Ph.D Students

CurrentYaolong Shen                

PhD Graduated [15]:  Dave Taylor (2007), Jill Tysse (2008), Ta Khongsap (2009), Lei Zhao (2010), Jinkui Wan (2010), Yung-Ning Peng (2012), Constance Baltera (2013), Sean Clark (2014), Huanchen Bao (2015, winner of 2020 Chevalley Prize), Chun-Ju Lai (2016), Mike Reeks (2018), Chris Leonard (2019), Thomas Sales (2020), Chris Chung (2020), Weinan Zhang (2023)    

Distinguished Math Majors (DMP) supervised [2]: Arun Kannan (2018), Zac Carlini (2023)

PhD Dissertations


XVI. Yaolong Shen (2024, expected) 

  1. ıSchur duality and Kazhdan-Lusztig basis expanded (joint with WW), 33 pp.,     arXiv:2108.00630
  2. Canonical bases of q-Brauer algebras and ıSchur dualities (joint with W. Cui), 23 pp.  arXiv:2203.020822
  3. Quantum supersymmetric pairs and ıSchur duality of type AIII, 43 pp. arXiv:2210.01233
  4. Canonical bases of the quantized Walled Brauer algebras, 27 pp. arXiv:2305.04164


XV. Weinan Zhang (2023) 


  1. A Drinfeld type presentation of affine quantum ıquantum groups II: split BCFG type, 25 pp.,   Lett. Math. Phys. 2022. arXiv:2102.03203
  2. An intrinsic approach to relative braid group symmetries on ıquantum groups (joint with WW), 89 pp.   arXiv:2201.01803
  3. Braid group action and quasi-split affine ıquantum groups I (joint with Ming Lu and WW), 42 pp. arXiv:2203.11286
  4. Relative braid group symmetries on ıquantum groups of Kac-Moody type, 44 pp.  arXiv:2209.12860


XIV. Chris Chung (2020) 

Ph.D. thesis:  Quantum covering groups and quantum symmetric pairs

  1. Quantum supergroups VI. Roots of 1, (joint with Chris Chung, WW), 21pp., Lett. Math. Phys.
  2. A Serre presentation for the ıquantum covering groups, 28pp.
  3. Canonical bases arising from ıquantum covering groups, 29 pp. arXiv:2107.06322


XIII. Thomas Sale (2020) 

Ph.D. thesis:  Quantum symmetric pairs and quantum supergroups at roots of 1

  1. Quantum supergroups VI. Roots of 1, (joint with Chris Chung, WW), 21pp., Lett. Math. Phys.
  2. Singular vector formulas for Verma modules of simple Lie superalgebras, 16pp., J. Algebra
  3. Quantum symmetric pairs at roots of 1, (joint with Huanchen Bao), 17pp. Adv. in Math.


XII. Chris Leonard (2019) 

Ph.D. thesis:  Categorification of tensor products of representations of current algebras and quantum groups

  1. Traces of tensor product categories, (with Mike Reeks), 41 pp.,
  2. Graded super duality for general linear Lie superalgebras, 25pp., Transform. Groups,


XI. Mike Reeks (2018) 

Ph.D. thesis:  Trace and center of the twisted Heisenberg category

  1. The center of the twisted Heisenberg category, factorial Schur Q-functions, and transition functions on the Schur graph,  (with Henry Kvinge, Can Oguz),
  2. Cocenters of Hecke-Clifford and spin Hecke algebras,  J. Algebra, (2017), 85-112.  
  3. Trace of the twisted Heisenberg category (with Can Oguz), Commun. Math. Phys., 36pp.
  4. Extended nilHecke algebra and symmetric functions in type B,  J. Pure Appl. Alg.,    
  5. Traces of tensor product categories, (with Chris Leonard), 41 pp.,


X. Chun-Ju Lai (2016) 

Ph.D. thesis:  Affine quantum symmetric pairs: multiplication formulas and canonical bases

  1. On Weyl modules over affine Lie algebras in prime characteristic, 30 pp., Transformation Groups,           
  2. An elementary construction of monomial bases of quantum affine gl_n,  (with Li LUO), 15 pp., J. LMS        
  3. Affine flag varieties and quantum symmetric pairs
    (with Zhaobing Fan,  Yiqiang Li,  Li Luo,  WW),   113 pages, Memoirs AMS            
  4. Affine Hecke algebras and quantum symmetric pairs
    (with Zhaobing Fan,  Yiqiang Li,  Li Luo,  WW),  87 pages, Memoirs AMS


IX. Huanchen Bao (2015)

Ph.D. thesis:  Canonical bases arising from quantum symmetric pairs and Kazhdan-Lusztig theory

  1. Geometric Schur duality of classical type, (with J. Kujawa, Y. Li, WW), Transformation Groups 23 (2018), 329-389,arXiv:1404.4000v3          
  2. Canonical bases in tensor products revisited, (with WW), Amer. J. Math. 138 (2016), 1731-1738
  3. A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs, (with WW), Asterisque 402 (2018), vii+134pp.


VIII. Sean Clark (2014) 

Ph.D. thesis:  Quantum Supergroups and Canonical Bases

  1. Canonical basis for quantum osp(1|2), (with WW), Lett. Math. Phys. 103 (2013), 207--231
  2. Quantum supergroups I. Foundations
    (with David Hill and WW), Transformation Groups 18 (2013), 1019--1053.
  3. Quantum supergroups II. Canonical basis
    (with David Hill and WW), Represent. Theory 18 (2014), 278--309.
  4. Quantum supergroups III. Twistors
    (with Zhaobing Fan, Yiqiang Li and WW), Commun. Math. Phys. 322 (2014), 415--436.
  5. Quantum shuffles and quantum supergroups of basic type
    (with David Hill and WW), 50 pages, Quantum Topology (to appear, 2015)
  6. Quantum supergroups IV. The modified form, Math. Z. 278 (2014), 493--528.

VII. Constance Baltera (2013)

Ph.D. thesis:  Coinvariant Algebras and Fake Degrees For Spin Weyl Groups

  1. Coinvariant algebras and fake degrees for spin Weyl groups of classical type(with WW), Math. Proc. Cambridge Philos. Soc. 156 (2014), 43--79.
  2. Coinvariant algebras and fake degrees for spin Weyl groups of exceptional type(with WW), J. Algebra (to appear 2015).arXiv:1306.1290


VI. Yung-Ning Peng (2012) 

Ph.D. thesis:  Parabolic Presentations of the Super Yangian Y_{M|N} and Applications

  1. Parabolic presentations of the super Yangian Y(gl_{M|N}),Comm. Math. Phys. 307 (2011), 229--259.
  2. On shifted super Yangians and a class of finite W-superalgebras, J. Algebra 422 (2015), 520--562.


V. Jinkui Wan (2010)

Ph.D. thesis:  Representations of Affine Hecke Algebras and Related Algebras

  1. Modular representations and branching rules for wreath Hecke algebras
    (with WW),  International Mathematics Research Notices (2008), Article ID: rnn128-31, 31 pages
  2. Wreath Hecke algebras and centralizer construction for wreath products, J. Algebra 323 (2010), 2371--2397.
  3. Completely splittable representations of affine Hecke-Clifford algebras, J. Algebr. Comb. 32 (2010),15-58.
  4. Spin invariant theory for the symmetric group, (with WW),  J. Pure Applied Algebra 215 (2011), 1569--1581.


IV. Lei Zhao (2010)

Ph.D. thesis:  Modular Representations of Lie Superalgebras

  1. Representations of Lie superalgebras in prime characteristic I,
    (with WW), Proc. London Math. Soc. 99 (2009), 145--167.
  2. Representations of Lie superalgebras in prime characteristic II: The queer series,
    (with WW), J. Pure Applied Algebra 215 (2011), 2515--2532.
  3. Typical blocks of Lie superalgebras in prime characteristic, Commun. in Alg. 39 (2011), 534--547.
  4. Representations of Lie superalgebras in prime characteristic III, Pacific J. Math 248 (2010), 493--510.


III. Ta Khongsap (2009)

Ph.D. thesis:  Spin Hecke Algebras

  1. Hecke-Clifford algebras and spin Hecke algebras I: The classical affine type,
    (with WW), Transformation Groups 13 (2008), 389--412.
  2. Hecke-Clifford algebras and spin Hecke algebras II: The rational double affine type,
    (with WW), Pacific J. Math. 238 (2008), 73--103.
  3. Hecke-Clifford algebras and spin Hecke algebras III: The trignometric type,
    J. Algebra 322 (2009), 2731--2750.
  4. Hecke-Clifford algebras and spin Hecke algebras IV: Odd double affine type,
    (with WW), Special Issue on Dunkl Operators and Related Topics, SIGMA 5 (2009), 012, 27 pages.


II. Jill Tysse (2008)

Ph.D. thesis:  The Centers of Spin Symmetric and Spin Hyperoctahedral Group Algebras     

  1. The centers of spin symmetric group algebras and Catalan numbers,
    (with WW),  J. Algebr. Combin. 29 (2009), 175--193.


I. David Taylor (2007)

Ph.D. thesis:  The Bloch-Okounkov Correlation Functions and Dimension Formulas for Modules of Infinite-Dimensional Lie Algebras 

  1. The Bloch-Okounkov correlation functions of classical type,
    (with WW),  Commun. Math. Phys. 276 (2007), 473--508.
  2. The Bloch-Okounkov correlation functions of negative levels,
    (with S.-J. Cheng and WW),  J. Algebra 319 (2008),  457--490.
  3. The Bloch-Okounkov correlation functions, a classical half-integral case,  
    Lett. Math. Phys. 85 (2008), 235--248.