HR job title
- Professor
- Contact Info
- 1 979 595 5328
- ORCiD
- 0000-0003-0087-7120
Sottile, Frank Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
Algebraic combinatorics, real and computational algebraic geometry, applications of algebraic geometry, Mathematical Physics, Hopf algebras, discrete and computational geometry, tropical geometry.
- Overview
- Publications
- Research
- Teaching
- Works By Students
- Background
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Overview
Publications
selected publications
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academicarticle
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del Campo, A. M., Sottile, F., & Williams, R. L.
(2023).
Classification of Schubert Galois Groups in Gr(4,9). Arnold Mathematical Journal.
1-41.
-
Breiding, P., Sottile, F., & Woodcock, J.
(2022).
Euclidean Distance Degree and Mixed Volume. Foundations of Computational Mathematics.
22(6), 1743-1765.
-
Nisse, M., & Sottile, F.
(2022).
Describing amoebas. PACIFIC JOURNAL OF MATHEMATICS.
317(1), 187-205.
-
Pir, A. F., & Sottile, F.
(2022).
Irrational Toric Varieties and Secondary Polytopes. Discrete and Computational Geometry: an international journal of mathematics and computer science.
67(4), 1053-1079.
-
Duff, T., Hein, N., & Sottile, F.
(2022).
Certification for polynomial systems via square subsystems. Journal of Symbolic Computation.
109, 367-385.
-
Brysiewicz, T., Rodriguez, J. I., Sottile, F., & Yahl, T.
(2021).
Decomposable sparse polynomial systems. The Journal of Software forAlgebra and Geometry: Macaulay2.
11(1), 53-59.
-
Brysiewicz, T., Rodriguez, J. I., Sottile, F., & Yahl, T.
(2021).
Solving decomposable sparse systems. Numerical Algorithms.
88(1), 453-474.
-
Huang, Y., Petroulakis, G., Sottile, F., & Zelenko, I.
(2021).
Nontrivial linear projections on the Grassmannian Gr(3)(C-6). Linear Algebra and Its Applications.
610, 488-505.
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Leykin, A., del Campo, A. M., Sottile, F., Vakil, R., & Verschelde, J.
(2021).
Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm. Mathematics of Computation.
90(329), 1407-1433.
-
Hauenstein, J. D., Leykin, A., Rodriguez, J. I., & Sottile, F.
(2021).
A numerical toolkit for multiprojective varieties. Mathematics of Computation.
90(327), 413-440.
-
Ngoc, D. o., Kuchment, P., & Sottile, F.
(2020).
Generic properties of dispersion relations for discrete periodic operators. Journal of Mathematical Physics.
61(10), 103502-103502.
-
DiPasquale, M., & Sottile, F.
(2020).
Bivariate semialgebraic splines. Journal of Approximation Theory.
254, 105392-105392.
-
Li, C., Ravikumar, V., Sottile, F., & Yang, M.
(2019).
A geometric proof of an equivariant Pieri rule for flag manifolds. Forum Mathematicum.
31(3), 779-783.
-
Hauenstein, J. D., Rodriguez, J. I., & Sottile, F.
(2018).
Numerical Computation of Galois Groups. Foundations of Computational Mathematics.
18(4), 867-890.
-
Morrison, A., & Sottile, F.
(2018).
Two Murnaghan-Nakayama Rules in Schubert Calculus. Annals of Combinatorics.
22(2), 363-375.
-
Leykin, A., Rodriguez, J. I., & Sottile, F.
(2018).
Trace Test. Arnold Mathematical Journal.
4(1), 113-125.
-
Huang, Y., Sottile, F., & Zelenko, I.
(2017).
Injectivity of Generalized Wronski Maps. Canadian Mathematical Bulletin.
60(4), 747-761.
-
DiPasquale, M., Sottile, F., & Sun, L.
(2017).
Semialgebraic splines. Computer Aided Geometric Design.
55, 29-47.
-
Hein, N., Sottile, F., & Zelenko, I.
(2017).
A Congruence Modulo Four for Real Schubert Calculus with Isotropic Flags. Canadian Mathematical Bulletin.
60(2), 309-318.
-
Hein, N., & Sottile, F.
(2017).
A lifted square formulation for certifiable Schubert calculus. Journal of Symbolic Computation.
79, 594-608.
-
Bates, D. J., Hauenstein, J. D., Niemerg, M. E., & Sottile, F.
(2016).
Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials. Numerical Algorithms.
73(1), 281-304.
-
Hauenstein, J. D., Hein, N., & Sottile, F.
(2016).
A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus. Foundations of Computational Mathematics.
16(4), 941-963.
-
Nisse, M., & Sottile, F.
(2016).
Higher convexity for complements of tropical varieties. Mathematische Annalen.
365(1-2), 1-12.
-
Hein, N., Sottile, F., & Zelenko, I.
(2016).
A congruence modulo four in real Schubert calculus. Journal für die Reine und Angewandte Mathematik.
714(714), 151-174.
-
Postinghel, E., Sottile, F., & Villamizar, N.
(2015).
Degenerations of real irrational toric varieties. Journal of London Mathematical Society.
92(2), 223-241.
-
Nisse, M., & Sottile, F.
(2015).
Higher convexity of coamoeba complements. Bulletin of the London Mathematical Society.
47(5), 853-865.
-
Hein, N., Hillar, C. J., del Campo, A. M., Sottile, F., & Teitler, Z.
(2015).
The Monotone Secant Conjecture in the Real Schubert Calculus. Experimental Mathematics.
24(3), 261-269.
-
Brooks, C. J., del Campo, A. M., & Sottile, F.
(2015).
Galois groups of Schubert problems of lines are at least alternating. Transactions of the American Mathematical Society.
367(6), 4183-4206.
-
Adeyemo, P., & Sottile, F.
(2014).
Cohomological consequences of the pattern map. Illinois Journal of Mathematics.
58(4), 997-1008.
-
Hauenstein, J. D., & Sottile, F.
(2014).
Newton Polytopes and Witness Sets. Mathematics in Computer Science.
8(2), 235-251.
-
Elizondo, E. J., LimaFilho, P., Sottile, F., & Teitler, Z.
(2014).
Arithmetic toric varieties. Mathematische Nachrichten.
287(2-3), 216-241.
-
Sottile, F.
(2013).
Book Review: Toric varieties. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
51(3), 505-510.
-
Passare, M., & Sottile, F.
(2013).
Discriminant coamoebas through homology. Journal of Commutative Algebra.
5(3), 413-440.
-
Soprunova, E., & Sottile, F.
(2013).
Lower Bounds in Real Algebraic Geometry and Orientability of Real Toric Varieties. Discrete and Computational Geometry: an international journal of mathematics and computer science.
50(2), 509-519.
-
Hein, N., Hillar, C. J., & Sottile, F.
(2013).
Lower bounds in real Schubert calculus. Sao Paulo Journal of Mathematical Sciences.
7(1), 33-33.
-
Nisse, M., & Sottile, F.
(2013).
The phase limit set of a variety. Algebra and Number Theory.
7(2), 339-352.
-
Forcey, S., Lauve, A., & Sottile, F.
(2013).
Cofree Compositions of Coalgebras. Annals of Combinatorics.
17(1), 105-130.
-
Hillar, C. J., & Sottile, F.
(2013).
Complex Static Skew-Symmetric Output Feedback Control. SIAM Journal of Control and Optimization.
51(4), 3011-3026.
-
Garca-Puente, L. D., Hein, N., Hillar, C., del Campo, A. M., Ruffo, J., Sottile, F., & Teitler, Z.
(2012).
The Secant Conjecture in the Real Schubert Calculus. Experimental Mathematics.
21(3), 252-265.
-
Hauenstein, J. D., & Sottile, F.
(2012).
Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems. ACM Transactions on Mathematical Software.
38(4), 28-20.
-
Bates, D. J., & Sottile, F.
(2011).
KhovanskiiRolle Continuation for Real Solutions. Foundations of Computational Mathematics.
11(5), 563-587.
-
Garc'ia-Puente, L. D., Sottile, F., & Zhu, C.
(2011).
Toric degenerations of Bzier patches. ACM TRANSACTIONS ON GRAPHICS.
30(5), 110-10.
-
Bihan, F., & Sottile, F.
(2011).
Fewnomial bounds for completely mixed polynomial systems. Advances in Geometry.
11(3), 541-556.
-
Sanyal, R., Sottile, F., & Sturmfels, B.
(2011).
ORBITOPES. Mathematika: a journal of pure and applied mathematics.
57(2), 275-314.
-
Lam, T., Lauve, A., & Sottile, F.
(2011).
Skew Littlewood-Richardson Rules from Hopf Algebras. International mathematics research notices.
2011(6), 1205-1209.
-
Garcia-Puente, L. D., & Sottile, F.
(2010).
Linear precision for parametric patches. Advances in Computational Mathematics.
33(2), 191-214.
-
Sottile, F.
(2010).
General isotropic flags are general (for Grassmannian Schubert calculus). Journal of Algebraic Geometry.
19(2), 367-370.
-
Grafvon Bothmer, H., Ranestad, K., & Sottile, F.
(2010).
Linear Precision for Toric Surface Patches. Foundations of Computational Mathematics.
10(1), 37-66.
-
Longinetti, M., Sgheri, L., & Sottile, F.
(2010).
Convex Hulls of Orbits and Orientations of a Moving Protein Domain. Discrete and Computational Geometry: an international journal of mathematics and computer science.
43(1), 54-77.
-
Forcey, S., Lauve, A., & Sottile, F.
(2010).
Hopf Structures on the Multiplihedra. SIAM Journal on Discrete Mathematics.
24(4), 1250-1271.
-
Sottile, F., Lauve, A., & Lam, T.
(2010).
Skew LittlewoodRichardson rules from Hopf algebras. Discrete Mathematics and Theoretical Computer Science.
DMTCS Proceedings vol. AN, 22nd International(Proceedings),
-
Sottile, F.
(2009).
Frontiers of reality in Schubert calculus. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
47(1), 31-71.
-
Bihan, F., & Sottile, F.
(2009).
Betti number bounds for fewnomial hypersurfaces via stratified Morse theory. Proceedings of the American Mathematical Society.
137(9), 2825-2833.
-
Leykin, A., & Sottile, F.
(2009).
Galois groups of Schubert problems via homotopy computation. Mathematics of Computation.
78(267), 1749-1765.
-
Purbhoo, K., & Sottile, F.
(2009).
A Littlewood-Richardson rule for Grassmannian permutations. Proceedings of the American Mathematical Society.
137(6), 1875-1882.
-
Beck, M., Haase, C., & Sottile, F.
(2009).
(Formulas of Brion, Lawrence, and Varchenko on rational generating functions for cones). The Mathematical Intelligencer.
31(1), 9-17.
-
Braden, T., Chen, L., & Sottile, F.
(2008).
THE EQUIVARIANT CHOW RINGS OF QUOT SCHEMES. PACIFIC JOURNAL OF MATHEMATICS.
238(2), 201-232.
-
Purbhoo, K., & Sottile, F.
(2008).
The recursive nature of cominuscule Schubert calculus. Advances in Mathematics.
217(5), 1962-2004.
-
Bihan, F., & Sottile, F.
(2008).
Dualit de Gale pour des intersections compltes. Annales de l'Institut Fourier.
58(3), 877-891.
-
Bates, D. J., Bihan, F., & Sottile, F.
(2007).
Bounds on the Number of Real Solutions to Polynomial Equations. 2007.
-
Leykin, A., & Sottile, F.
(2007).
Computing monodromy via parallel homotopy continuation. 97-98.
-
Ortiz-Rodrguez, A., & Sottile, F.
(2007).
Real hessian curves. Boletín de la Sociedad Matemática Mexicana.
13(1), 157-166.
-
Bronnimann, H., Devillers, O., Lazard, S., & Sottile, F.
(2007).
Lines Tangent to Four Triangles in Three-Dimensional Space. Discrete and Computational Geometry: an international journal of mathematics and computer science.
37(3), 369-380.
-
Beck, M., & Sottile, F.
(2007).
Irrational proofs for three theorems of Stanley. European Journal of Combinatorics.
28(1), 403-409.
-
Bihan, F., & Sottile, F.
(2007).
New Fewnomial Upper Bounds from Gale Dual Polynomial Systems. MOSCOW MATHEMATICAL JOURNAL.
7(3), 387-407.
-
Lenart, C., & Sottile, F.
(2006).
A Pieri-type formula for the K {K} -theory of a flag manifold. Transactions of the American Mathematical Society.
359(5), 2317-2342.
-
Lenart, C., Robinson, S., & Sottile, F.
(2006).
Grothendieck polynomials via permutation patterns and chains in the Bruhat order. American Journal of Mathematics.
128(4), 805-848.
-
Soprunova, E., & Sottile, F.
(2006).
Lower bounds for real solutions to sparse polynomial systems. Advances in Mathematics.
204(1), 116-151.
-
Goodman, J. E., Holmsen, A., Pollack, R., Ranestad, K., & Sottile, F.
(2006).
Cremona convexity, frame convexity and a theorem of Santal. Advances in Geometry.
6(2), 301-321.
-
Bertrand, B., Bihan, F., & Sottile, F.
(2006).
Polynomial systems with few real zeroes. Mathematische Zeitschrift.
253(2), 361-385.
-
Aguiar, M., & Sottile, F.
(2006).
Structure of the Loday-Ronco Hopf algebra of trees. Journal of Algebra.
295(2), 473-511.
-
Aguiar, M., Bergeron, N., & Sottile, F.
(2006).
Combinatorial Hopf algebras and generalized Dehn-Sommerville relations. Compositio Mathematica.
142(1), 1-30.
-
Ruffo, J., Sivan, Y., Soprunova, E., & Sottile, F.
(2006).
Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds. Experimental Mathematics.
15(2), 199-221.
-
Aguiar, M., & Sottile, F.
(2005).
Cocommutative Hopf algebras of permutations and trees. Journal of Algebraic Combinatorics: an international journal.
22(4), 451-470.
-
Brnnimann, H., Everett, H., Lazard, S., Sottile, F., & Whitesides, S.
(2005).
Transversals to Line Segments in Three-Dimensional Space. Discrete and Computational Geometry: an international journal of mathematics and computer science.
34(3), 381-390.
-
Megyesi, G., & Sottile, F.
(2005).
The Envelope of Lines Meeting a Fixed Line and Tangent to Two Spheres. Discrete and Computational Geometry: an international journal of mathematics and computer science.
33(4), 617-644.
-
Aguiar, M., & Sottile, F.
(2005).
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations. Advances in Mathematics.
191(2), 225-275.
-
Buch, A. S., Sottile, F., & Yong, A.
(2005).
Quiver coefficients are Schubert structure constants. Mathematical Research Letters.
12(4), 567-574.
-
Powers, V., Reznick, B., Scheiderer, C., & Sottile, F.
(2004).
A new approach to Hilbert's theorem on ternary quartics. Comptes Rendus Mathematique (Academie des Sciences).
339(9), 617-620.
-
Sottile, F.
(2003).
Elementary transversality in the Schubert calculus in any characteristic. Michigan Mathematical Journal.
51(3), 651-666.
-
Megyesi, G., Sottile, F., & Theobald, T.
(2003).
Common Transversals and Tangents to Two Lines and Two Quadrics in P. Discrete and Computational Geometry: an international journal of mathematics and computer science.
30(4), 543-571.
-
Sottile, F., & Theobald, T.
(2002).
Lines tangent to 2 n 2 2n-2 spheres in R n {mathbb R}^n. Transactions of the American Mathematical Society.
354(12), 4815-4829.
-
Bergeron, N., Mykytiuk, S., Sottile, F., & van Willigenburg, S.
(2002).
Shifted quasi-symmetric functions and the Hopf algebra of peak functions. Discrete Mathematics.
246(1-3), 57-66.
-
Bergeron, N., & Sottile, F.
(2002).
A Pieri-type formula for isotropic flag manifolds. Transactions of the American Mathematical Society.
354(7), 2659-2705.
-
De Loera, J. A., Sottile, F., & Sturmfels, B.
(2002).
Discrete and Computational Geometry: Guest editors' foreword. Discrete and Computational Geometry: an international journal of mathematics and computer science.
27(1), 1-2.
-
Roby, T., Sottile, F., Stroomer, J., & West, J.
(2001).
Complementary Algorithms for Tableaux. Journal of Combinatorial Theory Series A.
96(1), 127-161.
-
Bergeron, N., & Sottile, F.
(2001).
Skew Schubert functions and the Pieri formula for flag manifolds. Transactions of the American Mathematical Society.
354(2), 651-673.
-
Sottile, F., & Sturmfels, B.
(2001).
A sagbi basis for the quantum Grassmannian. Journal of Pure and Applied Algebra.
158(2-3), 347-366.
-
Sottile, F.
(2000).
Some real and unreal enumerative geometry for flag manifolds. Michigan Mathematical Journal.
48(SUPPL.), 573-592.
-
Bergeron, N., Goulden, I., & Sottile, F.
(2000).
Preface. Discrete Mathematics.
225(1-3), 1-1.
-
Bergeron, N., Mykytiuk, S., Sottile, F., & van Willigenburg, S.
(2000).
Noncommutative Pieri Operators on Posets. Journal of Combinatorial Theory Series A.
91(1-2), 84-110.
-
Sottile, F.
(2000).
Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro. Experimental Mathematics.
9(2), 161-182.
-
Sottile, F.
(1999).
Real rational curves in Grassmannians. Journal of the American Mathematical Society.
13(2), 333-341.
-
Bergeron, N., & Sottile, F.
(1999).
Hopf Algebras and Edge-Labeled Posets. Journal of Algebra.
216(2), 641-651.
-
Bergeron, N., & Sottile, F.
(1999).
A Monoid for the Grassmannian Bruhat Order. European Journal of Combinatorics.
20(3), 197-211.
-
Sottile, F.
(1999).
The special Schubert calculus is real. Electronic Research Announcements in Mathematical Sciences.
5(5), 35-39.
-
Huber, B., Sottile, F., & Sturmfels, B.
(1998).
Numerical Schubert Calculus. Journal of Symbolic Computation.
26(6), 767-788.
-
Bergeron, N., & Sottile, F.
(1998).
Schubert polynomials, the Bruhat order, and the geometry of flag manifolds. DUKE MATHEMATICAL JOURNAL.
95(2), 373-423.
-
Rosenthal, J., & Sottile, F.
(1998).
Some remarks on real and complex output feedback. Systems & Control Letters.
33(2), 73-80.
-
Sottile, F.
(1997).
PieriS Formula Via Explicit Rational Equivalence. Canadian Journal of Mathematics.
49(6), 1281-1298.
-
Sottile, F.
(1997).
Real enumerative geometry and effective algebraic equivalence. Journal of Pure and Applied Algebra.
117, 601-615.
-
Sottile, F.
(1997).
Enumerative geometry for the real Grassmannian of lines in projective space. DUKE MATHEMATICAL JOURNAL.
87(1), 59-85.
-
Benkart, G., Sottile, F., & Stroomer, J.
(1996).
Tableau Switching: Algorithms and Applications. Journal of Combinatorial Theory Series A.
76(1), 11-43.
-
Sottile, F.
(1996).
Pieri's formula for flag manifolds and Schubert polynomials. Annales de l'Institut Fourier.
46(1), 89-110.
-
del Campo, A. M., Sottile, F., & Williams, R. L.
(2023).
Classification of Schubert Galois Groups in Gr(4,9). Arnold Mathematical Journal.
1-41.
-
book
-
Sottile, F.
(2011).
Real Solutions to Equations from Geometry. American Mathematical Soc..
-
Sottile, F.
(2011).
Real Solutions to Equations from Geometry. American Mathematical Soc..
-
chapter
-
Nash, E. D., Pir, A. F., Sottile, F., & Ying, L. i.
(2017).
The Convex Hull of Two Circles in 3. Fields Institute Communications.
Combinatorial Algebraic Geometry.
(pp. 297-319).
Springer Nature.
-
Nisse, M., & Sottile, F.
(2013).
Non-Archimedean Coamoebae. Contemporary Mathematics.
Tropical and Non-Archimedean Geometry.
(pp. 73-91).
American Mathematical Society (AMS).
-
Hillar, C., Garca-Puente, L., Martn del Campo, A., Ruffo, J., Teitler, Z., Johnson, S. L., & Sottile, F.
(2010).
Experimentation at the frontiers of reality in Schubert calculus. Contemporary Mathematics.
Gems in Experimental Mathematics.
(pp. 365-380).
American Mathematical Society (AMS).
-
Emiris, I. Z., Sottile, F., & Theobald, T.
(2009).
List of Workshop Participants. Ima Volumes in Mathematics and Its Applications.
Nonlinear Computational Geometry.
(pp. 235-239).
Springer Nature.
-
Sottile, F., & Theobald, T.
(2008).
Line problems in nonlinear computational geometry. Contemporary Mathematics.
Surveys on Discrete and Computational Geometry.
(pp. 411-432).
American Mathematical Society (AMS).
-
Roby, T., Sottile, F., Stroomer, J., & West, J.
(2000).
Jeux de tableaux. Formal Power Series and Algebraic Combinatorics.
(pp. 332-343).
Springer Nature.
-
Nash, E. D., Pir, A. F., Sottile, F., & Ying, L. i.
(2017).
The Convex Hull of Two Circles in 3. Fields Institute Communications.
Combinatorial Algebraic Geometry.
(pp. 297-319).
Springer Nature.
-
conference paper
-
Sottile, F.
(2020).
General witness sets for numerical algebraic geometry. 418-425.
-
del Campo, A. M., & Sottile, F.
(2016).
Experimentation in the Schubert Calculus. 295-335.
-
Brooks, C. J., Del Campo, A. M., & Sottile, F.
(2012).
An inequality of Kostka numbers and Galois groups of Schubert problems. Discrete Mathematics and Theoretical Computer Science.
981-992.
-
Sottile, F., Lauve, A., & Forcey, S.
(2011).
Cofree compositions of coalgebras. Discrete Mathematics and Theoretical Computer Science.
363-374.
-
Sottile, F., & Zhu, C.
(2011).
Injectivity of 2D Toric Bzier Patches. 235-238.
-
Lam, T., Lauve, A., & Sottile, F.
(2010).
Skew Littlewood-Richardson Rules from Hopf Algebras. 355-366.
-
Sottile, F., Vakil, R., & Verschelde, J.
(2010).
Solving schubert problems with Littlewood-Richardson homotopies. 179-186.
-
Craciun, G., Garca-Puente, L. D., & Sottile, F.
(2010).
Some Geometrical Aspects of Control Points for Toric Patches. Lecture Notes in Computer Science.
111-135.
-
Sottile, F., Lauve, A., & Forcey, S.
(2009).
New Hopf Structures on Binary Trees. Discrete Mathematics and Theoretical Computer Science.
411-420.
-
Bihan, F., Rojas, J. M., & Sottile, F.
(2008).
On the sharpness of fewnomial bounds and the number of components of fewnomial hypersurfaces. Ima Volumes in Mathematics and Its Applications.
15-+.
-
Purbhoo, K., & Sottile, F.
(2006).
The Horn recursion for Schur P- and Q- functions. 267-274.
-
Sottile, F., & Theobald, T.
(2005).
Real k k -flats tangent to quadrics in R n mathbb {R}^n. Proceedings of the American Mathematical Society.
2835-2844.
-
Lenart, C., & Sottile, F.
(2003).
Skew Schubert polynomials. Proceedings of the American Mathematical Society.
3319-3328.
-
Sottile, F.
(2020).
General witness sets for numerical algebraic geometry. 418-425.
-
institutional repository document
-
Sottile, F.
(2023).
Some problems at the interface of approximation theory and algebraic geometry
-
Bates, D. J., Breiding, P., Chen, T., Hauenstein, J. D., Leykin, A., & Sottile, F.
(2023).
Numerical Nonlinear Algebra
-
Garcia, J. L., Maluccio, K., Sottile, F., & Yahl, T.
(2022).
Real solutions to systems of polynomial equations in Macaulay2
-
Faust, M., & Sottile, F.
(2022).
Critical points of discrete periodic operators
-
Sottile, F., & Yahl, T.
(2021).
Galois Groups in Enumerative Geometry and Applications
-
Leykin, A., del Campo, A. M., Sottile, F., Vakil, R., & Verschelde, J.
(2021).
Numerical Schubert Calculus in Macaulay2
-
Breiding, P., Sottile, F., & Woodcock, J.
(2020).
Euclidean distance degree and mixed volume
-
Burr, M., Sottile, F., & Walker, E.
(2020).
Numerical homotopies from Khovanskii bases
-
Brysiewicz, T., Rodriguez, J. I., Sottile, F., & Yahl, T.
(2020).
Decomposable sparse polynomial systems
-
Huang, Y., Petroulakis, G., Sottile, F., & Zelenko, I.
(2020).
Nontrivial linear projections of the Grassmannian Gr_3(C^6)
-
Sottile, F.
(2020).
General witness sets for numerical algebraic geometry
-
Brysiewicz, T., Rodriguez, J. I., Sottile, F., & Yahl, T.
(2020).
Solving Decomposable Sparse Systems
-
Li, C., Sottile, F., & Zhang, C.
(2019).
On the fundamental group of open Richardson varieties
-
Sottile, F., Williams, R., & Ying, L. i.
(2019).
Galois Groups of Composed Schubert Problems
-
Do, N. T., Kuchment, P., & Sottile, F.
(2019).
Generic properties of dispersion relations for discrete periodic operators
-
Hauenstein, J. D., Leykin, A., Rodriguez, J. I., & Sottile, F.
(2019).
A numerical toolkit for multiprojective varieties
-
DiPasquale, M., & Sottile, F.
(2019).
Bivariate Semialgebraic Splines
-
del Campo, A. M., Sottile, F., & Williams, R.
(2019).
Classification of Schubert Galois groups in Gr(4,9)
-
Duff, T., Hein, N., & Sottile, F.
(2018).
Certification for Polynomial Systems via Square Subsystems
-
Li, C., Ravikumar, V., Sottile, F., & Yang, M.
(2018).
A geometric proof of an equivariant Pieri rule for flag manifolds
-
Pir, A., & Sottile, F.
(2018).
Irrational toric varieties and secondary polytopes
-
Nisse, M., & Sottile, F.
(2018).
Describing Amoebas
-
Leykin, A., del Campo, A. M., Sottile, F., Vakil, R., & Verschelde, J.
(2018).
Numerical Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm
-
Sottile, F.
(2017).
Ibadan Lectures on Toric Varieties
-
Nash, E. D., Pir, A. F., Sottile, F., & Ying, L. i.
(2016).
Convex Hull of Two Circles in R^3
-
Huang, Y., Sottile, F., & Zelenko, I.
(2016).
Injectivity of generalized Wronski maps
-
Leykin, A., Rodriguez, J. I., & Sottile, F.
(2016).
Trace test
-
Sottile, F.
(2016).
Real Algebraic Geometry for Geometric Constraints
-
Hauenstein, J. D., Rodriguez, J. I., & Sottile, F.
(2016).
Numerical computation of Galois groups
-
DiPasquale, M., Sottile, F., & Sun, L.
(2016).
Semialgebraic Splines
-
Morrison, A., & Sottile, F.
(2015).
Two Murnaghan-Nakayama rules in Schubert calculus
-
Adeyemo, P., & Sottile, F.
(2015).
Equivariant cohomology theories and the pattern map
-
Bates, D. J., Hauenstein, J. D., Niemerg, M. E., & Sottile, F.
(2015).
Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials
-
Hein, N., & Sottile, F.
(2015).
A lifted square formulation for certifiable Schubert calculus
-
Nisse, M., & Sottile, F.
(2014).
Higher convexity for complements of tropical varieties
-
Adeyemo, P., & Sottile, F.
(2014).
Cohomological consequences of the pattern map
-
Hauenstein, J. D., Hein, N., & Sottile, F.
(2014).
A primal-dual formulation for certifiable computations in Schubert calculus
-
Hein, N., Sottile, F., & Zelenko, I.
(2014).
A congruence modulo four in real Schubert calculus with isotropic flags
-
Nisse, M., & Sottile, F.
(2014).
Higher convexity of coamoeba complements
-
Assaf, S., Bergeron, N., & Sottile, F.
(2014).
A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
-
Sottile, F., & White, J.
(2013).
Double transitivity of Galois Groups in Schubert Calculus of Grassmannians
-
Postinghel, E., Sottile, F., & Villamizar, N.
(2013).
Degenerations of real irrational toric varieties
-
Hein, N., Hillar, C. J., & Sottile, F.
(2013).
Lower Bounds in Real Schubert Calculus
-
del Campo, A. M., & Sottile, F.
(2013).
Experimentation in the Schubert Calculus
-
Hauenstein, J. D., Hein, N., & Sottile, F.
(2012).
Certifiable Numerical Computations in Schubert Calculus
-
Hein, N., Sottile, F., & Zelenko, I.
(2012).
A congruence modulo four in real Schubert calculus
-
Hauenstein, J. D., & Sottile, F.
(2012).
Newton polytopes and witness sets
-
Brooks, C. J., del Campo, A. M., & Sottile, F.
(2012).
Galois groups of Schubert problems of lines are at least alternating
-
Brooks, C. J., del Campo, A. M., & Sottile, F.
(2012).
An inequality of Kostka numbers and Galois groups of Schubert problems
-
Passare, M., & Sottile, F.
(2012).
Discriminant coamoebas through homology
-
Hillar, C. J., & Sottile, F.
(2011).
Complex static skew-symmetric output feedback control
-
Nisse, M., & Sottile, F.
(2011).
Non-Archimedean coamoebae
-
Hein, N., Hillar, C. J., del Campo, A. M., Sottile, F., & Teitler, Z.
(2011).
The monotone secant conjecture in the real Schubert calculus
-
Sottile, F., & Zhu, C.
(2011).
Injectivity of 2D Toric Bzier Patches
-
Nisse, M., & Sottile, F.
(2011).
The Phase Limit Set of a Variety
-
Soprunova, E., & Sottile, F.
(2011).
Lower bounds in real algebraic geometry and orientability of real toric varieties
-
Forcey, S., Lauve, A., & Sottile, F.
(2010).
Cofree compositions of coalgebras
-
Forcey, S., Lauve, A., & Sottile, F.
(2010).
Cofree compositions of coalgebras (extended abstract)
-
Hauenstein, J. D., & Sottile, F.
(2010).
alphaCertified: certifying solutions to polynomial systems
-
Rusek, K., Shakalli, J., & Sottile, F.
(2010).
Dense Fewnomials
-
Garcia-Puente, L., Hein, N., Hillar, C. J., del Campo, A. M., Ruffo, J., Sottile, F., & Teitler, Z.
(2010).
The Secant Conjecture in the real Schubert calculus
-
Garcia-Puente, L. D., Sottile, F., & Zhu, C.
(2010).
Toric degenerations of Bezier patches
-
Elizondo, E. J., Lima-Filho, P., Sottile, F., & Teitler, Z.
(2010).
Arithmetic toric varieties
-
Sottile, F., Vakil, R., & Verschelde, J.
(2010).
Solving Schubert Problems with Littlewood-Richardson Homotopies
-
Sanyal, R., Sottile, F., & Sturmfels, B.
(2009).
Orbitopes
-
Forcey, S., Lauve, A., & Sottile, F.
(2009).
Hopf structures on the multiplihedra
-
Forcey, S., Lauve, A., & Sottile, F.
(2009).
New Hopf Structures on Binary Trees (Extended Abstract)
-
Lam, T., Lauve, A., & Sottile, F.
(2009).
Skew Littlewood-Richardson rules from Hopf algebras
-
Sottile, F.
(2009).
Frontiers of Reality in Schubert Calculus
-
Hillar, C., Garcia-Puente, L., del Campo, A. M., Ruffo, J., Teitler, Z., Johnson, S. L., & Sottile, F.
(2009).
Experimentation at the Frontiers of Reality in Schubert Calculus
-
Bihan, F., & Sottile, F.
(2009).
Fewnomial bounds for completely mixed polynomial systems
-
Craciun, G., Garcia-Puente, L., & Sottile, F.
(2008).
Some geometrical aspects of control points for toric patches
-
von Bothmer, H., Ranestad, K., & Sottile, F.
(2008).
Linear precision for toric surface patches
-
Bihan, F., & Sottile, F.
(2008).
Betti number bounds for fewnomial hypersurfaces via stratified Morse theory
-
Sottile, F.
(2008).
General isotropic flags are general (for Grassmannian Schubert calculus)
-
Longinetti, M., Sgheri, L., & Sottile, F.
(2007).
Convex Hulls of Orbits and Orientations of a Moving Protein Domain
-
Leykin, A., & Sottile, F.
(2007).
Galois groups of Schubert problems via homotopy computation
-
Purbhoo, K., & Sottile, F.
(2007).
A Littlewood-Richardson rule for Grassmannian Permutations
-
Bates, D. J., Bihan, F., & Sottile, F.
(2007).
Bounds on the number of real solutions to polynomial equations
-
Bihan, F., & Sottile, F.
(2007).
Gale duality for complete intersections
-
Garcia-Puente, L., & Sottile, F.
(2007).
Linear precision for parametric patches
-
Bihan, F., Rojas, J. M., & Sottile, F.
(2007).
On the Sharpness of fewnomial bound and the number of components of a fewnomial hypersurface
-
Sottile, F., & Theobald, T.
(2006).
Line problems in nonlinear computational geometry
-
Sottile, F.
(2006).
Real solutions to equations from geometry
-
Sottile, F.
(2006).
New fewnomial upper bounds from Gale dual polynomial systems
-
Purbhoo, K., & Sottile, F.
(2006).
The recursive nature of cominuscule Schubert calculus
-
Purbhoo, K., & Sottile, F.
(2006).
The Horn recursion for Schur P- and Q- functions: Extended Abstract
-
Braden, T., Chen, L., & Sottile, F.
(2006).
The Equivariant Chow rings of quot schemes
-
Ruffo, J., Sivan, Y., Soprunova, E., & Sottile, F.
(2005).
Experimentation and conjectures in the real Schubert calculus for flag manifolds
-
Beck, M., Haase, C., & Sottile, F.
(2005).
Theorems of Brion, Lawrence, and Varchenko on rational generating functions for cones
-
Ortiz-Rodrguez, A., & Sottile, F.
(2005).
Real Hessian Curves
-
Brnnimann, H., Devillers, O., Lazard, S., & Sottile, F.
(2005).
Line tangents to four triangles in three-dimensional space
-
Bertrand, B., Bihan, F., & Sottile, F.
(2005).
Polynomial systems with few real zeroes
-
Ruffo, J., Sivan, Y., Soprunova, E., & Sottile, F.
(2005).
Experimentation and conjectures in the real Schubert calculus for flag manifolds (extended abstract)
-
Beck, M., & Sottile, F.
(2005).
Irrational proofs for three theorems of Stanley
-
Sottile, F.
(2005).
Tropical Interpolation
-
Soprunova, E., & Sottile, F.
(2004).
Lower Bounds for Real Solutions to Sparse Polynomial Systems
-
Goodman, J. E., Holmsen, A., Pollack, R., Ranestad, K., & Sottile, F.
(2004).
Cremona Convexity, Frame Convexity, and a Theorem of Santal
-
Aguiar, M., & Sottile, F.
(2004).
Structure of the Loday-Ronco Hopf algebra of trees
-
Lenart, C., & Sottile, F.
(2004).
A Pieri-type formula for the K-theory of a flag manifold
-
Lenart, C., Robinson, S., & Sottile, F.
(2004).
Grothendieck polynomials via permutation patterns and chains in the Bruhat order
-
Powers, V., Reznick, B., Scheiderer, C., & Sottile, F.
(2004).
A New Proof of Hilbert's Theorem on Ternary Quartics
-
Aguiar, M., & Sottile, F.
(2004).
Cocommutative Hopf algebras of permutations and trees
-
Buch, A. S., Sottile, F., & Yong, A.
(2003).
Quiver coefficients are Schubert structure constants
-
Aguiar, M., Bergeron, N., & Sottile, F.
(2003).
Combinatorial Hopf algebras and generalized Dehn-Sommerville relations
-
Brnnimann, H., Everett, H., Lazard, S., Sottile, F., & Whitesides, S.
(2003).
The number of transversals to line segments in R^3
-
Megyesi, G., & Sottile, F.
(2003).
The envelope of lines meeting a fixed line that are tangent to two spheres
-
Sottile, F.
(2002).
Toric ideals, real toric varieties, and the algebraic moment map
-
Kharlamov, V., & Sottile, F.
(2002).
Maximally inflected real rational curves
-
Sottile, F., & Theobald, T.
(2002).
Real k-flats tangent to quadrics in R^n
-
Megyesi, G., Sottile, F., & Theobald, T.
(2002).
Common transversals and tangents to two lines and two quadrics in P^3
-
Aguiar, M., & Sottile, F.
(2002).
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations
-
Aguiar, M., & Sottile, F.
(2002).
Structure of the Malvenuto-Reutenauer Hopf algebra of permutations (Extended Abstract)
-
Lenart, C., & Sottile, F.
(2002).
Skew Schubert polynomials
-
Sottile, F.
(2001).
Enumerative Real Algebraic Geometry
-
Sottile, F., & Theobald, T.
(2001).
Lines Tangent to 2n-2 spheres in R^n
-
Sottile, F.
(2001).
Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials
-
Sottile, F.
(2000).
Rational curves on Grassmannians: systems theory, reality, and transversality
-
Sottile, F.
(2000).
Elementary Transversality in the Schubert calculus in any Characteristic
-
Sottile, F.
(2000).
An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2
-
Roby, T., Sottile, F., Stroomer, J., & West, J.
(2000).
Complementary Algorithms For Tableaux
-
Sottile, F.
(2000).
Some real and unreal enumerative geometry for flag manifolds
-
Bergeron, N., Mykytiuk, S., Sottile, F., & van Willigenburg, S.
(2000).
Non-commutative Pieri operators on posets
-
Sottile, F., & Sturmfels, B.
(1999).
A sagbi basis for the quantum Grassmannian
-
Sottile, F.
(1999).
Real Rational Curves in Grassmannians
-
Sottile, F.
(1999).
The special Schubert calculus is real
-
Sottile, F.
(1999).
Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro
-
Bergeron, N., Mykytiuk, S., Sottile, F., & van Willigenburg, S.
(1999).
Shifted Quasi-Symmetric Functions and the Hopf algebra of peak functions
-
Bergeron, N., & Sottile, F.
(1998).
A Pieri-type formula for isotropic flag manifolds
-
Bergeron, N., & Sottile, F.
(1997).
A Monoid for the Universal K-Bruhat Order
-
Bergeron, N., & Sottile, F.
(1997).
Hopf Algebras and Edge-Labeled Posets
-
Bergeron, N., & Sottile, F.
(1997).
Skew Schubert functions and the Pieri formula for flag manifolds
-
Sottile, F.
(1997).
Pieri-type formulas for maximal isotropic Grassmannians via triple intersections
-
Huber, B., Sottile, F., & Sturmfels, B.
(1997).
Numerical Schubert calculus
-
Bergeron, N., & Sottile, F.
(1997).
Identities of Structure Constants for Schubert polynomials and Orders on S_n
-
Bergeron, N., & Sottile, F.
(1997).
Schubert polynomials, the Bruhat order, and the geometry of flag manifolds
-
Rosenthal, J., & Sottile, F.
(1997).
Some Remarks on Real and Complex Output Feedback
-
Sottile, F.
(1996).
Enumerative geometry for real varieties
-
Sottile, F.
(1996).
Real enumerative geometry and effective algebraic equivalence
-
Sottile, F.
(1996).
Pieri's Formula Via Explicit Rational Equivalence
-
Sottile, F.
(1995).
Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective Space
-
Sottile, F.
(1995).
Pieri's rule for flag manifolds and Schubert polynomials
-
Benedetti, C., Bergeron, N., Colmenarejo, L., Saliola, F., & Sottile, F.
A quantum Murnaghan--Nakayama rule for the flag manifold
-
Nisse, M., & Sottile, F.
Phase limit sets of linear spaces and discriminants
-
Sottile, F.
(2023).
Some problems at the interface of approximation theory and algebraic geometry
Research
principal investigator on
co-principal investigator on
Teaching
teaching activities
- MATH220 Foundations Of Math Instructor
- MATH221 Hnr-sev Variable Calculus Instructor
- MATH300 Foundations Of Math Instructor
- MATH300 Foundations Of Math Instructor
- MATH491 Hnr-research Instructor
- MATH629 History Of Mathematics Instructor
- MATH645 Survey Math Problems I Instructor
- MATH648 Computational Alg Geom Instructor
- MATH653 Algebra I Instructor
- MATH654 Algebra Ii Instructor
- MATH662 Seminar In Algebra Instructor
- MATH666 Seminar In Geometry Instructor
- MATH685 Directed Studies Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Buczynska, Weronika J. (2010-10). Phylogenetic Toric Varieties on Graphs.
-
Hein, Nickolas Jason (2013-06). Reality and Computation in Schubert Calculus.
-
Irving, Corey 1977- (2012-11). Wachspress Varieties.
-
Martin Del Campo Sanchez, Abraham (2012-10). Galois Groups of Schubert Problems.
-
Pir, Ata Firat (2018-08). Irrational Toric Varieties.
-
Ruffo, James Vincent (2009-05). A straightening law for the Drinfel'd Lagrangian Grassmannian.
-
Williams, Robert Lee (2017-08). Restrictions on Galois Groups of Schubert Problems.
Background
education and training
- Ph.D. in Mathematics, University of Chicago - (Chicago, Illinois, United States) 1994
- M.S. in Mathematics, University of Chicago - (Chicago, Illinois, United States) 1989
- M.A. in Maths, University of Cambridge - (Cambridge, United Kingdom) 1986
- B.S. in Physics, Michigan State University - (East Lansing, Michigan, United States) 1985
awards and honors
- Fellow, conferred by American Mathematical Society - (Providence, Rhode Island, United States), 2013
- Kavli Frontiers of Science Fellow, conferred by National Academy of Sciences - (Washington D.C., District of Columbia, United States), 2007
- Faculty Early Career Development (CAREER) Program, conferred by National Science Foundation - (Arlington, Virginia, United States), 2005
- Clay Research Scholars, conferred by Clay Mathematics Institute - (Peterborough, New Hampshire, United States), 2003
- Faculty Early Career Development (CAREER) Program, conferred by National Science Foundation - (Arlington, Virginia, United States), 2002
Contact
first name
- Frank
has last name
- Sottile
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- sottile@tamu.edu