Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Professor
KANNO, Hiroaki
Degree 1
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Doctor of Science （ Kyoto University ）
Research Areas 2
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Others / Others / Elementary Particle/Atomic Nucleus/Cosmic Ray/Space Physics
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Others / Others / Geometry
Current Research Project and SDGs 1
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Topological Quantum Field Theory
Education 2
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Kyoto University Graduate School, Division of Natural Science
- 1989
Country： Japan
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Kyoto University Faculty of Science
- 1984
Country： Japan
Professional Memberships 2
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日本物理学会
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日本数学会
Papers 54
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Awata, H; Hasegawa, K; Kanno, H; Ohkawa, R; Shakirov, S; Shiraishi, J; Yamada, Y
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS Vol. 20 2024
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Solitons in open N=2 string theory
Hamanaka, M; Huang, SC; Kanno, H
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS Vol. 2023 ( 4 ) 2023.4
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Awata, H; Hasegawa, K; Kanno, H; Ohkawa, R; Shakirov, S; Shiraishi, J; Yamada, Y
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS Vol. 19 2023
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Quasi-Hopf twist and elliptic Nekrasov factor
Cheewaphutthisakun, P; Kanno, H
JOURNAL OF HIGH ENERGY PHYSICS ( 12 ) 2021.12
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MacMahon KZ equation for Ding-Iohara-Miki algebra
Cheewaphutthisakun, P; Kanno, H
JOURNAL OF HIGH ENERGY PHYSICS ( 4 ) 2021.4
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Quiver matrix model of ADHM type and BPS state counting in diverse dimensions
Kanno, H
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS Vol. 2020 ( 11 ) 2020.11
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Shiraishi functor and non-Kerov deformation of Macdonald polynomials
Awata, H; Kanno, H; Mironov, A; Morozov, A
EUROPEAN PHYSICAL JOURNAL C Vol. 80 ( 10 ) 2020.10
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Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei
JOURNAL OF HIGH ENERGY PHYSICS ( 8 ) 2020.8
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On a complete solution of the quantum Dell system
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei
JOURNAL OF HIGH ENERGY PHYSICS ( 4 ) 2020.4
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Can tangle calculus be applicable to hyperpolynomials?
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei
NUCLEAR PHYSICS B Vol. 949 2019.12
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Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Suetake Kazuma, Zenkevich Yegor
JOURNAL OF HIGH ENERGY PHYSICS ( 4 ) 2019.4
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Equivariant U(N) Verlinde algebra from Bethe/gauge correspondence
Kanno Hiroaki, Sugiyama Katsuyuki, Yoshida Yutaka
JOURNAL OF HIGH ENERGY PHYSICS ( 2 ) 2019.2
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Nontorus link from topological vertex
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey
PHYSICAL REVIEW D Vol. 98 ( 4 ) 2018.8
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(q,t)-KZ Equations for quantum toroidal algebra and Nekrasov partition function on ALE spaces Reviewed
H.Awata, H.Kanno, A.Mironov, A.Morozov, K.Suetake and Y.Zenkevich
Journal of High Energy Physics Vol. 1803 ( 3 ) 2018.3
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Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey, Ohkubo Yusuke, Zenkevich Yegor
PHYSICAL REVIEW D Vol. 96 ( 2 ) 2017.7
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Anomaly in RTT relation for DIM algebra and network matrix models
Awata Hidetoshi, Kanno Hiroaki, Mironov Andrei, Morozov Alexei, Morozov Andrey, Ohkubo Yusuke, Zenkevich Yegor
NUCLEAR PHYSICS B Vol. 918 page： 358 - 385 2017.5
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Anomaly in RTT relation for DIM algebra and Network Matrix Models Reviewed
H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Nuclear Physics B Vol. 918 page： 358-385 2017.3
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Generalized Knizhnik-Zamolodchikov Equation for Ding-Iohara-Miki algebra, Reviewed
H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Phys. Rev. D Vol. 96 page： 026021 2017
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Toric Calabi-Yau manifolds as Quantum Integrable Systems; R-matrix and RTT relations
H.Awata, H.Kanno, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Journal of High Energy Physics Vol. 1610 page： 047 2016.10
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Explicit Examples of DIM Constraints for Network Matrix Models Reviewed
H.Awata, H.Kanno, T.Matsumoto, A.Mironov, Alex.Morozov, And.Morozov, Y.Ohkubo and Y.Zenkevich
Journal of High Energy Physics Vol. 1607 page： 103 2016.7
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Hyperkaehler Metrics from Monopole Walls Reviewed
M.Hamanaka, H.Kanno and D.Muranaka
Phys. Rev. Vol. D 89 2014.3
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W_3 irregular states and isolated N=2 superconformal field theories Reviewed
H.Kanno, K.Maruyoshi, S.Shiba and M.Taki
Journal of High Energy Physics Vol. 1303 page： 147 2013.3
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Changing the preferred direction of the refined topological vertex Reviewed
H.Awata and H.Kanno
Journal of Geometry and Physics Vol. 64 page： 91-110 2013
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Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String Reviewed
H.Awata, H.Fuji, H.Kanno, M.Manabe and Y.Yamada
Advances in Theoretical and Mathematical Physics Vol. 16 ( 3 ) page： 725 - 804 2012.6
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Generalized Whittaker states for instanton counting with fundamental hypermultiplets Reviewed
H.Kanno and M.Taki
Journal of High Energy Physics Vol. 1205 page： 052 2012.5
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Instanton counting with a surface operator and the chain-saw quiver
H.Kanno, and Y.Tachikawa
Journal of High Energy Physics Vol. 11 ( 06 ) page： 119 2011.6
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Macdonald operators and homological invariants of the colored Hopf link Reviewed
H.Awata and H.Kanno
J. Phys. A: Math. Theor. Vol. 44 page： 375201 2011
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Quiver matrix model and and topological partition function in six dimensions Reviewed
H.Awata and H.Kanno
Journal of High Energy Physics Vol. 9 ( 7 ) page： 076 2009.7
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Refined BPS state counting from Nekrasov's formula and Macdonald functions Reviewed
H.Awata and H.Kanno
International Journal of Modern Physics A Vol. 24 ( 12 ) page： 2253-2306 2009
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Instanton Counting and the Chiral Ring Relations in Supersymmetric Gauge Theories Reviewed
H.Kanno
Adv. Stud. Pure Math. Vol. 55 page： 51-67 2009
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Instanton Calculus and Chiral One-point Functions in Supersymmetric Gauge Theories Reviewed
S.Fujii, H.Kanno, S.Moriyama and S.Okada
Adv. Theor. Math. Phys. Vol. 12 page： 1401-1428 2008
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Instanton Calculus and Loop Operator in Supersymmetric Gauge Theory Reviewed
H.Kanno and S.Moriyama
Phys. Rev.D Vol. 77 page： 126001 2008
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Universal Character and Large N Factorizationin Topological Gauge/String Theory Reviewed
H.Kanno
Nuclear Physics Vol. B745 [PM] page： 165-175 2006
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Instanton counting, Macdonald function and the moduli space of D-branes Reviewed
H.Awata and H.Kanno
Journal of High Energy Physics Vol. 5 page： 039 2005
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Whitham Prepotential and Superpotential Reviewed
H.Itoyama and H.Kanno
Nuclear Physics Vol. B686 page： 155-164 2004
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Geometric transitions, Chern-Simons gauge theory and Veneziano type amplitudes Reviewed
T.Eguchi and H.Kanno
Physics Letters Vol. B585 page： 163-172 2004
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*Topological Strings and Nekrasov's Formulas Reviewed
T.Eguchi and H.Kanno
Journal of High Energy Physics Vol. 12 page： 006 2003
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Supereigenvalue Model and Dijkgraaf-Vafa Proposal Reviewed
H.Itoyama and H.Kanno
Physics Letters Vol. B573 page： 227-234 2003
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On Spin(7) Holonomy Metric Based on SU(3)/U(1) II Reviewed
H.Kanno and Y.Yasui
Journal of Geometry and Physics Vol. 43 page： 310-326 2002
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On Spin(7) Holonomy Metric Based on SU(3)/U(1) Reviewed
H.Kanno and Y.Yasui
Journal of Geometry and Physics Vol. 43 page： 293-309 2002
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Octonionic Yang-Mills instanton on quaternionic line bundle of Spin(7) holonomy
H.Kanno and Y.Yasui
Journal of Geometry and Physics Vol. 34 page： 302 2000
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Five-Dimensional Gauge Theories and Local Mirror Symmetry Reviewed
T.Eguchi and H.Kanno
Nuclear Physics Vol. B586 page： 331 2000
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*Special Quantum Field Theories in Eight and Other Dimensions Reviewed
L.Baulieu, H.Kanno and I.M.Singer
Communications in Mathematical Physics Vol. 194 page： 149 1998
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Donaldson-Witten functions of massless N=2 supersymmetric QCD
H.Kanno and S.-K.Yang
Nuclear Physics Vol. B535 page： 512 1998
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Picard-Fuchs equation and prepotential of five-dimensional SUSY gauge theory compactified on a circle
Nuclear Physics Vol. B530 page： 73 1998
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Two-toroidal Lie Algebra as Current Algebra of Four-dimensional Kaehler WZW Model Reviewed
T.Inami, H.Kanno, T.Ueno and C.S.Xiong
Physics Letters Vol. B399 page： 97 1997
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Topological strings with scaling violation and Toda lattice hierarchy Reviewed
H.Kanno and Y.Ohta
Nuclear Physics Vol. B442 page： 179 1995
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BRST cohomology ring in 2D gravity coupled to minimal models
H.Kanno and M.H.Sarmadi
International Journal of Modern Physics Vol. A9 page： 39 1994
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Toda lattice hierarchy and the topological description of the c=1 string theory
T.Eguchi and H.Kanno
Physics Letters Vol. B331 page： 330 1994
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Woo algebra in a two-dimensional black hole Reviewed
T.Eguchi, H.Kanno and S.-K.Yang
Physics Letters B Vol. 298 page： 73 1993
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Topological strings, flat coordinates and gravitational descendants Reviewed
T.Eguchi, H.Kanno, Y.Yamada and S.-K.Yang
Physics Letters B Vol. 305 page： 235 1993
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SO(2, C) invariant ring structure of BRST cohomology and singular vectors in 2D gravity with C<1 matter Reviewed
N.Chair, V.K.Dobrev and H.Kanno
Physics Letters B Vol. 283 page： 194 1992
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*Lie superalgebraic approach to super Toda lattice and gereralized super KdV Equations Reviewed
T.Inami and H.Kanno
Communications in Mathematical Physics Vol. 136 page： 519 1991
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*Weil algebra structure and geometrical meaning of BRST transformation in topological guantum field theory Reviewed
Zeitschrift fur Physik C Vol. 43 page： 477 1989
Books 1
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BRS Cohomology in Topological String Theory and Integrable Systems
BRS Symmetry 1996
Research Project for Joint Research, Competitive Funding, etc. 1
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ゲージ・重力理論対応と可積分系
2008.10 - 2010.3
大幸財団
Grant type：Competitive
KAKENHI (Grants-in-Aid for Scientific Research) 5
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Grant number：23K03087 2023.4 - 2027.3
科学研究費助成事業 基盤研究(C)
菅野 浩明
Authorship：Principal investigator
Grant amount：\2860000 （ Direct Cost: \2200000 、 Indirect Cost：\660000 ）
座標と運動量がともに二重周期性を持つ可積分系である二重楕円型可積分系について，超対称ゲージ理論との対応関係を通して，その性質を明らかにする．互いに可換なハミルトニアンの同時固有関数は，対応する超対称ゲージ理論側で枠付き放物層の数え上げに関する分配関数で与えられると予想されている．楕円量子群の表現論を用いて，分配関数を絡み作用素の同変指標として書き換えることにより，分配関数の満たす差分方程式を求める．また二重楕円型可積分系は座標と運動量の入れ替えに関して自己双対性をもつことが期待されている．分配関数のもつ対称性を明らかにすることによって自己双対性が実現されていることを示す．
2次元共形場理論の共形ブロックは Virasoro 代数の表現論において基本的な役割を果たすが，変形 Virasoro 代数の共形ブロックの数学的定義は，まだ与えられていない．5次元版の AGT 対応は面欠陥付きの K 理論的 Nekrasov 分配関数と変形 Virasoro 代数の共形ブロックの対応を予想するので，このような Nekrasov 分配関数を変形 Virasoro 代数の共形ブロックとみなして，その性質を調べるという立場が可能である．面欠陥付きの Nekrasov 分配関数は，幾何学的には放物層の数え上げにより定義される．
近年 Sh.Shakirov 氏は，このような分配関数に対する，新しいタイプの非定常差分方程式 (Shakirov 方程式）を発見した．この非定常差分方程式は有理曲線上の共形ブロックに対する BPZ 方程式の量子変形版とみなすことができる．一方で BPZ 方程式はパンルヴェ方程式やカレント代数の共形ブロックに対する Knizhnik-Zamolodchikov (KZ) 方程式と対応することが知られている．我々は，適切なゲージ変換を用いて Shakirov 方程式を書き換えることにより，この方程式が VI 型の非定常離散パンルヴェ方程式の量子化となっていることを明らかにした．VI 型離散パンルヴェ方程式の時間発展はアフィン Kac-Moody 代数 D_5^{(1)} の拡大アフィンワイル群の適切な並進元によって定義される．この並進元を非可換な（量子化された）力学変数の空間上で表現したものが Shakirov 方程式のハミルトニアンとなっている．
枠付き放物層の数え上げから定義される K 理論的 Nekrasov 分配関数が満たす非定常差分方程式が量子化された離散パンルヴェ方程式と見なされることが示されたことは，放物層の数え上げと量子可積分系の関係に関する新たな展望を開くものである．また変形 Virasoro 代数の共形ブロックとの関係についても次のような意味から興味深い．表現論的に変形 Virasoro 代数の取り扱いが難しい理由の一つは，余積が定義できないため量子群とならないことであった．パンルヴェ方程式の量子化は，モノドロミー保存変形の立場からアフィン量子代数の表現論で重要な役割をはたす量子 KZ 方程式と結びつく．したがって今年度得られた結果は，変形 Virasoro 代数の共形ブロックに対する表現論的アプローチに道を開くものである．本研究課題は楕円型可積分系に関するものであるので，以上の結果を楕円 Virasoro 代数へ拡張することは今後の課題である．
ここまでの研究では楕円型量子可積分系に関する課題に進展がなかった．離散パンルヴェ方程式には楕円型の拡張も存在するので，今年度の研究成果が楕円型に拡張できるか検討を行う．また K 理論的 Nekrasov 分配関数の観点から，楕円型への拡張を行うためには随伴表現に従う物質場を考える必要があり，これにはパンルヴェ方程式を超えた世界を考えることが必要となる可能性がある．一方で，今年度の成果から派生する新たな課題として，ゲージ群のランクが高い場合への拡張も視野に入れて研究を進める予定である． -
Difference equations associated with quantum toroidal algebra and hyper-Kaehler quotient
Grant number：18K03274 2018.4 - 2024.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Kanno Hiroaki
Authorship：Principal investigator
Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）
We have derived difference equations of KZ type for the correlation functions or the trace of the products of intertwining operators of the quantum toroidal algebra of type gl_1. We also investigated the structure of solutions and clarified the relation to the Nekrasov partition function of elliptic type. We have investigated the non-stationary difference equation for the K-theoretic Nekrasov partition function with a surface defect, which we can regard as a conformal block of the deformed Virasoro algebra. We have proved that by gauge
transformation the equation is transformed to a quantized version of discrete Painreve VI equation. The underlying moduli space is the affine Laumon space, which is only Kaehler quotient. In this sense this equation belongs to a new class of difference equations which was not expected in the beginning of the project. -
Research of lattices, automorphic forms and moduli spaces
Grant number：15H05738 2015.5 - 2020.3
Kondo Shigeyuki
Authorship：Coinvestigator(s)
We studied symmetries of manifolds from a wide-angle. We obtained a complete classification of Enriques surfaces with finite automorphism group and results on automorphisms of K3 and Enriques surfaces related with complex dynamical systems, and discovered a new phenomenon of Enriques surfaces by using the theory of a famous lattice, called Leech lattice, in sphere packing problem. And we studied moduli problems. In particular, we determined an important invariant, called the Kodaira dimensions, of some moduli spaces by applying the theory of automorphic forms. We also obtained several results related with Mathematical Physics and representation theory, for example, a duality phenomenon in Mathieu moonshine.
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M ブレインと量子可積分系
2012.4
科学研究費補助金 基盤研究(C)
Authorship：Principal investigator
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弦双対性が予言するアクセサリパラメータ付き特殊関数
2007 - 2009
科学研究費補助金 萌芽研究，課題番号：19654007
菅野 浩明
Authorship：Principal investigator
Teaching Experience (On-campus) 1
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Linear Algebra II
2011