Curtis Wendlandt

Doctoral Candidate in Mathematics

 Name Curtis Wendlandt Affiliation University of Alberta Department Mathematics Research Area Representation theory Position PhD student Office CCIS L3-256 Contact cwendlan(at)ualberta(dot)ca

I am mathematics PhD student studying the representation theory of quantum groups under the supervision of Prof. Nicolas Guay at the University of Alberta in Edmonton, Canada.

Publications

1. Coproduct for Yangians of affine Kac-Moody algebras, with Nicolas Guay and Hiraku Nakajima. Advances in Mathematics 338 (2018), 865-911. pdf.
2. Representations of twisted Yangians of types B, C, D: II, with Nicolas Guay and Vidas Regelskis. Transformation Groups (in press). pdf.
3. The R-matrix presentation for the Yangian of a simple Lie algebra. Communications in Mathematical Physics 363 (2018), no. 1, 289–332. pdf.
4. Equivalences between three presentations of orthogonal and symplectic Yangians, with Nicolas Guay and Vidas Regelskis. Letters in Mathematical Physics (2018), doi:10.1007/s11005-018-1108-6. pdf.
5. Representations of twisted Yangians of types B, C, D: I, with Nicolas Guay and Vidas Regelskis. Selecta Mathematica (N.S.), 23 (2017), no.3, 2071-2156. pdf.
6. Twisted Yangians of small rank, with Nicolas Guay and Vidas Regelskis. Journal of Mathematical Physics, 57 (2016), no.4, 041703, 28 pp. pdf.

Preprints

1. From Yangians to Yangian doubles. Preliminary draft available upon request.
2. Vertex Representations for Yangians of Kac-Moody algebras, with Nicolas Guay and Vidas Regelskis. Submitted for publication. pdf.

Current projects

1. Representations of twisted Yangians of types B, C, D: III, with Nicolas Guay and Vidas Regelskis.
2. The universal meromorphic $$R$$-matrix of $$Y_\hbar(\mathfrak{g})$$, with Sachin Gautam and Valerio Toledano Laredo.
3. R-matrix presentation of orthogonal and symplectic quantum loop algebras and their representations, with Nicolas Guay and Vidas Regelskis.

Time & Location: Wednesdays at 4pm, CAB 563

This is a student seminar which has the format of an informal reading course. Our goal for this semester is to give a detailed exposition to the theory of Yangians. However, we also welcome any talks related to the representation theory of quantum groups. Here is a list of past and upcoming talks (to be updated sporadically).

 (09/26) M. Rupert Lie bialgebras I: Definitions and Examples (10/03) M. Rupert Lie bialgebras II: Manin triples and the Lie bialgebra double (10/10) C. Wendlandt Lie bialgebras III: The graded double of the Yangian Lie bialgebra (10/17) C. Wendlandt Lie bialgebras IV: Pseudo-quasitriangularity of the current algebra (10/24) C. Wendlandt Lie bialgebras V: Rationality properties of the current algebra (10/31) No Seminar (11/07) C. Wendlandt Yangians I: Quantization and definition (11/14) C. Wendlandt Yangians II: Hopf structure and $$\mathbb{C}$$-form (11/21) C. Wendlandt Yangians III: PBW theorem and the Rees algebra (11/28) C. M. Rupert Yangians IV: Finite-dimensional representations

[Notes]

The seminar is organized by Matt Rupert and myself. If you are interested in giving a talk or would like to be added to our mailing list, please email me at cwendlan(at)ualberta(dot)ca.