Junliang Shen    沈俊亮     

Publications.

Selected papers by subject with introductions:

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Preprints:

1. The intrinsic cohomology ring of the universal compactified Jacobian over the moduli space of stable curves (joint with Y. Bae, D. Maulik, and Q. Yin) arXiv 2509.05577.

2. 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. 

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. The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles (joint with D. Maulik, Q. Yin, and R. Zhang). Invent. Math. 241, 309–324, (2025). ArXiv 2408.14775. 

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

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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

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

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

Other published expository writing:

1. Cohomology of the moduli of Higgs bundles and the P=W conjecture. ICCM Proceeding 2020.   (pdf). 

2. Geometry and Representation Theory around the P=W Conjecture (joint with T. Hausel, D. Maulik, A. Mellit, and O. Schiffmann). Arbeitsgemeinschaft 2024.  (pdf)

3. Algebraic cycles and Hitchin system. Oberwolfach report 2024. (pdf)

4. Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture. ZAG Handbook of Modern Algebraic Geometry 2025.  (pdf)

5. The D-equivalence conjecture for K3[n]-type. Oberwolfach report 2025. (pdf)