Research Publications

1. Conjecture on first-order theta-blocks. (Russian) Uspekhi Mat. Nauk 72:5(437) (2017), 191-192; translation in Russian Math. Surveys 72:5 (2017), 968--970. (with V. Gritsenko)

2. Powers of Jacobi triple product, Cohen’s numbers and the Ramanujan \Delta-function.  Eur. J. Math. 4:2 (2018), 561--584. (with V. Gritsenko)  arXiv

3. Weight 3 antisymmetric paramodular forms. (Russian) Math. Sb. 210 (2019), no. 12, 43-66; translation in Sb. Math. 210 (2019), no. 12, 1702–1723. (with V. Gritsenko) arXiv

4. Theta block conjecture for paramodular forms of weight 2.  Proc. Amer. Math. Soc. 148 (2020), 1863-1878. (with V. Gritsenko) arXiv

5. Graded rings of integral Jacobi forms.  J. Number Theory 214 (2020), 382-298. (with V. Gritsenko)  arXiv

6. On some free algebras of orthogonal modular forms.  Adv. Math. 373 (2020), 107332, 22 pp. (with B. Williams) arXiv 

7. Reflective modular forms: a Jacobi forms approach.   Int. Math. Res. Not. IMRN. 2021 no. 3 (2021), 2081-2107.  arXiv

8. Weyl invariant Jacobi forms: a new approach. Adv. Math. 384 (2021), 107752, 13 pp. arXiv 

9. The classification of free algebras of orthogonal modular forms.  Compos. Math. 157 (2021), no. 9, 2026-2045. arXiv 

10. Weyl invariant E8 Jacobi forms. Commun. Number Theory Phys. 15 (2021) no. 3, 517-573.  arXiv 

11. On some free algebras of orthogonal modular forms II.  Res. Number Theory 7 (2021), no. 3, Paper No. 47, 21 pp.  arXiv 

12. Borcherds products of half-integral weight.  J. Number Theory 238 (2022), 944-950.  (with B. Williams) arXiv 

13. Theta blocks related to root systems.  Math. Ann. 384 (2022), No. 3-4, 1157-1180. (with M. Dittmann) arXiv 

14. Reflective modular forms on lattices of prime level. Trans. Amer. Math. Soc. 375 (2022), no. 5, 3451-3468.  arXiv 

15. Conway invariant Jacobi forms on the Leech lattice. Forum Math. 34 (2022), No. 6, 1591-1619.  (with K. Sun) arXiv 

16. Graded rings of Hermitian modular forms with singularities. Manuscripta Math. 170 (2023), 283-311. (with B. Williams) arXiv 

17. Siegel modular forms of degree two and level five. Ramanujan J. 60 (2023), 597-613. (with B. Williams)

18. Simple lattices and free algebras of modular forms. Adv. Math. 413 (2023), 108835, 51 pp.  (with B. Williams)  arXiv 

19. On weak Jacobi forms of rank two.  J. Algebra. 634 (2023), 722-754. (with B. Williams)  arXiv 

20. 2-reflective lattices of signature (n,2) with n>=8.  Int. Math. Res. Not. IMRN. 2023 no. 20 (2023), 17953-17971. arXiv

21. Weyl invariant E8 Jacobi forms and E-strings. Commun. Number Theory Phys. 17 (2023) no. 3, 553-582. (with K. Sun)  arXiv 

22. Automorphic products that are singular modulo primes.  Res. Number Theory.  10 (2024), no. 1, Paper No. 8, 16 pp. (with B. Williams)  arXiv 

23. The classification of 2-reflective modular forms. J. Eur. Math. Soc. 26 (2024), no. 1, pp. 111-151.  arXiv 

24. On intermediate Lie algebra E7+1/2.   Lett. Math. Phys. 114 (2024), no. 1, Paper No. 13, 33 pp. (with K. Lee & K. Sun). arXiv 

Accepted

1. Projective spaces as orthogonal modular varieties. Transform. Groups. publish online. (with B. Williams) arXiv   Data 

2. Modular forms with poles on hyperplane arrangements. to appear in Algebraic Geometry.  (with B. Williams)   arXiv 

Preprints

1. Free algebras of modular forms on ball quotients (with B. Williams). arXiv: 2105.14892. 

2. The fake monster algebra and singular Borcherds products  (with B. Williams). arXiv: 2207.14518.

3. Mathieu moonshine and Borcherds products (with B. Williams). arXiv: 2208.00574.

4. On the classification of reflective modular forms.  arXiv: 2301.12606.

5. On the non-existence of singular Borcherds products. (with B. Williams). arXiv: 2301.13367. 

6. There are no extremal eutactic stars other than root systems.  arXiv: 2302.00184. 

7. Hyperbolization of affine Lie algebras.  (with K. Sun & B. Williams). arXiv: 2312.03234. 

8. Orbits of Jacobi forms and Theta relations. (with V. Gritsenko). arXiv: 2312.13864. 

9. On intermediate Lie algebras. (with K. Lee & K. Sun). arXiv: 2403.14311. 

10. Sums of four polygonal numbers: precise formulas. (with J. Li). arXiv: 2405.14710.