Junliang Shen    沈俊亮     

Publications.

Selected papers by subject with introductions:

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Preprints:

1. The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles (joint with J. Hotchkiss, D. Maulik, Q. Yin, and R. Zhang). ArXiv 2502.09774, submitted.

2. The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles (joint with D. Maulik, Q. Yin, and R. Zhang). ArXiv 2408.14775, submitted. 

3. Algebraic cycles and Hitchin systems (joint with D. Maulik and Q. Yin). ArXiv 2407.05188, submitted.

4. Cohomological stabilization, perverse filtrations, and refined BPS invariants for del Pezzo surfaces (joint with F. Si, W. Pi, and F. Zhang). ArXiv 2406.10004, submitted.

5. On generalized Beauville decompositions (joint with Y. Bae, D. Maulik, and Q. Yin). ArXiv 2402.08861, submitted.

Accepted:

6. Fourier-Mukai transforms and the decomposition theorem for integrable systems (joint with D. Maulik and Q. Yin). ArXiv 2301.05825, To appear at Algebr. Geom.

Publications:

7 Perverse filtrations and Fourier transforms (joint with D. Maulik and Q. Yin). Acta Math. 234 (2025), Number 1, 1-69. ArXiv 2308.13160. 

8. The P=W conjecture for GL_n (joint with D. Maulik). Ann. of Math. 200 (2024), Issue 2, 529-556. ArXiv 2209.02568.

9. Perverse fitrations, Chern filtrations, and refined BPS invariants for local P2 (joint with Y. Kononov and W. Pi). Adv. Math.  433 (2023). 1209294. ArXiv 2211.06991

10. Generators for the cohomology ring of the moduli of one-dimensional sheaves on P^2. (joint with W. Pi). Algebr. Geom. 10 (4) (2023) 504–520. ArXiv 2204. 05866

11. Perverse-Hodge complexes for Lagrangian fibrations (joint with Q. Yin). Épijournal Géom. Algébrique, Special volume in honor of Claire Voisin. Article No. 6 (2023). ArXiv 2201.11283

12. On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties (joint with C. Felisetti and Q. Yin).  Tran. Amer. Math. Soc. 375(2022), no.4, 2987-3001. ArXiv 2108.02464

13. Cohomology of the moduli space of Higgs bundles via positive characteristic (joint with M. A. de Cataldo, D. Maulik, and S. Zhang).  J. Eur. Math. Soc. 27 (2025), no. 4, pp. 1385–1405. ArXiv 2105.03043

14. On the intersection cohomology of the moduli of SL_n-Higgs bundles on a curve (joint with D. Maulik).  J. Topol. 15 (3) (2022), 1034-1057. ArXiv 2103.01285

15. Cohomological χ-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles (joint with D. Maulik). Geom. Topol. 27:4 (2023), 1539-1586. ArXiv 2012.06627

16. Endoscopic decompositions and the Hausel-Thaddeus conjecture (joint with D. Maulik). Forum Math. Pi. 9 (2021), Paper No. e8, 49 pp. ArXiv 2008.08520

17. On the P=W conjecture for SL_n (joint with M. A. de Cataldo and D.  Maulik). Selecta Math.(N.S.) 28 (2022), No.5. Paper No. 90. ArXiv 2002.03336

18. Hitchin fibrations, abelian surfaces, and the P=W conjecture (joint with M. A. de Cataldo and D.  Maulik).  J. Amer. Math. Soc. 35 (3), 2022, 911-953.  ArXiv 1909.1188

19. P=W for Lagrangian fibrations and degenerations of hyper-Kaehler manifolds, (joint with A. Harder, Z. Li, and Q. Yin). Forum Math. Sigma. 9 (2021), Paper No. e50, 6 pp. ArXiv 1908.07510

20. Topology of Lagrangian fibrations and Hodge theory of hyper-Kaehler manifolds,  (joint with Q. Yin , an appendix by C. Voisin). Duke. Math. J. 171 (2022), no. 1, 209–241. ArXiv 1812.10673

21. Perverse filtrations, Hilbert schemes, and the P=W conjecture for parabolic Higgs bundles, (joint with Z. Zhang). Algebr. Geom. 8 (4) (2021) 465 - 489. ArXiv 1810.05330

22. Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants, (joint with G. Oberdieck and Q. Yin ).  Adv. Math. 357 (2019), 106829, 28 pp.  ArXiv 1805.07001

23. K3 categories, one-cycles on cubic fourfolds, and the Beauville-Voisin filtration, (joint with Q. Yin ).  J. Inst. Math. Jussieu.19 (2020), no. 5, 1601-1627. ArXiv 1712.07170

24. Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties, (joint with Q. Yin  and  X. Zhao ). Compos. Math. 156 (2020), no. 1, 179–197.  ArXiv 1705.06953

25. Reduced Donaldson-Thomas invariants and the ring of dual numbers, (joint with G. Oberdieck),  Proc. Lond. Math. Soc. (3) 118  (2019), no. 1, 191-220. ArXiv 1612.03102

26. Curve counting on elliptic Calabi-Yau 3-folds via derived categories, (joint with G. Oberdieck).  J. Eur. Math. Soc.  22 (2020), no. 3, 967-1002.  ArXiv 1608.07073

27. On O'Grady's generalized Franchetta conjecture, (joint with N. Pavic and Q. Yin),  Int. Math. Res. Not. (2017), 16, 4971-4983.  ArXiv 1604.02939

28. Hodge numbers of generalized Kummer schemes via relative power structures, (joint with A. Morrison). Moscow Math. J. 21 (2021), no.4. 807–830. Major revision from ArXiv 1505.02989

29. The Euler characteristics of generalized Kummer schemes, Math. Z. 281 (2015),  no. 3-4,1183-1189.  ArXiv 1502.03973

30. Cobordism invariants of the moduli space of stable pairs, J. Lond. Math. Soc (2) 94  (2016),  no.2, 427-446.  ArXiv 1409.4576