Junliang Shen 沈俊亮
I joined the faculty of the math department of Yale University in the summer of 2021 as an Assistant Professor. I was a C. L. E. Moore instructor at MIT from 09.2018 - 05. 2021. I obtained my Ph.D in mathematics from ETH Zürich in June 2018 under the supervision of Rahul Pandharipande.
My research concerns algebraic geometry and related fields. My research is partially supported by the NSF grant DMS 2301474 and a Sloan Research Fellowship.
(New)
11.18. 2023: Séminaire Bourbaki by Victoria Hoskins: "Two proofs of the P=W conjecture after Maulik-Shen, Hausel-Mellit-Minets-Schiffmann".
11.28 - 12.01. 2023: Michigan Lectures in Algebraic Geometry: New perspectives of the topology of algebraic maps I,II,III, 2023.
03.31 - 04.05. 2024: Arbeitsgemeinschaft: Geometry and Representation Theory around the P=W Conjecture.
06.27 - 07.04. 2025: Summer school: "Enumerative Geometry and Geometric Representation Theory", Pisa, Italy.
@ South end of deer island
Some seminars:
(0) Reading Seminar (Fall 2024): Derived categories of GIT quotients.
(1) Yale's Geometry, Symmetry, and Physics Seminar.
(2) Algebra and Geometry lecture series.
Awards and honors:
SwissMAP Innovator Prize 2018.
NSF individual grant DMS 2000726 (transferred to DMS 2134315). 2020 - 2023.
NSF individual grant DMS 2301474. 2023 - 2026.
Séminaire Bourbaki on the P=W conjecture, after Maulik-Shen and Hausel-Mellit-Minets-Schiffmann 2023.
Sloan Research Fellowship. 2024-2026.
Publications.
Selected papers by subject with introductions:
Preprints:
1. The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles (joint with D. Maulik, Q. Yin, and R. Zhang). ArXiv 2408.14775v2.
(The updated version v2 removed the numerical constraint from the previous version v1; therefore this established the full D-equivalence conjecture for any varieties of K3[n]-deformation type.)
2. Algebraic cycles and Hitchin systems (joint with D. Maulik and Q. Yin). ArXiv 2407.05188.
3. 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.
4. On generalized Beauville decompositions (joint with Y. Bae, D. Maulik, and Q. Yin). ArXiv 2402.08861, submitted.
5. Perverse filtrations and Fourier transforms (joint with D. Maulik and Q. Yin). ArXiv 2308.13160, submitted.
6. Fourier-Mukai transforms and the decomposition theorem for integrable systems (joint with D. Maulik and Q. Yin). ArXiv 2301.05825, submitted.
Accepted:
7. The P=W conjecture for GL_n (joint with D. Maulik). ArXiv 2209.02568, to appear at Annals of Math.
Publications:
8. 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
9. 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
10. Perverse-Hodge complexes for Lagrangian fibrations (joint with Q. Yin). Épijournal Géom. Algébrique, Special volume in honor of Claire Voisin. Article No. 6 (2023). 2201.11283
11. 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
12. 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. (2023), pp. 1–21 ArXiv 2105.03043
13.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
14. 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
15. Endoscopic decompositions and the Hausel-Thaddeus conjecture (joint with D. Maulik). Forum Math. Pi. 9 (2021), Paper No. e8, 49 pp. ArXiv 2008.08520
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. The Euler characteristics of generalized Kummer schemes, Math. Z. 281 (2015), no. 3-4,1183-1189. ArXiv 1502.03973
29. Cobordism invariants of the moduli space of stable pairs, J. Lond. Math. Soc (2) 94 (2016), no.2, 427-446. ArXiv 1409.4576