Junliang Shen    沈俊亮     

Publications.

Selected papers by subject with introductions:

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Preprints:

1. Topology of Galois conjugate character varieties (joint with S. Zhang). ArXiv 2607.12154, submitted.

2. Dualizable abelian fibrations (joint with D. Maulik and Q. Yin). ArXiv 2602.19318, submitted.

3. On the Orlov conjecture for hyper-Kähler varieties via hyperholomorphic bundles (joint with D. Maulik and Q. Yin). ArXiv 2601.20289, submitted.

4. 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, submitted.

5. 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. 

6. 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.

Publications

7. Topology of abelian fibrations, Proc. ICM 2026, Vol. 3: Invited Lectures (Sections 1-4), SIAM, Philadelphia, PA, 2026, 659-673. Link.

8. Cohomology of compactified  Jacobians for locally planar integral curves. Bootcamp Proc. 2025 SRI in Algebr. Geom., to appear. .arXiv 2512.14995.

9. 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. 

10. Algebraic cycles and Hitchin systems (joint with D. Maulik and Q. Yin). Ann. Sci. Éc. Norm. Supér. (4) 59 (2026), no.3, 637-682. ArXiv 2407.05188.

11. On generalized Beauville decompositions (joint with Y. Bae, D. Maulik, and Q. Yin). Selecta Math. (N.S.). 32 (2026), no. 3, Paper No. 45. ArXiv 2402.08861.

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

13. Fourier-Mukai transforms and the decomposition theorem for integrable systems (joint with D. Maulik and Q. Yin). Algebr. Geom.  3 (2) (2026) 266-304. ArXiv 2301.05825. 

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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

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

36. 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 Proceedings 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)