa Cruz.

• Identities of structure constants for Schubert polynomials and orders on the symmetric group, 16 July 1997, Formal Power Series and Algebraic Combinatorics, 14 - 18 July 1997, Vienna, Austria. Extended Abstract, Résumé.
• Identities of Littlewood-Richardson coefficients for Schubert polynomials, 15 April 1997, Symmetric Functions and Representation Theory Workshop, 14 - 18 April 1997, MSRI, Berkeley. Abstract.
• Real enumerative geometry and effective algebraic equivalence, 6 June 1996, Effective Methods in Algebraic Geometry, 4 - 8 June 1996, Eindhoven, The Netherlands. Expanded and published version of talk.
• Real enumerative geometry for the Grassmannian of lines in projective space, 2 July 1995, Real Algebraic and Analytic Geometry, 29 June - 4 July 1995, Segovia, Spain.
• A Geometric approach to the combinatorics of Schubert polynomials, 29 May 1995, Formal Power Series and Algebraic Combinatorics, 29 May - 2 June 1995, Marne-la-Valée, Paris. Extended Abstract, Résumé.

• Fewnomial bounds from Gale dual systems, Workshop on Effective Real Analytic Geometry, ICMS 6 May 2008, abstract.
• Gale duality for complete intersections, Special session on Arrangements and Related Topics, AMS Sectional Meeting in Baton Rouge, LA 30 March 2008. Abstract. Text of talk.
• Gale Duality for Complete Intersections, Workshop on Tropical Geometry, Oberwolfach, 9--15 December 2007. abstract.
• Real Solutions to Polynomial Equations, Japanese-American Frontiers of Science, Japan, 1-3 December 2007. abstract poster.
• Linear precision for toric patches, COMPASS 07, Computational Methods for Algebraic Spline Surfaces, September 12, 2007, Strobl, Austria. Abstract. text of talk .
• New fewnomial upper bounds, poster, IMA workshop on Complexity, coding, and communications, 16--20 April 2007.
• Optimal fewnomial bounds from Gale dual polynomial systems, Speedmath talk, AMS Session on Algebra and Number Theory, AMS national meeting, New Orleans. 6 January 2007. Abstract.
• Simple counting of integer points via irrationality, Special session on Extremal and Probabilistic Combinatorics, AMS Sectional Meeting in Fayetteville, Ar 3-5 November 2006. Abstract.
• The convexity behind Santaló's Helley-type Theorem, 9 October 2005. Special session on geometric transversal theory, AMS Eastern Sectional Meeting in Annandale-on-Hudson, NY. 8-9 October 2005. Abstract.
• The Horn recursions for Schur P- and Q- functions, 9 October 2005. Special session on Algebraic and Geometric Combinatorics, AMS Eastern Sectional Meeting in Annandale-on-Hudson, NY. 8-9 October 2005. Abstract.
• Bounds for real solutions to sparse polynomial systems, 7 August 2005, in Commutative Algebra and Algebraic Geometry session in the XVI Coloquio Latinoamericano de Álgebra, 1 - 9 August 2005, Colonia, Uruguay. Abstract.
• Lower bounds in enumerative real algebraic geometry from sign-imbalanced posets, Special Session on Geometry and Combinatorics, AMS National Meeting in Pheonix, AZ 7-10 January, 2004.   Abstract.
• Structure of the Malvenuto-Reutenauer Hopf algebra of permutations, 4 May 2002, Special Session on Combinatorial Hopf Algebras, AMS Eastern Sectional Meeting in Montréal, Quebec, Canada 4-5 May 2002.   Abstract.
• Skew Schubert polynomials, 2 March 2002, Special Session on Algebraic Combinatorics, AMS Central Sectional Meeting in Ann Arbor, 1-3 March, 2002.   Abstract.
• Common transversals and tangents in P³, 8 January 2002, Special Session on Computational Commutative Algebra and Algebraic Geometry, AMS 2002 National Meeting in San Diego, CA, 6-9 January, 2002.   Abstract.
• The Hopf algebra of permutations of Malvenuto and Reutenauer, 9 January 2002, Special Session on Algebraic Combinatorics, AMS 2002 National Meeting in San Diego, CA, 6-9 January, 2002.   Abstract.
• A sagbi basis for the quantum Grassmannian, 21 April 2001, Algebra Weekend, University of Missouri, Columbia. Abstract.
• Maximally inflected curves, 13 January 2001, Special Session on Computational Algebraic Geometry for Curves and Surfaces, AMS National Meeting in New Orleans, Louisiana.   Abstract. Text of Talk.
• Elementary transversality in the Schubert calculus, 5 November 2000, Special Session on Algebraic Geometry, AMS Regional Meeting in New York. Abstract.
• Polytopes and isotropic Schubert calculus, 20 October 2000, Bay Area Discrete Mathematics Day, University of California at Davis. Abstract.
• Polytopes and isotropic Schubert calculus, 14 October 2000, Combinatorialists of New England, Smith College. Abstract.
• Real rational curves in Grassmannians, April 2 2000, Special Session on Enumerative Geometry in Physics, AMS Spring regional meeting in Lowell, Massachusetts. Abstract.
• A Pieri-type formula for the symplectic flag manifold, 20 March 1998, Combinatorics and Enumerative Geometry Special Session, AMS regional meeting in Liousville, Kentucky. Abstract.
• Real enumerative geometry and Shapiros' conjecture, 8 November 1997, Applications of Algebraic Geometry Session, Midwest algebraic geometry conference, 7-9 November 1997, Notre Dame, Indiana. Abstract.
• The control of linear systems and Shapiros's conjecture, 18 October 1997, Concrete aspects of real polynomials Special Session, AMS regional meeting in Atlanta. Abstract.
• Monoids, Orders, and Schubert Polynomials, 18 June 1997, Atelier Combinatoire Algebrique, 9 - 20 June 1997, centre de recherches mathématiques, Montréal, Quebec, Canada.
• Multiplying Schubert polynomials and chains in the Bruhat order, 3 May 1997, Algebraic Combinatorics Special Session, AMS regional meeting in Detroit. Abstract.
• Numerical Schubert calculus, 12 April 1997, Algorithms in Real Algebraic Geometry Special Session, AMS regional meeting in College Park, Maryland. Abstract.
• Enumerative geometry for real varieties, 8 January 1997, Computational Geometry Special Session, AMS National Meeting in San Diego. Abstract.
• Symmetries of Littlewood-Richardson coefficients for flag manifolds, 2 November 1996, Algebraic Geometry Special Session, AMS regional meeting in Columbia, Missouri. Abstract.
• Symmetries of Littlewood-Richardson coefficients for Schubert polynomials, 26 April 1996, Ontario Combinatorics Workshop, Fields Institute, Toronto, Canada.
• Symmetries of Littlewood-Richardson coefficients for Schubert polynomials and flag varieties, 28 October 1995, Route 81 Conference onCommuative Algebra and Algebraic Geometry, Syracuse.
• Real enumerative geometry for the Grassmannian of lines in projective space, 1 October 1994, Route 81 Conference on Commuative Algebra and Algebraic Geometry, Queen's University.
• Real enumerative geometry for the Grassmann variety of lines in projective space, 20 December 1993, Real Algebraic Geometry - Topology Conference, 17-21 December 1993, Michigan State University.

• Galois groups of Schubert problems via numerical homotopy computation, Colloquium, Centre for Applied Mathematics, Notre Dame University, 26 February 2008 abstract.
• Bounds for real solutions to structured polynomial systems, Trinity University, 18 February 2008. Abstract.
• Bounds for real solutions to structured polynomial systems, University of Illinois-Chicago, 26 October 2007. Abstract.
• Frontiers of reality in Schubert calculus, Sam Houston State University, 21 September 2007. Abstract.
• Bounds for real solutions to structured polynomial systems, UNC-Chapel Hill, 11 January 2007. Abstract.
• Bounds for real solutions to structured polynomial systems, Texas State University, San Marcos, 1 December 2006. Abstract.
• Bounds for real solutions to structured polynomial systems, IUPUI, 13 October 2006. Abstract.
• Bounds for real solutions to structured polynomial systems, Universität Stuttgart, 8 May 2006. Abstract.
• Bounds for real solutions to structured polynomial systems, Universität Innsbruck, 4 April 2006. Abstract.
• Polytopes and Polynomial Systems, Vorlesung lecture at the Graduiertenkolleg, Technische Universität Berlin, 13 February 2006. Abstract
• Bounds for real solutions to structured polynomial systems, Universität Konstanz, 12 January 2006. Abstract.
• Bounds for real solutions to structured polynomial systems, Université Genève, 17 November 2005. Abstract.
• Bounds for real solutions to structured polynomial systems, Texas A&M University, 11 October 2005. Abstract.
• Tropical Interpolation, 12 January 2005, University of British Columbia. Abstract. Expository Article
• Certificates of Algebraic Positivity, 15 September 2004, Sam Houston State University. Abstract
• Certificates of Algebraic Positivity, 9 September 2004, Rice University. Abstract
• Algebraic Certificates of Positivity, 21 April 2004, San Fransisco State University. Abstract
• Algebraic Certificates of Positivity, 8 April 2004, University of California at San Diego. Abstract
• Real rational curves, 24 November 2003, Fachbereich Mathematik und Informatik, Universität Marburg. Abstract
• Enumerative Real Algebraic Geometry, 12 September 2003. Virginia Polytechnic Institute and State University. Abstract.
• Enumerative Real Algebraic Geometry, 4 April 2003. University of Saskatchewan. Abstract.
• Enumerative Real Algebraic Geometry, 28 February 2003, Texas A & M University. Abstract.
• Enumerative Real Algebraic Geometry, 3 February 2003, North Carolina State University. Abstract.
• Enumerative real algebraic geometry, 29 January 2003, University of Colorado, Boulder. Abstract.
• A Gromov-Witten invariant in the real world, 14 November 2002, Michigan State University. Abstract.
• A Gromov-Witten invariant in the real world , 27 November 2001, Purdue University. Abstract
• A Gromov-Witten invariant in the real world , 9 November 2001, SUNY Albany. Abstract
• A Gromov-Witten invariant in the real world, 8 March 2001, University of Massachusetts at Amherst. Abstract.
• A Gromov-Witten invariant in the real world, 17 January 2001, Texas Tech University. Abstract.
• Quantum cohomology in the real world, 30 November 2000, Dartmouth College. Abstract.
• Quantum cohomology in the real world, 27 October 2000, Connecticut Valley Colloquium, Mt. Holyoke College. Abstract.
• Control of linear systems and the real Schubert calculus, 3 December 1999, University of Wisconsin, Parkside. Abstract.
• Control of linear systems and the real Schubert calculus, 26 October 1999, University of California, Santa Cruz. Abstract.
• The Control of linear systems and the real Schubert calculus, 23 September 1999, University of North Carolina. Abstract.
• Real Schubert calculus, 10 February 1999, University of Colorado, Boulder. Abstract.
• Real Schubert calculus, 21 January 1999, University of Notre Dame. Abstract.
• Feedback control of linear systems and the real Schubert calculus, 17 November 1998, University of Washington. Abstract.
• Feedback control of linear systems and the real Schubert calculus, 27 October 1998, Santa Clara University. Abstract: text-only, with picture, or postscript. Slides from the talk.
• The real, complete story on conics, 9 October 1998, California State University, Hayward. Abstract: text-only, with picture, or postscript.
• Concrete Schubert calculus, 2 February 1998, Texas A & M University. Abstract.
• Combinatorics of the symmetric group and flag manifolds, 11 March 1997, New Mexico State University. Abstract.
• Making the Schubert calculus effective, 7 March 1997, University of Texas at El Paso. Abstract.
• Is the Schubert calculus effective?, 24 September 1996, University of Notre Dame. Abstract.
• Combinatorics of symmetric groups and flag manifolds, 21 September 1995, SUNY Buffalo.

• Introduction to Applicable Algebraic geometry, a short course of 10 lectures, 23 July -- 3 August 2007, IMA PI Summer Program on Applicable Algebraic Geometry. Outline of course. Real solutions to equations from geometry, a short course of 8 lectures 14--16, 21--23, 28, & 29 November 2005, Centre Émile Borel, Institut Henri Poincaré, Paris. Abstract and Outline.
• Examples and Applications of Computational Algebraic Geometry, 17-21 November 2003, Oberwolfach-Seminar on Computational Algebraic Geometry, Mathematisches Forschunginstitute Oberwolfach.
• Real enumerative geometry and solving systems of equations, A short course of 4 lectures, 26 May, and 2, 9, 16 June 1999, IRMA Strasbourg. Abstract.

• Khovanskii-Rolle continuation for real solutions, Geometry Seminar, Chambéry, 28 April 2008, abstract.
• Gale duality for complete intersections, San Francisco State University, 19 March 2008. Abstract.
• Khovanskii-Rolle continuation for real solutions, Applied Mathematics Seminar, Michigan State University, 29 February 2008. Abstract.
• Betti number bounds for fewnomial hypersurfaces via stratified Morse theory, Algebraic Geometry Seminar, Texas A&M University, 28 January 2008. abstract.
• Galois groups of Schubert problems via numerical homotopy computation, Algebraic Geometry Seminar, Texas A&M University, 14 January 2008. abstract.
• A Littlewood-Richardson rule for Grassmannian Schubert problems, Algebra and Combinatotrics Seminar, Texas A&M, 12 November 2007. Abstract.
• Khovanskii-Rolle continuation for real solutions, Algebraic Geometry Seminiar, University of Illinois-Chicago, 25 October 2007. Abstract.
• Khovanskii-Rolle continuation for real solutions, Seminiar, Texas A&M University, 22 October 2007. Abstract.
• Lower bounds for real solutions to equations, Open Problems Seminar, Texas A&M, 5 October 2007.
• Bounds in real algebraic geometry from Gale dual polynomial systems, Seminar, Technische Universität München, 14 September 2007.
• A commutative algebra approach to Pieri and Littlewood-Richardson rules, Open Problems Seminar, Texas A&M, 7 September 2007.
• On "Towards a Schubert calculus for the complex reflection groups", Open Problems Seminar, Texas A&M, 29 August 2007.
• Gale duality for complete intersections, TAMU Algebraic Geometry Seminar, 27 August 2007. Abstract.
• Gale dual systems and bounds in real algebraic geometry, Seminar on Applicable Algebraic Geometry, IMA PI Summer Graduate School on Applicable Algebraic Geometry. 2 August 2007. Abstract.
• On "Towards a Schubert calculus for the complex reflection groups", Summer seminar on complex reflection groups, University of Minnesota, 28 June 2007.
• The Horn recursion in the Schubert calculus, Seminar, University of Minnesota. 6 April 2007. Abstract.
• Optimal fewnomial bounds from Gale dual polynomial systems, Algebraic Geometry Seminar, University of Wisconsin, 27 April 2007. Abstract.
• Optimal fewnomial bounds from Gale dual polynomial systems, Seminar, Institute for Mathematics and its Applications, 4 April 2007. Abstract.
• Optimal fewnomial bounds from Gale dual polynomial systems, Seminar, University of Texas. 8 February 2007. Abstract.
• Optimal fewnomial bounds from Gale dual polynomial systems, Seminar, UNC-Chapel Hill. 12 January 2007. Abstract.
• New Fewnomial Upper Bounds from Gale Dual Polynomial Systems, Algebra and Combinatorics Seminar, TAMU. 1 September 2006. Abstract.
• Equivariant Chow ring of the quot scheme, Geometry Seminar, Universität Zürich. 6 June 2006. Abstract
• Combinatorial Hopf Algebras, Oberseminar Hopfalgebren und Quantengruppen, Universität München, 1 June 2006.
• The Horn recursion in the Schubert calculus, Algebraic Geometry Seminar, Universität Bayreuth, 10 Mai 2006. Abstract
• Polytopes and Polynomial Systems, Seminar, Universität Innsbruck, 4 April 2006. Abstract.
• Linear precision for multi-sided toric patches, CMA guest lecture, Centre of Mathematics for Applications, University of Oslo. 15 March 2006. Abstract
• Equivariant Chow ring of the quot scheme, Topology/Algebra Seminar, University of Bergen. 14 March 2006. Abstract
• The Horn recursion in the Schubert calculus, Seminar in Algebra and Algebraic Geometry, University of Oslo, 13 Mars 2006. Abstract
• The convexity behind Santaló's Helley-type Theorem, 1 February 2006. Mittagsseminar, Technische Universität Müchen. Abstract.
• The Horn recursion for the Schubert calculus I and II, Geometry Seminar, Grenoble, 12 December 2005. Grenoble
• The Horn recursion for the Schubert calculus, COWS seminar, Warwick, 1 December 2005. Abstract.
• Equivariant Chow ring of the quot scheme, Algebraic Seminar,Institut de Mathematiques de Jussieu, 24 November 2005. Abstract
• The Shapiro Conjecture, Geometry Seminar, LAMA, Université de Savoie, Chambery 18 November 2005. Abstract
• Bounds for real solutions to polynomial systems, Mittagsseminar, Technische Universit Universität München 26 October 2005. Abstract.
• Bounds for real solutions to structured polynomial systems, Algebraic Geometry Seminar, University of Illinois at Chicago, 6 October 2005. Abstract.
• Equivariant Chow ring of the Quot Scheme, 3 May 2005, Algebra Seminar, University of Texas. Abstract
• The Horn recursion in the cominuscule Schubert calculus, Geometry Seminar, 6 April 2005, The Ohio State University. Abstract.
• The Horn recursion in the cominuscule Schubert calculus, Geometry Seminar, 24 March 2005, Texas A&M University. Abstract.
• Equivariant Cohomology of the Quot Scheme, 3 December 2004, Algebraic Geometry Seminar, Texas A&M. Quot
• Tropical Interpolation, 25 November 2004, UNAM, Mexico City. Abstract. Expository Article
• Equivariant Cohomology of the Quot Scheme, 24 November 2004, CINVESTAV, Mexico City. Abstract.
• Lower bounds for real polynomial systems from sign-imbalanced posets, 23 November 2004, UNAM, Mexico City. Abstract
• Tropical Interpolation, 19 November 2004, Joint CIMAT-U. Morelia, Algebraic Geometry Seminar. Abstract. Expository Article
• Lower bounds for real polynomial systems from sign-imbalanced posets, 28 May 2004, Combinatorics Seminar, University of California at Davis.
• Lower bounds in Enumerative Real Algebraic Geometry, 3 May 2004, Algebra Seminar, Stanford University.
• Lower bounds for real polynomial systems from sign-imbalanced posets, 26 March 2004, Combinatorics Seminar, University of Michigan.
• Lower bounds for real polynomial systems from sign-imbalanced posets, 4 March 2004, Algebraic Geometry Seminar, Colorado State University.
• Lower bounds in Enumerative Real Algebraic Geometry, 17 February 2004, Commutative Algebra and Algebraic Geometry Seminar, University of California, Berkeley.
• Lower bounds for real polynomial systems from sign-imbalanced posets, 4 February 2004, Combinatorics and Geometry Seminar, University of Washington. Abstract
• Grothendieck Polynomial Formulas, 26 January 2004, Combinatorics Seminar, University of California at Berkeley. Abstract
• The Real story of linear series on P¹, 7 November 2003, Columbia University Algebraic geometry Seminar. Abstract
• Common transversals and tangents, June 16 2003, INRIA, Nancy. Abstract.
• Enumerative real algebraic geometry, 31 January 2003, Valley Geometry Seminar, University of Massachusetts, Amherst. Abstract.
• Combinatorial Hopf algebras, 15 November 2002, University of Michigan Combinatorics Seminar. Abstract.
• Enumerative real algebraic geometry, TU-München, 11 April 2002. Abstract.
• Common transversals and tangents in P³, 20 March 2002, CRANTS Seminar, SUNY Albany, Abstract.
• Common transversals and tangents in P³, 14 March 2002, Rutgers University, Abstract.
• Common transversals and tangents in P³, 30 November 2001, Valley Geometry Seminar, University of Massachusetts at Amherst. Abstract.
• The Malvenuto---Reutenauer Hopf algebra of permutations, October 30 2001, SUNY Binghamton. Abstract.
• Common transversals and tangents in P³, October 29 2001, Cornell University. Abstract.
• The Hopf algebra of permutations of Malvenuto and Reutenauer, 24 October 2001, MIT Combinatorics Seminar.   Abstract.
• Enumerative real algebraic geometry, 1 July 2001, Geometry Seminar, UMIST, Manchester, England. Abstract.
• Enumerative real algebraic geometry, 18 June 2001, IRMA Strasbourg, France. Abstract.
• Elementary transversality in the Schubert calculus, 9 April 2001, Geometry-Algebra-Singularities-Combinatorics Seminar, Northeastern University. Abstract.
• A sagbi basis for the quantum Grassmannian, 23 March 2001, Combinatorics Seminar, University of Michigan. Abstract.
• Some real and unreal enumerative geometry, 12 February 2001, Algebra Seminar, Boston University. Abstract.
• Maximally inflected curves, 16 January 2001, Logic-Topology-Algebraic Geometry Seminar, Texas Tech University Abstract.
• Quantum reality: rational curves in real Grassmannians, 21 November 2000, Geometry Seminar, Courant Institute for the Mathematical Sciences. Abstract.
• Eulerian actions on posets and the combinatorics of peaks, 28 April 2000, Combinatorics Seminar, University of Minnesota, Minneapolis. Abstract.
• A sagbi basis for the quantum Grassmannian, 3 April 2000, Geometry-Algebra-Singularities-Combinatorics Seminar, Northeastern University. Abstract.
• Schubert calculus in the control of linear systems, 31 March 2000, Special Geometry Seminar, University of Massachusetts-Amherst. Abstract.
• Some real and unreal enumerative geometry for flag manifolds, 14 March 2000, Algebraic Geometry Seminar, University of California, Berkeley. Abstract.
• Eulerian actions on posets and the combinatorics of peaks, 13 March 2000, Combinatorics Seminar, University of California, Berkeley. Abstract.
• Pieri operators on posets, 16 February 2000, Combinatorics Seminar, MIT. Abstract.
• Real rational curves in Grassmannians, 19 January 2000, University of Toronto. Abstract.
• A sagbi basis for the quantum Grassmannian, 17 January 2000, Applied Algebra Seminar, York University, Toronto. Abstract.
• Maximally inflected curves, 27 October 1999, Topology Seminar, University of California, Davis. Abstract.
• Pieri operators on posets, 25 October 1999, Combinatorics Seminar, University of California, Berkeley. Abstract.
• Non-commutative Pieri operators on posets, 4 October 1999, Combinatorics Seminar, Michigan State University. Abstract.
• Feedback control of linear systems and the real Schubert calculus, 24 Juin 1999, Séminaire de Géométrie Algebrique, Université de Genève. Abstract.
• Standard monomial theory for the quantum Grassmannian, 15 Juin 1999, Séminaire Theorie de representations et applications, IRMA, Université de Strasbourg.
• Real rational curves in, and from Grassmannians, 10 Juin 1999, Séminaire de Géométrie réelle, IRMAR, Université de Rennes 1. Abstract.
• Feedback control of linear systems and the real Schubert calculus, 27 mai 1999, Séminaire de Géométrie Algèbrique, IRMA, Université de Strasbourg. Abstract.
• A SAGBI basis for the quantum Grassmannian, 3 May 1999, Combinatorics Seminar, University of Wisconsin-Madison. Abstract.
• Real rational curves in Grassmannians, 22 March 1999, Differential Geometry Seminar, University of Wisconsin-Madison. Abstract.
• Real Schubert calculus, 29 January 1999, Seminar, Northeastern University. Abstract.
• Real Schubert calculus, 27 January 1999, Seminar, University of Massachusetts, Amherst. Abstract.
• Pieri operators on posets, 20 January 1999, Seminar, University of Notre Dame. Abstract.
• Real Schubert calculus, 19 January 1999, Seminar, University of Illinois, Urbana.
• Real Schubert calculus, 10 January 1999, Seminar, Georgia Institute of Technology.
• The special Schubert calculus is real, 9 December 1998, Algebraic Geometry Seminar, Uiversity of Utah; Abstract.
• Real Schubert calculus: special and quantum, 1 December 1998, Algebraic Geometry, Commutative Algebra, and Combinatorics Seminar, University of California at Berkeley.
• Non-commutative Pieri operators on posets, 19 November 1998, Algebra Seminar, University of Washington; Abstract.
• New advances in enumerative real algebraic geometry, 12 November 1998, Working group in real algebraic geometry, MSRI Abstract.
• Maps of flag manifolds: Schubert classes and singularities, 20 April 1998, Geometry/Topology Seminar, McMaster University; Abstract.
• Pieri-type formulas for flag manifolds, 23 February 1998, Universität Zürich; Abstract.
• Hopf algebras of edge-labeled posets, 20 February 1998, Lie Theory Semninar, University of Wisconsin-Madison. Abstract.
• Pieri-type formulas for flag manifolds, 18 February 1998, Algebraic Geometry Seminar, University of Chicago, Abstract.
• Pieri-type formulas for Schubert polynomials, 9 February 1998, Applied Algebra Seminar, York University. Abstract.
• A Pieri-type formula for flag manifolds, 6 February 1998, The Ohio State University, Abstract.
• Hopf algebras and edge-labeled posets, 6 October 1997, Applied Algebra Seminar, York University. Abstract.
• Control theory, numerical Schubert calculus, and real polynomial systems, 3 July 1997, Seminaire Formes et Formules, Université de Nice & INRIA Sophia-Antipolis. Abstract.
• The Control of linear systems and real enumerative geometry, 24 June 1997, Séminaire de Géométrie Algebrique, Université de Genève. Abstract.
• Orders on the symmetric group and the multiplication of Schubert polynomials, 11 April 1997, George Washington University Combinatorics Seminar. Abstract.
• Numerical Schubert calculus, 8 April 1997, Couraunt Institute of Mathematical Sciences Geometry Seminar. Abstract.
• The intersection form for flag varieties, 6 March 1997, Texas A & M University Algebraic Geometry Seminar. Abstract.
• The Intersection form for flag varieties, 4 February 1997, University of Utah Algebraic Geometry Seminar.
• Schubert polynomials and chains in the Bruhat order on S_n, 22 October 1996, University of California at San Diego Combinatorics Seminar. Abstract.
• Intersection theory for spherical varieties, 3 October 1996, University of Illinois at Urbana-Champaign Algebra Seminar. Abstract.
• Structure constants for Schubert polynomials and the Bruhat order, 1 October 1996, University of Illinois at Urbana-Champaign Combinatorics and Graph Theory Seminar. Abstract.
• Enumerative geometry for real varieties, 25 September 1996, University of Notre Dame Algebraic Geometry Seminar. Abstract.
• Is the Schubert calculus effective?, 9 September 1996, University of California at Berkeley Discrete Mathematics Seminar. Abstract.
• Symmetries of Littlewood-Richardson coefficients for flag varieties, 24 July 1996, University of British Columbia Algebraic Geometry Seminar.
• Real enumerative geometry and effective algebraic equivalence, 20 May 1996, Northeastern University Singularities and Geometry Seminar. Abstract.
• Symmetries of Littlewood-Richardson coefficients for Schubert polynomials, 17 May 1996, MIT Combinatorics Seminar.
• Symmetries of Littlewood-Richardson coefficients for Schubert Polynomials and flag vareities, 30 November 1995, University of Waterloo Combinatorics Seminar.
• Real enumerative geometry for the Grassmannian of lines in projective space, 16 June 1995, Séminaire de Géométrie Algebrique, Université Genève.
• Pieri's rule for flag varieties, 16 February 1995, CICMA Algebraic Geometry Seminar, Centre de recherches de mathématiques, Montréal.
• Pieri's rule for Schubert polynomials, 2 December 1994, MIT Combinatorics Seminar.
• A geometric Pieri's rule, 20 October 1994, University of Illinois at Urbana-Champaign Algebra Seminar.
• The Schubert calculus for the Grassmannian of lines in projective space is totally real, 25 October 1993, Michigan State University Topology Seminar.