(P): postdoc; (G): graduate student; (U): undergraduate student; (H): high school student; (M): mentor.

1) Refereed

Post-Purdue hire:

21. A. Tsymbaliuk, Difference operators via GKLO-type homomorphisms: shuffle approach and application to quantum Q-systems. Letters in Mathematical Physics 113 (2023), Paper No. 22, 43pp. (pdf)

20. R. Frassek, I. Karpov (U), and A. Tsymbaliuk, Transfer matrices of rational spin chains via novel BGG-type resolutions. Communications in Mathematical Physics 400 (2023), 1‒82. (pdf)

19. R. Frassek (P) and A. Tsymbaliuk, Rational Lax matrices from antidominantly shifted extended Yangians: BCD types. Communications in Mathematical Physics 392 (2022), 545‒619. (pdf)

18. N. Nekrasov (M) and A. Tsymbaliuk, Surface defects in gauge theory and KZ equation. Letters in Mathematical Physics 112 (2022), Paper No. 28, 53pp. (pdf)

17. R. Frassek (P), V. Pestun, and A. Tsymbaliuk, Lax matrices from antidominantly shifted Yangians and quantum affine algebras: A-type. Advances in Mathematics 401 (2022), Paper No. 108283, 73pp. (pdf)

16. A. Tsymbaliuk, PBWD bases and shuffle algebra realizations for $U_v(L\mathfrak{sl}_n), U_{v_1,v_2}(L\mathfrak{sl}_n), U_v(L\mathfrak{sl}(m|n))$ and their integral forms. Selecta Mathematica (New Series) 27 (2021), Paper No. 35, 48pp. (pdf)

15. A. Tsymbaliuk, Duality of Lusztig and RTT integral forms of $U_v(L\mathfrak{sl}_n)$. Journal of Pure and Applied Algebra 225 (2021), no. 1, Paper No. 106469, 14pp. (pdf)

14. A. Tsymbaliuk, Shuffle algebra realizations of type A super Yangians and quantum affine superalgebras for all Cartan data. Letters in Mathematical Physics 110 (2020), 2083‒2111. (pdf)

13. M. Finkelberg and A. Tsymbaliuk (appendices by A. Weekes (P) and A. Tsymbaliuk), Shifted quantum affine algebras: integral forms in type A. Arnold Mathematical Journal 5 (2019), 197‒283. (pdf)

Pre-Purdue hire:

12. R. Gonin (G) and A. Tsymbaliuk, On Sevostyanov's construction of quantum difference Toda lattices. International Mathematics Research Notices (2019), no. 12, 8885‒8945. (pdf)

11. M. Finkelberg and A. Tsymbaliuk, Multiplicative slices, relativistic Toda and shifted quantum affine algebras. Progress in Mathematics 330 (2019), 133‒304. (pdf)

10. A. Tsymbaliuk, Several realizations of Fock modules for toroidal $\ddot{U}_{q,d}(\mathfrak{sl}_n)$. Algebras and Representation Theory 22 (2019), 177‒209. (pdf)

9. M. Bershtein and A. Tsymbaliuk, Homomorphisms between different quantum toroidal and affine Yangian algebras. Journal of Pure and Applied Algebra 223 (2019), no. 2, 867‒899. (pdf)

8. A. Tsymbaliuk, Classical limits of quantum toroidal and affine Yangian algebras. Journal of Pure and Applied Algebra 221 (2017), no. 10, 2633‒2646. (pdf)

7. A. Tsymbaliuk, The affine Yangian of $\mathfrak{gl}_1$ revisited. Advances in Mathematics 304 (2017), 583‒645. (pdf)

6. B. Feigin (M) and A. Tsymbaliuk, Bethe subalgebras of $U_q(\widehat{\mathfrak{gl}}_n)$ via shuffle algebras. Selecta Mathematica (New Series) 22 (2016), 979‒1011. (pdf)

5. A. Tsymbaliuk, Infinitesimal Hecke algebras of $\mathfrak{so}_N$. Journal of Pure and Applied Algebra 219 (2015), no. 6, 2046‒2061. (pdf)

4. I. Losev and A. Tsymbaliuk, Infinitesimal Cherednik algebras as W-algebras. Transformation Groups 19 (2014), no. 2, 495‒526. (pdf)

3. F. Ding (H) and A. Tsymbaliuk, Representations of infinitesimal Cherednik algebras. Representation Theory (electronic) 17 (2013), 557‒583. (pdf)

2. B. Feigin (M) and A. Tsymbaliuk, Equivariant K-theory of Hilbert schemes via shuffle algebra. Kyoto Journal of Mathematics 51 (2011), no. 4, 831‒854. (pdf)

1. A. Tsymbaliuk, Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces. Selecta Mathematica (New Series) 16 (2010), 173‒200. (pdf)

2) In-press journal articles (post-Purdue)

22. A. Tsymbaliuk, Book Shuffle approach towards quantum affine and toroidal algebras. To appear in SpringerBriefs in Mathematical Physics (2023), 124pp. (pdf)

3) Submitted (post-Purdue)

S3. Y. Avdieiev (H) and A. Tsymbaliuk, Affine standard Lyndon words: A-type. arXiv:2305.16299 (2023), 32pp. (pdf)

S2. Y. Hu (P) and A. Tsymbaliuk, Shuffle algebras and their integral forms: specialization map approach in types $B_n$ and $G_2$. arXiv:2305.00810 (2023), 46pp. (pdf)

S1. A. Negut and A. Tsymbaliuk, Quantum loop groups and shuffle algebras via Lyndon words. arXiv:2102.11269 (2021), 75pp. (pdf)