Sean Ian Clark

Here is my CV (.pdf)

### Research Interests

### Collaborators

Weiqiang Wang

Dave Hill

My primary research interests lie in representation theory, and its connections with algebraic combinatorics, topology, geometry, and categorification. Specifically, my interests include:

- Lie (super)algebras and Category O
- Quantum (super)groups
- Crystal and canonical bases
- Hecke Algebras and KLR algebras
- Diagrammatic algebras
- Categorified quantum groups

Dave Hill

arXiv.org 2. "Super tableaux and a branching rule for the general linear Lie superalgebra", joint work with Yung-Ning Peng and Sittipong Thamrongpairoj, Linear and Multilinear Algebra, DOI:10.1080/03081087.2013.860599

arXiv.org 3. "Quantum supergroups I. Foundations", joint work with David Hill and Weiqiang Wang, Transformation Groups 18 (2013), pp. 1019-1053

arXiv.org 4. "Quantum Supergroups III. Twistors", joint work with Zhaobing Fan, Yiqiang Li, Weiqiang Wang, Comm. Math. Phys. 332 (2014), pp. 415-436

arXiv.org 5. "Quantum supergroups IV. The modified form", Math. Zeit. 278 (2014), pp. 493-528

arXiv.org 6. "Quantum supergroups II. Canonical basis", joint work with David Hill and Weiqiang Wang, Represent. Theory 18 (2014), pp. 278-309

arXiv.org 7. "Quantum supergroups V. Braid group action", joint work with David Hill, Comm. Math. Phys. 344 (2016), pp. 25-65

arXiv.org 8. "Quantum shuffles and quantum supergroups of basic type", joint work with David Hill and Weiqiang Wang, Quant. Top. 7 (2016), pp. 553-638.

arXiv.org 10. "Canonical bases for the quantum enveloping algebra of gl(m|1) and its modules"

2. "Canonical bases for quantum Kac-Moody superalgebras", given at AMS Fall Southeastern Sectional Meeting, New Orleans, Louisiana (2012-10-14); talk related to the following publications:[1][3]

3. "Kac-Moody quantum supergroups and global crystal bases", given at Workshop on Super Representation Theory, Institute of Mathematics, Academia Sinica, Taipei, Taiwan (2013-05-10); talk related to the following publications:[3][6] Slides

4. "A canonical basis for covering quantum groups.", given at AMS Western Sectional Meeting, Riverside, California (2013-11-02); talk related to the following publications:[3][5][6] Slides

5. "Canonical bases and quantum shuffle superalgebras of basic type", given at Workshop on Super Representation Theory, Institute of Mathematics, Academia Sinica, Taipei, Taiwan (2013-12-20); talk related to the following publications:[8] Slides

6. "Quantum supergroups and canonical bases", given at University of Virginia (2014-04-04); talk related to the following publications:[3][4][5][6] Slides

7. "Do Super Cats Make Odd Knots?", given at Max Planck Institute for Mathematics (2015-11-05); talk related to the following publications:[9] Slides

8. "Quantum enveloping gl(m|1) and canonical bases", given at Algebraic Groups, Quantum Groups and Geometry, University of Virginia (2016-05-25); talk related to the following publications:[10] Slides

9. "Relating osp(1|2n) and so(2n+1) knot invariants", poster presentation at the 2nd US-Mexico Conference on Representation theory, Categorification, and Noncommutative Algebra, University of Southern California (2016-05-31); talk related to the following publications:[9] Poster

10. "Quantum enveloping gl(m|1) and canonical bases", given at the 2nd US-Mexico Conference on Representation theory, Categorification, and Noncommutative Algebra, University of Southern California (2016-06-01); talk related to the following publications:[10] Slides