Allen Knutson

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All published works

Action	Title	Year	Authors
+ PDF Chat	Generic pipe dreams, lower-upper varieties, and Schwartz-MacPherson classes	2024	Allen Knutson Paul Zinn-Justin
+ PDF Chat	The commutant of divided difference operators, Klyachko's genus, and the comaj statistic	2024	Christian Gaetz Rebecca Goldin Allen Knutson
+	Schubert calculus and quiver varieties	2023	Allen Knutson
+	Schubert puzzles and integrability III: separated descents	2023	Allen Knutson Paul Zinn-Justin
+ PDF Chat	A Bruhat Atlas for the Mehta–van der Kallen Stratification of T∗GLn/B	2022	Allen Knutson Steven V Sam
+ PDF Chat	Schubert Polynomials, Pipe Dreams, Equivariant Classes, and a Co-transition Formula	2022	Allen Knutson
+	The Duistermaat-Heckman formula and Chern-Schwartz-MacPherson classes	2022	Allen Knutson
+	Schubert puzzles and integrability II: multiplying motivic Segre classes	2021	Allen Knutson Paul Zinn-Justin
+ PDF	The Mirković–Vilonen basis and Duistermaat–Heckman measures	2021	Pierre Baumann Joel Kamnitzer Allen Knutson
+	Schubert structure operators and $K^\ast_T (G/B)$	2021	Rebecca Goldin Allen Knutson
+	Schubert puzzles and integrability II: multiplying motivic Segre classes	2021	Allen Knutson Paul Zinn-Justin
+	A Bruhat atlas for the Mehta-van der Kallen stratification of $T^* GL_n/B$	2021	Allen Knutson Steven V Sam
+	Schubert structure operators and K_T(G/B)	2019	Rebecca Goldin Allen Knutson
+ PDF	Grassmann–Grassmann conormal varieties, integrability, and plane partitions	2019	Allen Knutson Paul Zinn-Justin
+ PDF Chat	The Mirkovic-Vilonen basis and Duistermaat-Heckman measures	2019	Pierre Baumann Joel Kamnitzer Allen Knutson
+ PDF Chat	Three combinatorial formulas for type A quiver polynomials and K-polynomials	2019	Ryan Kinser Allen Knutson Jenna Rajchgot
+	Restricting Schubert classes to symplectic Grassmannians using self-dual puzzles	2019	Iva Halacheva Allen Knutson Paul Zinn-Justin
+	Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula	2019	Allen Knutson
+	Schubert structure operators and K_T(G/B)	2019	Rebecca Goldin Allen Knutson
+ PDF	Schubert calculus and puzzles	2018	Allen Knutson
+ PDF Chat	Randomly Juggling Backwards	2018	Allen Knutson
+	Restricting Schubert classes to symplectic Grassmannians using self-dual puzzles	2018	Iva Halacheva Allen Knutson Paul Zinn-Justin
+ PDF Chat	The Multidegree of the Multi-Image Variety	2017	Laura Escobar Allen Knutson
+	Schubert puzzles and integrability I: invariant trilinear forms	2017	Allen Knutson Paul Zinn-Justin
+	The multidegree of the multi-image variety	2017	Laura Escobar Allen Knutson
+	Grassmann-Grassmann conormal varieties, integrability, and plane partitions	2016	Allen Knutson Paul Zinn-Justin
+	Randomly juggling backwards	2016	Allen Knutson
+	A K_T-deformation of the ring of symmetric functions	2015	Allen Knutson Mathias Lederer
+	A K_T-deformation of the ring of symmetric functions	2015	Allen Knutson Mathias Lederer
+	Positive formulae for K-types of SL_3(R)-irreps and a Blattner formula for smooth K-orbit closures	2014	Allen Knutson
+	The Brauer loop scheme and orbital varieties	2014	Allen Knutson Paul Zinn-Justin
+	Schubert calculus and shifting of interval positroid varieties	2014	Allen Knutson
+ PDF	Interval positroid varieties and a deformation of the ring of symmetric functions	2014	Allen Knutson Mathias Lederer
+	Positive formulae for K-types of SL_3(R)-irreps and a Blattner formula for smooth K-orbit closures	2014	Allen Knutson
+ PDF	Positroid varieties: juggling and geometry	2013	Allen Knutson Thomas Lam David E Speyer
+ PDF	Singularities of Richardson varieties	2013	Allen Knutson Alexander Woo Alexander Yong
+ PDF Chat	Projections of Richardson varieties	2012	Allen Knutson Thomas Lam David E Speyer
+	Singularities of Richardson varieties	2012	Allen Knutson Alexander Woo Alexander Yong
+	A stratification of the space of allk-planes inC n	2012	Allen Knutson
+ PDF	Product and Puzzle Formulae for $GL_n$ Belkale-Kumar Coefficients	2011	Allen Knutson Kevin Purbhoo
+	Positroid Varieties: Juggling and Geometry	2011	Allen Knutson Thomas Lam David E Speyer
+	Product and puzzle formulae for GL_n Belkale-Kumar coefficients	2010	Allen Knutson Kevin Purbhoo
+	Projections of Richardson Varieties	2010	Allen Knutson Thomas Lam David E Speyer
+	The Brauer loop scheme and orbital varieties	2010	Allen Knutson Paul Zinn-Justin
+	Puzzles, positroid varieties, and equivariant K-theory of Grassmannians	2010	Allen Knutson
+ PDF Chat	Complete moduli spaces of branchvarieties	2010	Valery Alexeev Allen Knutson
+ PDF	A Compactly Supported Formula for Equivariant Localization and Simplicial Complexes of Bialynicki-Birula Decompositions	2010	Allen Knutson
+	Projections of Richardson Varieties	2010	Allen Knutson Thomas Lam David E Speyer
+	Product and puzzle formulae for GL_n Belkale-Kumar coefficients	2010	Allen Knutson Kevin Purbhoo
+	The Brauer loop scheme and orbital varieties	2010	Allen Knutson Paul Zinn-Justin
+	Frobenius splitting and Möbius inversion	2009	Allen Knutson
+	Frobenius splitting, point-counting, and degeneration	2009	Allen Knutson
+	Compatibly Frobenius split subschemes are rigid	2009	Allen Knutson
+ PDF Chat	Gröbner geometry of vertex decompositions and of flagged tableaux	2009	Allen Knutson Ezra Miller Alexander Yong
+	Positroid varieties I: juggling and geometry	2009	Allen Knutson Thomas Lam David E Speyer
+ PDF Chat	Schubert Patches Degenerate to Subword Complexes	2008	Allen Knutson
+	Schubert patches degenerate to subword complexes	2008	Allen Knutson
+	A compactly supported formula for equivariant localization, and, simplicial complexes of Bialynicki-Birula decompositions	2008	Allen Knutson
+	Tableau complexes	2008	Allen Knutson Ezra Miller Alexander Yong
+	Schubert patches degenerate to subword complexes	2008	Allen Knutson
+	A compactly supported formula for equivariant localization, and, simplicial complexes of Bialynicki-Birula decompositions	2008	Allen Knutson
+ PDF Chat	Orbifold cohomology of torus quotients	2007	Rebecca Goldin Tara S. Holm Allen Knutson
+	A scheme related to the Brauer loop model	2007	Allen Knutson Paul Zinn-Justin
+	Automatically reduced degenerations of automatically normal varieties	2007	Allen Knutson
+ PDF Chat	Four positive formulae for type A quiver polynomials	2006	Allen Knutson Ezra Miller Mark Shimozono
+	Complete moduli spaces of branchvarieties	2006	Valery Alexeev Allen Knutson
+	Kempf collapsing and quiver loci	2006	Allen Knutson Mark Shimozono
+ PDF	Balanced Normal Cones and Fulton-MacPherson's Intersection Theory	2006	Allen Knutson
+	Complete moduli spaces of branchvarieties	2006	Valery Alexeev Allen Knutson
+	Balanced normal cones and Fulton-MacPherson's intersection theory	2005	Allen Knutson
+ PDF	Gröbner geometry of Schubert polynomials	2005	Allen Knutson Ezra Miller
+	A scheme related to the Brauer loop model	2005	Allen Knutson Paul Zinn-Justin
+	Orbifold cohomology of torus quotients	2005	Rebecca Goldin Tara S. Holm Allen Knutson
+ PDF	Problems from the Cottonwood Room	2005	Matthias Beck Beifang Chen Lenny Fukshansky Christian Haase Allen Knutson Bruce Reznick Sinai Robins Annette Schürmann
+	Gröbner geometry of vertex decompositions and of flagged tableaux	2005	Allen Knutson Ezra Miller Alexander Yong
+	Tableau complexes	2005	Allen Knutson Ezra Miller Alexander Yong
+	A scheme related to the Brauer loop model	2005	Allen Knutson Paul Zinn-Justin
+	Orbifold cohomology of torus quotients	2005	Rebecca Goldin Tara S. Holm Allen Knutson
+	Balanced normal cones and Fulton-MacPherson's intersection theory	2005	Allen Knutson
+	Some schemes related to the commuting variety	2004	Allen Knutson
+ PDF	A Positive Proof of the Littlewood-Richardson Rule using the Octahedron Recurrence	2004	Allen Knutson Terence Tao Christopher T. Woodward
+	None	2004	Allen Knutson Alexander Yong
+	A formula for K-theory truncation Schubert calculus	2004	Allen Knutson Alexander Yong
+	The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone	2003	Allen Knutson Terence Tao Christopher T. Woodward
+ PDF Chat	Puzzles and (equivariant) cohomology of Grassmannians	2003	Allen Knutson Terence Tao
+	Subword complexes in Coxeter groups	2003	Allen Knutson Ezra Miller
+	A positive proof of the Littlewood-Richardson rule using the octahedron recurrence	2003	Allen Knutson Terence Tao Christopher T. Woodward
+	Some schemes related to the commuting variety	2003	Allen Knutson
+	A Schubert calculus recurrence from the noncomplex W-action on G/B	2003	Allen Knutson
+	Four positive formulae for type A quiver polynomials	2003	Allen Knutson Ezra Miller Mark Shimozono
+	Subword complexes in Coxeter groups	2003	Allen Knutson Ezra Miller
+	A positive proof of the Littlewood-Richardson rule using the octahedron recurrence	2003	Allen Knutson Terence Tao Christopher T. Woodward
+	Some schemes related to the commuting variety	2003	Allen Knutson
+	Gr\"obner geometry of Schubert polynomials	2001	Allen Knutson Ezra Miller
+ PDF	Descent-Cycling in Schubert Calculus	2001	Allen Knutson
+	Puzzles and (equivariant) cohomology of Grassmannians	2001	Allen Knutson Terence Tao
+	The honeycomb model of GL(n) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone	2001	Allen Knutson Terence Tao Christopher T. Woodward
+	Lectures on Symplectic Geometry	2001	Ana Cannas da Silva Allen Knutson Chris Woodward David S. Metzler Eckhard Meinrenken Elisa Prato Eugene Lerman Jonathan Weitsman Lisa C. Jeffrey Reyer Sjamaar
+	Gröbner geometry of Schubert polynomials	2001	Allen Knutson Ezra Miller
+	The symplectic and algebraic geometry of Horn's problem	2000	Allen Knutson
+	Descent-cycling in Schubert calculus	2000	Allen Knutson
+ PDF Chat	A limit of toric symplectic forms that has no periodic Hamiltonians	2000	Jean-Claude Hausmann Allen Knutson
+	Honeycombs and sums of Hermitian matrices	2000	Allen Knutson Terence Tao
+	Descent-cycling in Schubert calculus	2000	Allen Knutson
+	Equivariant K-theory and Equivariant Cohomology	1999	Ioanid Roşu Allen Knutson
+	Cohomology rings of symplectic cuts	1999	Jean-Claude Hausmann Allen Knutson
+ PDF	The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture	1999	Allen Knutson Terence Tao
+ PDF Chat	Equivariant sheaves	1999	Allen Knutson Eric Sharpe
+	A Littelmann-type formula for Duistermaat-Heckman measures	1999	Allen Knutson
+	The symplectic and algebraic geometry of Horn's problem	1999	Allen Knutson
+	Equivariant K-theory and Equivariant Cohomology	1999	Ioanid Roşu Allen Knutson
+	Apiary views of the Berenstein-Zelevinsky polytope, and Klyachko's saturation conjecture	1998	Allen Knutson Terence Tao
+	The honeycomb model of the Berenstein-Zelevinsky polytope I. Klyachko's saturation conjecture	1998	Allen Knutson Terence Tao
+	The cohomology ring of symplectic cuts	1998	Jean-Claude Hausmann Allen Knutson
+ PDF	Sheaves on toric varieties for physics	1998	Allen Knutson Eric Sharpe
+ PDF	The cohomology ring of polygon spaces	1998	Jean-Claude Hausmann Allen Knutson
+	A limit of toric symplectic forms that has no periodic Hamiltonians	1998	Jean-Claude Hausmann Allen Knutson
+	The honeycomb model of GL(n) tensor products I: proof of the saturation conjecture	1998	Allen Knutson Terence Tao
+	The cohomology ring of polygon spaces	1997	Jean-Claude Hausmann Allen Knutson
+	The cohomology ring of polygon spaces	1997	Jean-Claude Hausmann Allen Knutson
+	Polygon spaces and grassmannians	1997	Jean-Claude Hausmann Allen Knutson
+	Polygon spaces and Grassmannians	1996	Jean-Claude Hausmann Allen Knutson
+	Polygon spaces and Grassmannians	1996	Jean-Claude Hausmann Allen Knutson

Common Coauthors

Coauthor	Papers Together
Paul Zinn-Justin	15
Ezra Miller	12
Terence Tao	12
Jean-Claude Hausmann	10
Alexander Yong	8
Rebecca Goldin	7
David E Speyer	6
Christopher T. Woodward	5
Thomas Lam	4
Tara S. Holm	3
Kevin Purbhoo	3
Mark Shimozono	3
Mathias Lederer	3
Valery Alexeev	3
Iva Halacheva	2
Joel Kamnitzer	2
Pierre Baumann	2
Steven V Sam	2
Alexander Woo	2
Eric Sharpe	2
Thomas Lam	2
Ioanid Roşu	2
Eugene Lerman	1
Eckhard Meinrenken	1
João T.V. Matos	1
Ana Cannas da Silva	1
Beifang Chen	1
Rahul Pandharipande	1
Henrique Bursztyn	1
Bruce Reznick	1
Shaun Martin	1
Olga Radko	1
David S. Metzler	1
Tolga Etgü	1
Christian Gaetz	1
Jenna Rajchgot	1
Peter Přibík	1
Sarah Packman	1
Chris Tuffley	1
Ina Lindemann	1
Matthias Beck	1
Catriona Byrne	1
Christian Haase	1
Jiang-Hua Lu	1
Alan Weinstein	1
David Martínez	1
Susan Harrington	1
Laura De Marco	1
Stephen J. Bigelow	1
Megumi Harada	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	Gröbner geometry of Schubert polynomials	2005	Allen Knutson Ezra Miller	23
+	Flags, Schubert polynomials, degeneracy loci, and determinantal formulas	1992	William Fulton	20
+ PDF Chat	Puzzles and (equivariant) cohomology of Grassmannians	2003	Allen Knutson Terence Tao	16
+	Subword complexes in Coxeter groups	2003	Allen Knutson Ezra Miller	15
+	Combinatorial Commutative Algebra	2005	Ezra Miller Bernd Sturmfels	14
+ PDF	Commutative algebra with a view toward algebraic geometry	1996	David Eisenbud	12
+	Cohomology of Quotients in Symplectic and Algebraic Geometry	1984	Frances Kirwan	11
+ PDF	The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture	1999	Allen Knutson Terence Tao	11
+	Young Tableaux: With Applications to Representation Theory and Geometry	1996	William Fulton	10
+ PDF	A Littlewood-Richardson rule for the K-theory of Grassmannians	2002	Anders Skovsted Buch	10
+	Bruhat order of Coxeter groups and shellability	1982	Anders Björner Michelle L. Wachs	10
+ PDF	RC-Graphs and Schubert Polynomials	1993	Nantel Bergeron Sara Billey	10
+	On the variety of a highest weight module	1984	Anthony Joseph	9
+	Schubert varieties are arithmetically Cohen-Macaulay	1985	A. Ramanathan	9
+ PDF	Some Combinatorial Properties of Schubert Polynomials	1993	Sara Billey William Jockusch Richard P. Stanley	8
+ PDF Chat	Positivity in equivariant Schubert calculus	2001	William Graham	8
+	A DECOMPOSITION PROPERTY FOR SIMPLICIAL COMPLEXES AND ITS RELATION TO DIAMETERS AND SHELLINGS	1979	Louis J. Billera J. Scott Provan	8
+	Introduction to Toric Varieties.	1993	William Fulton	8
+	The Yang-Baxter equation, symmetric functions, and Schubert polynomials	1996	Sergey Fomin Anatol N. Kirillov	8
+	Equivariant Chow groups for torus actions	1997	Michel Brion	7
+	Equivariant cohomology, Koszul duality, and the localization theorem	1997	Mark Goresky Robert Kottwitz Robert MacPherson	7
+ PDF	Eigenvalues of sums of Hermitian matrices	1962	Alfred Horn	7
+	Kostant polynomials and the cohomology ring for G/B	1999	Sara Billey	6
+ PDF Chat	Chern class formulas for quiver varieties	1999	Anders Skovsted Buch William Fulton	6
+ PDF Chat	Grothendieck classes of quiver varieties	2002	Anders Skovsted Buch	6
+ PDF	Eigenvalues, invariant factors, highest weights, and Schubert calculus	2000	William Fulton	6
+ PDF	Positivity and Kleiman transversality in equivariant $K$-theory of homogeneous spaces	2010	Dave Anderson Stephen Griffeth Ezra Miller	6
+	The nil Hecke ring and cohomology of GP for a Kac-Moody group G	1986	Bertram Kostant Shrawan Kumar	6
+	Frobenius Splitting Methods in Geometry and Representation Theory	2005	Michel Brion Shrawan Kumar	6
+	The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone	2003	Allen Knutson Terence Tao Christopher T. Woodward	6
+	Reflection Groups and Coxeter Groups	1990	James E. Humphreys	6
+	Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces	1994	Victor Guillemin	6
+ PDF	The symplectic geometry of polygons in Euclidean space	1996	Michael Kapovich John J. Millson	5
+	The moment map and equivariant cohomology	1984	Michael Atiyah R. Bott	5
+	Initial Complexes of Prime Ideals	1995	Michael Kalkbrener Bernd Sturmfels	5
+ PDF	A geometric Littlewood–Richardson rule	2006	Ravi Vakil	5
+ PDF	Canonical bases arising from quantized enveloping algebras	1990	G. Lusztig	5
+	LS algebras and application to Schubert varieties	2000	Rocco Chirivì	5
+	Homotopy properties of greedoids	1985	Anders Björner Bernhard Körte László Lovász	5
+	Gröbner bases and Stanley decompositions of determinantal rings	1990	Bernd Sturmfels	5
+ PDF	None	1992	Arkady Berenstein Andrei Zelevinsky	5
+ PDF	On the Number of Reduced Decompositions of Elements of Coxeter Groups	1984	Richard P. Stanley	4
+	A scheme related to the Brauer loop model	2007	Allen Knutson Paul Zinn-Justin	4
+	Projective normality of flag varieties and Schubert varieties	1985	S. Ramanan A. Ramanathan	4
+ PDF Chat	Inhomogenous Model of Crossing Loops and Multidegrees of Some Algebraic Varieties	2005	Philippe Di Francesco Paul Zinn-Justin	4
+	Supersymmetry and Equivariant de Rham Theory	1999	Victor Guillemin Shlomo Sternberg Jochen Brüning	4
+ PDF Chat	The algebraic Bethe ansatz for rational braid-monoid lattice models	1997	M.J. Martins P B Ramos	4
+	Note on a paper of Samuel concerning asymptotic properties of ideals	1957	Masayoshi Nagata	4
+	Equivariant intersection theory	1998	Dan Edidin William Graham	4
+ PDF Chat	Four positive formulae for type A quiver polynomials	2006	Allen Knutson Ezra Miller Mark Shimozono	4