Joel Kamnitzer

Joel Kamnitzer is a Canadian mathematician who specializes in geometric representation theory. He is a professor at the University of Toronto, where his research focuses on areas such as quiver varieties, Schubert varieties, and the combinatorics underlying representation theory. He completed his PhD at the University of California, Berkeley in 2005 under the supervision of Allen Knutson. Beyond his scholarly articles, Kamnitzer is recognized for contributions that bridge geometric and combinatorial methods in the study of Lie algebras and related structures.

All published works

Action	Title	Year	Authors
+ PDF Chat	Fixed points of reverse Hessenberg convolution varieties	2024	Joel Kamnitzer
+	Heaps, crystals, and preprojective algebra modules	2024	Anne Dranowski Balázs Elek Joel Kamnitzer Calder Morton-Ferguson
+ PDF Chat	Gaudin models and moduli space of flower curves	2024	Aleksei Ilin Joel Kamnitzer Leonid Rybnikov
+ PDF Chat	Lie algebra actions on module categories for truncated shifted yangians	2024	Joel Kamnitzer Ben Webster Alex Weekes Oded Yacobi
+	Perfect bases in representation theory: three mountains and their springs	2023	Joel Kamnitzer
+ PDF Chat	BFN Springer Theory	2023	Justin Hilburn Joel Kamnitzer Alex Weekes
+ PDF Chat	Computing fusion products of MV cycles using the Mirković–Vybornov isomorphism	2023	Roger Bai Anne Dranowski Joel Kamnitzer
+	The moduli space of cactus flower curves and the virtual cactus group	2023	Aleksei Ilin Joel Kamnitzer Yu Li Piotr Przytycki Leonid Rybnikov
+ PDF Chat	Symplectic resolutions, symplectic duality, and Coulomb branches	2022	Joel Kamnitzer
+ PDF Chat	The geometry of algebraic varieties: special issue in honour of Olivier Debarre	2022	Daniel Huybrechts Joel Kamnitzer
+ PDF Chat	Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians	2022	Joel Kamnitzer Khoa Pham Alex Weekes
+	Heaps, crystals, and preprojective algebra modules	2022	Anne Dranowski Balázs Elek Joel Kamnitzer Calder Morton-Ferguson
+	Perfect bases in representation theory: three mountains and their springs	2022	Joel Kamnitzer
+	Symplectic resolutions, symplectic duality, and Coulomb branches	2022	Joel Kamnitzer
+	Lie algebra actions on module categories for truncated shifted Yangians	2022	Joel Kamnitzer Ben Webster Alex Weekes Oded Yacobi
+ PDF Chat	The quantum Hikita conjecture	2021	Joel Kamnitzer Michael McBreen Nicholas Proudfoot
+	Associated graded of Hodge modules and categorical $${\mathfrak {sl}}_2$$ actions	2021	Sabin Cautis C. A. F. Dodd Joel Kamnitzer
+ PDF Chat	The Mirković–Vilonen basis and Duistermaat–Heckman measures	2021	Pierre Baumann Joel Kamnitzer Allen Knutson
+ PDF Chat	Crystals and monodromy of Bethe vectors	2020	Iva Halacheva Joel Kamnitzer Leonid Rybnikov Alex Weekes
+	BFN Springer Theory	2020	Justin Hilburn Joel Kamnitzer Alex Weekes
+	Hamiltonian reduction for affine Grassmannian slices	2020	Joel Kamnitzer
+	Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians	2020	Joel Kamnitzer Khoa Pham Alex Weekes
+	BFN Springer Theory	2020	Justin Hilburn Joel Kamnitzer Alex Weekes
+ PDF Chat	Highest weights for truncated shifted Yangians and product monomial crystals	2019	Joel Kamnitzer Peter Tingley Ben Webster Alex Weekes Oded Yacobi
+ PDF Chat	The Mirkovic-Vilonen basis and Duistermaat-Heckman measures	2019	Pierre Baumann Joel Kamnitzer Allen Knutson
+	On category O for affine Grassmannian slices and categorified tensor products	2019	Joel Kamnitzer Peter Tingley Ben Webster Alex Weekes Oded Yacobi
+	The quantum Hikita conjecture	2018	Joel Kamnitzer Michael McBreen Nicholas Proudfoot
+ PDF Chat	On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products	2018	Joel Kamnitzer Peter Tingley Ben Webster Alex Weekes Oded Yacobi
+	The quantum Hikita conjecture	2018	Joel Kamnitzer Michael McBreen Nicholas Proudfoot
+ PDF Chat	ON A REDUCEDNESS CONJECTURE FOR SPHERICAL SCHUBERT VARIETIES AND SLICES IN THE AFFINE GRASSMANNIAN	2017	Joel Kamnitzer Dinakar Muthiah Alex Weekes
+ PDF Chat	Quantum K-theoretic geometric Satake: the case	2017	Sabin Cautis Joel Kamnitzer
+ PDF Chat	Categorical geometric symmetric Howe duality	2017	Sabin Cautis Joel Kamnitzer
+	Comultiplication for shifted Yangians and quantum open Toda lattice	2017	Michael Finkelberg Joel Kamnitzer Khoa Pham Leonid Rybnikov Alex Weekes
+	Reducedness of affine Grassmannian slices in type A	2017	Joel Kamnitzer Dinakar Muthiah Alex Weekes Oded Yacobi
+ PDF Chat	Knot homology via derived categories of coherent sheaves IV, coloured links	2017	Sabin Cautis Joel Kamnitzer
+	Reducedness of affine Grassmannian slices in type A	2016	Joel Kamnitzer Dinakar Muthiah Alex Weekes Oded Yacobi
+	Categorical geometric symmetric Howe duality	2016	Sabin Cautis Joel Kamnitzer
+	Comultiplication for shifted Yangians and quantum open Toda lattice	2016	Michael Finkelberg Joel Kamnitzer Khoa Pham Leonid Rybnikov Alex Weekes
+	On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian	2016	Joel Kamnitzer Dinakar Muthiah Alex Weekes
+	Associated graded of Hodge modules and categorical sl_2 actions	2016	Sabin Cautis C. A. F. Dodd Joel Kamnitzer
+	A combinatorial geometric Satake equivalence	2016	Joel Kamnitzer
+	Associated graded of Hodge modules and categorical sl_2 actions	2016	Sabin Cautis C. A. F. Dodd Joel Kamnitzer
+	Categorical geometric symmetric Howe duality	2016	Sabin Cautis Joel Kamnitzer
+	Reducedness of affine Grassmannian slices in type A	2016	Joel Kamnitzer Dinakar Muthiah Alex Weekes Oded Yacobi
+	On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian	2016	Joel Kamnitzer Dinakar Muthiah Alex Weekes
+	Comultiplication for shifted Yangians and quantum open Toda lattice	2016	Michael Finkelberg Joel Kamnitzer Khoa Pham Leonid Rybnikov Alex Weekes
+	Highest weights for truncated shifted Yangians and product monomial crystals	2015	Joel Kamnitzer Peter Tingley Ben Webster Alex Weekes Oded Yacobi
+	Highest weights for truncated shifted Yangians and product monomial crystals	2015	Joel Kamnitzer Peter Tingley Ben Webster Alex Weekes Oded Yacobi
+	Knot homology via derived categories of coherent sheaves IV, coloured links	2014	Sabin Cautis Joel Kamnitzer
+ PDF Chat	Yangians and quantizations of slices in the affine Grassmannian	2014	Joel Kamnitzer Ben Webster Alex Weekes Oded Yacobi
+ PDF Chat	Webs and quantum skew Howe duality	2014	Sabin Cautis Joel Kamnitzer Scott Morrison
+	A combinatorial geometric Satake equivalence	2014	Joel Kamnitzer
+	A combinatorial geometric Satake equivalence	2014	Joel Kamnitzer
+	Knot homology via derived categories of coherent sheaves IV, coloured links	2014	Sabin Cautis Joel Kamnitzer
+	A category of kernels for equivariant factorizations and its implications for Hodge theory . Affine Mirković-Vilonen polytopes . Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow . The space of metrics of positive scalar curvature	2014	Matthew R. Ballard David Favero Ludmil Katzarkov Pierre Baumann Joel Kamnitzer Peter Tingley Alex Eskin Maxim Kontsevich Anton Zorich Bernhard Hanke
+ PDF Chat	Cyclic sieving, rotation, and geometric representation theory	2013	Bruce Fontaine Joel Kamnitzer
+ PDF Chat	Rank 2 affine MV polytopes	2013	Pierre Baumann Thomas Dunlap Joel Kamnitzer Peter Tingley
+ PDF Chat	Affine Mirković-Vilonen polytopes	2013	Pierre Baumann Joel Kamnitzer Peter Tingley
+ PDF Chat	Buildings, spiders, and geometric Satake	2013	Bruce Fontaine Joel Kamnitzer Greg Kuperberg
+ PDF Chat	Coherent sheaves on quiver varieties and categorification	2013	Sabin Cautis Joel Kamnitzer Anthony Licata
+	Categorification of Lie algebras [d'apres Rouquier, Khovanov-Lauda]	2013	Joel Kamnitzer
+	Cyclic sieving, rotation, and geometric representation theory	2012	Bruce Fontaine Joel Kamnitzer
+ PDF Chat	Réflexions dans un cristal	2012	Pierre Baumann Stéphane Gaussent Joel Kamnitzer
+	R\'eflexions dans un cristal	2012	Pierre Baumann Stéphane Gaussent Joel Kamnitzer
+ PDF Chat	Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions	2012	Sabin Cautis Joel Kamnitzer Anthony Licata
+	Preprojective algebras and MV polytopes	2012	Pierre Baumann Joel Kamnitzer
+	Rank 2 affine MV polytopes	2012	Pierre Baumann Thomas Dunlap Joel Kamnitzer Peter Tingley
+ PDF Chat	Braiding via geometric Lie algebra actions	2012	Sabin Cautis Joel Kamnitzer
+	Rank 2 affine MV polytopes	2012	Pierre Baumann Thomas R. Dunlap Joel Kamnitzer Peter Tingley
+	Réflexions dans un cristal	2012	Pierre Baumann Stéphane Gaussent Joel Kamnitzer
+	Cyclic sieving, rotation, and geometric representation theory	2012	Bruce Fontaine Joel Kamnitzer
+	Affine Mirkovi\'c-Vilonen polytopes	2011	Pierre Baumann Joel Kamnitzer Peter Tingley
+	Coherent Sheaves on Quiver Varieties and Categorification	2011	Sabin Cautis Joel Kamnitzer Anthony Licata
+	Buildings, spiders, and geometric Satake	2011	Bruce Fontaine Joel Kamnitzer Greg Kuperberg
+	Geometric constructions of the irreducible representations of 𝐺𝐿_{𝑛}	2011	Joel Kamnitzer
+	Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A	2011	Joel Kamnitzer Chandrika Sadanand
+	Buildings, spiders, and geometric Satake	2011	Bruce Fontaine Joel Kamnitzer Greg Kuperberg
+	Coherent Sheaves on Quiver Varieties and Categorification	2011	Sabin Cautis Joel Kamnitzer Anthony Licata
+	Affine Mirković-Vilonen polytopes	2011	Pierre Baumann Joel Kamnitzer Peter Tingley
+	Preprojective algebras and MV polytopes	2010	Pierre Baumann Joel Kamnitzer
+ PDF Chat	Preprojective algebras and MV polytopes	2010	Pierre Baumann Joel Kamnitzer
+ PDF Chat	Coherent sheaves and categorical sl2 actions	2010	Sabin Cautis Joel Kamnitzer Anthony Licata
+ PDF Chat	The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points	2010	Pavel Etingof André Henriques Joel Kamnitzer Eric M. Rains
+	Mirković-Vilonen cycles and polytopes	2010	Joel Kamnitzer
+	Braid groups and geometric categorical Lie algebra actions	2010	Sabin Cautis Joel Kamnitzer
+	Functions of Several Complex Variables 32Xxx	2010	Pavel Etingof Joel Kamnitzer Eric M. Rains
+	Modules with 1-dimensional socle and components of Lusztig quiver varieties in type A	2010	Joel Kamnitzer Chandrika Sadanand
+	Preprojective algebras and MV polytopes	2010	Pierre Baumann Joel Kamnitzer
+ PDF Chat	Categorical geometric skew Howe duality	2009	Sabin Cautis Joel Kamnitzer Anthony Licata
+	Derived equivalences for cotangent bundles of Grassmannians via categorical sl(2) actions	2009	Sabin Cautis Joel Kamnitzer Anthony Licata
+	Lectures on geometric constructions of the irreducible representations of GL_n	2009	Joel Kamnitzer
+	Derived equivalences for cotangent bundles of Grassmannians via categorical sl(2) actions	2009	Sabin Cautis Joel Kamnitzer Anthony Licata
+ PDF Chat	Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case	2008	Sabin Cautis Joel Kamnitzer
+ PDF Chat	The crystal commutor and Drinfeld’s unitarized R-matrix	2008	Joel Kamnitzer Peter Tingley
+ PDF Chat	A definition of the crystal commutor using Kashiwara’s involution	2008	Joel Kamnitzer Peter Tingley
+	Knot homology via derived categories of coherent sheaves, I: The sl(2)-case	2008	Sabin Cautis Joel Kamnitzer
+	The Beilinson-Drinfeld Grassmannian and symplectic knot homology	2008	Joel Kamnitzer
+ PDF Chat	Hives and the fibres of the convolution morphism	2007	Joel Kamnitzer
+	The crystal structure on the set of Mirković–Vilonen polytopes	2007	Joel Kamnitzer
+	The crystal commutor and Drinfeld's unitarized R-matrix	2007	Joel Kamnitzer Peter Tingley
+	Hives and the fibres of the convolution morphism	2007	Joel Kamnitzer
+	Knot homology via derived categories of coherent sheaves I, sl(2) case	2007	Sabin Cautis Joel Kamnitzer
+ PDF Chat	Crystals and coboundary categories	2006	André Henriques Joel Kamnitzer
+	A definition of the crystal commutor using Kashiwara's involution	2006	Joel Kamnitzer Peter Tingley
+ PDF Chat	The octahedron recurrence and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi mathvariant="fraktur">g</mml:mi><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="fraktur">n</mml:mi></mml:mrow></mml:msub></mml:math> crystals	2005	André Henriques Joel Kamnitzer
+	The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points	2005	Pavel Etingof André Henriques Joel Kamnitzer Eric M. Rains
+	The crystal structure on the set of Mirkovic-Vilonen polytopes	2005	Joel Kamnitzer
+	Mirkovic-Vilonen cycles and polytopes	2005	Joel Kamnitzer
+	Crystals and coboundary categories	2004	André Henriques Joel Kamnitzer
+	The octahedron recurrence and gl(n) crystals	2004	André Henriques Joel Kamnitzer
+ PDF Chat	Central Binomial Sums, Multiple Clausen Values, and Zeta Values	2001	Jonathan M. Borwein D.J. Broadhurst Joel Kamnitzer
+	Central Binomial Sums, Multiple Clausen Values and Zeta Values	2000	Jonathan M. Borwein D. J. Broadhurst Joel Kamnitzer

Common Coauthors

Coauthor	Papers Together
Sabin Cautis	24
Alex Weekes	23
Peter Tingley	16
Oded Yacobi	11
Pierre Baumann	10
Anthony Licata	8
Ben Webster	8
André Henriques	6
Dinakar Muthiah	6
Pierre Baumann	6
Leonid Rybnikov	6
Bruce Fontaine	6
Greg Kuperberg	3
Pavel Etingof	3
Anne Dranowski	3
Nicholas Proudfoot	3
Stéphane Gaussent	3
Michael Finkelberg	3
C. A. F. Dodd	3
Khoa Pham	3
Michael McBreen	3
Eric M. Rains	3
Justin Hilburn	3
Thomas Dunlap	2
Aleksei Ilin	2
Jonathan M. Borwein	2
Calder Morton-Ferguson	2
Allen Knutson	2
Chandrika Sadanand	2
Khoa Pham	2
Thomas R. Dunlap	1
Piotr Przytycki	1
Alex Eskin	1
Daniel Huybrechts	1
Thomas Schick	1
Maxim Kontsevich	1
D. J. Broadhurst	1
Wolfgang Steimle	1
Balázs Elek	1
Matthew R. Ballard	1
Ludmil Katzarkov	1
Balázs Elek	1
Bernhard Hanke	1
Anton Zorich	1
David Favero	1
Iva Halacheva	1
Scott Morrison	1
David J. Broadhurst	1
Roger Bai	1
Yu Li	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Geometric Langlands duality and representations of algebraic groups over commutative rings	2007	Ivan Mirković Kari Vilonen	26
+	Perverse sheaves on a Loop group and Langlands' duality	1995	Victor Ginzburg	16
+	Introduction to Quantum Groups	2010	G. Lusztig	15
+	Knot homology via derived categories of coherent sheaves, I: The sl(2)-case	2008	Sabin Cautis Joel Kamnitzer	14
+	A polytope calculus for semisimple groups	2003	Jared E. Anderson	14
+ PDF Chat	Geometric construction of crystal bases	1997	Masaki Kashiwara Yoshihisa Saito	14
+ PDF Chat	Crystals and coboundary categories	2006	André Henriques Joel Kamnitzer	12
+ PDF Chat	Canonical bases arising from quantized enveloping algebras	1990	G. Lusztig	12
+ PDF Chat	Categorical geometric skew Howe duality	2009	Sabin Cautis Joel Kamnitzer Anthony Licata	11
+ PDF Chat	Knot homology via derived categories of coherent sheaves II, $\mathfrak{sl}_{m}$ case	2008	Sabin Cautis Joel Kamnitzer	11
+ PDF Chat	Derived equivalences for symmetric groups and 𝔰𝔩<sub>2</sub>-categorification	2008	Joseph Chuang Raphaël Rouquier	10
+	Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras	1994	Hiraku Nakajima	10
+	2-Kac-Moody algebras	2008	Raphaël Rouquier	10
+	Quiver varieties and Kac-Moody algebras	1998	Hiraku Nakajima	10
+ PDF Chat	On quiver varieties and affine Grassmannians of type A	2003	Ivan Mirković Maxim Vybornov	10
+	The crystal structure on the set of Mirković–Vilonen polytopes	2007	Joel Kamnitzer	10
+ PDF Chat	Tensor product multiplicities, canonical bases and totally positive varieties	2001	Arkady Berenstein Andrei Zelevinsky	9
+	Derived equivalences for cotangent bundles of Grassmannians via categorical sl(2) actions	2009	Sabin Cautis Joel Kamnitzer Anthony Licata	9
+ PDF Chat	On a Class of Representations of the Yangian and Moduli Space of Monopoles	2005	A. Gerasimov S. Kharchev D. V. Lebedev Sergey Oblezin	9
+	Representation Theory and Complex Geometry	2009	Neil Chriss Victor Ginzburg	9
+ PDF Chat	Highest weights for truncated shifted Yangians and product monomial crystals	2019	Joel Kamnitzer Peter Tingley Ben Webster Alex Weekes Oded Yacobi	8
+ PDF Chat	PBW Basis of Quantized Universal Enveloping Algebras	1994	Yoshihisa Saito	8
+	Quiver varieties and Beilinson-Drinfeld Grassmannians of type A	2007	Ivan Mirković Maxim Vybornov	8
+ PDF Chat	Yangians and quantizations of slices in the affine Grassmannian	2014	Joel Kamnitzer Ben Webster Alex Weekes Oded Yacobi	8
+	Fourier-Mukai Transforms in Algebraic Geometry	2006	Daniel Huybrechts	8
+ PDF Chat	Equivalences and stratified flops	2011	Sabin Cautis	8
+	Quiver varieties and finite dimensional representations of quantum affine algebras	2000	Hiraku Nakajima	8
+	Mirković-Vilonen cycles and polytopes	2010	Joel Kamnitzer	8
+	REPRESENTATION THEORY AND COMPLEX GEOMETRY	1999	I. Grojnowski	8
+	A diagrammatic approach to categorification of quantum groups I	2009	Mikhail Khovanov Aaron D. Lauda	8
+ PDF Chat	Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions	2012	Sabin Cautis Joel Kamnitzer Anthony Licata	8
+	On crystal bases of the Q-analogue of universal enveloping algebras	1991	Masaki Kashiwara	7
+	Equidimensionality of convolution morphisms and applications to saturation problems	2005	Thomas J. Haines	7
+	Crystals via the affine Grassmannian	2001	Alexander Braverman Dennis Gaitsgory	7
+ PDF Chat	Quantizations of conical symplectic resolutions II: category $\mathcal {O}$ and symplectic duality	2018	Tom Braden Anthony Licata Nicholas Proudfoot Ben Webster	7
+ PDF Chat	Braiding via geometric Lie algebra actions	2012	Sabin Cautis Joel Kamnitzer	7
+	Canonical Bases Arising from Quantized Enveloping Algebras. II	1990	G. Lusztig	7
+ PDF Chat	Coherent sheaves and categorical sl2 actions	2010	Sabin Cautis Joel Kamnitzer Anthony Licata	7
+ PDF Chat	A categorification of quantum $\mathrm{sl}(n)$	2010	Mikhail Khovanov Aaron D. Lauda	6
+	Comultiplication for shifted Yangians and quantum open Toda lattice	2017	Michael Finkelberg Joel Kamnitzer Khoa Pham Leonid Rybnikov Alex Weekes	6
+ PDF Chat	A diagrammatic approach to categorification of quantum groups III	2008	Mikhail Khovanov Aaron D. Lauda	6
+ PDF Chat	Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N} = 4$ gauge theories, II	2018	Alexander Braverman Michael Finkelberg Hiraku Nakajima	6
+	On category O for affine Grassmannian slices and categorified tensor products	2019	Joel Kamnitzer Peter Tingley Ben Webster Alex Weekes Oded Yacobi	6
+ PDF Chat	Uhlenbeck Spaces via Affine Lie Algebras	2007	Alexander Braverman Michael Finkelberg Dennis Gaitsgory	6
+ PDF Chat	A Kohno-Drinfeld theorem for quantum Weyl groups	2002	Valerio Toledano-Laredo	6
+	Kac–Moody groups and cluster algebras	2011	Christof Geiß Bernard Leclerc Jan Schröer	6
+	The crystal base and Littelmann’s refined Demazure character formula	1993	Masaki Kashiwara	6
+ PDF Chat	Total positivity in Schubert varieties	1997	Arkady Berenstein Andrei Zelevinsky	6
+ PDF Chat	An Algebro-Geometric Realization of the Cohomology Ring of Hilbert Scheme of Points in the Affine Plane	2016	Tatsuyuki Hikita	6
+	A guide to quantum groups	1994	Vyjayanthi Chari Andrew Pressley	6