A project devoted to the study of various mathematical structures related to cohomological Hall algebras of sheaves on smooth complex surfaces, from the points of view of representation theory (quantum groups, vertex algebras, Hopf algebras,...), algebraic geometry (moduli of sheaves or complexes, Donaldson-Thomas theory,...), combinatorics and mathematical physics (string theory and gauge theory, AGT conjectures,...).

The team currently comprises :

-Olivier Schiffmann (PI), Marian Aprodu, Vasile Brinzanescu, Sorin Dascalescu, Andrei Negut, Dragos Frătilă, Mihai Pavel (Postdoc), Jean Douçot (Postdoc),  Andrei Stoenică (PhD student), Calin Spiridon (PhD Student), 

Past activities :

Kickoff Meeting : IMAR, Sept. 4-8 2023 'Introduction to Cohomological Hall algebras'

Conference  Arithmetic and Algebraic Geometry Week  Conference Iasi, Sept. 1-5 2025

Preprints / Publications :

-M. Aprodu, G. Farkas, C. Raicu, A. Sammartano, A.I. Suciu,  Higher resonance schemes and Koszul modules of simplicial complexes, arXiv:2309.00609

-A. Mellit, A. Minets, O. Schiffmann, E. Vasserot, Coherent sheaves on surfaces, COHAS and deformed W_{1+\infty}-algebras., arXiv:2311.13415 

-A. Neguţ, Generators of the preprojective COHA of a quiver, arXiv:2311.07566, Bull. Lond. Math. Soc. 57 (2025), no. 8, 2561--2570. 

-O. Schiffmann, E. Vasserot, Cohomological Hall algebras of quivers and Yangians,  arXiv:2312.15803

-M. Aprodu, L. Filimon, Sections of K3 surfaces with Picard number 2 and Mercat's conjecture, arXiv:2401.08389, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 68(116) (2025), no. 2, 149–158. 

-D. Mégy,  M. Pavel, M. Toma, Semistability conditions defined by ample classes , arXiv:2402.07758, Geom. Dedicata 219 (2025), no. 1, Paper No. 18, 19 pp. 

-M. Pavel, J. Ross; M. Toma, Uniform boundedness of semistable pure sheaves on projective manifolds , arXiv:2403.12855, Pure Appl. Math. Q. 21 (2025), no. 4, 1491–1517. 

-M. Aprodu, Y. Kim,  Resonance, syzygies, and rank-3 Ulrich bundles on the del Pezzo threefold V_5 , arXiv:2404.12051

-M. Aprodu, G. Farkas, C. Raicu, A. I. Suciu, Reduced resonance schemes and Chen ranks, J. Reine Angew. Math. 814 (2024), 205–240. 

-A. Neguţ, F. Sala, O. Schiffmann, Shuffle algebras for quivers as quantum groups, Math. Ann. 391 (2025), no. 2, 2981–3021. 

-M. Pavel, M. Toma, Slope-semistability and moduli of coherent sheaves: a survey., arXiv:2407.13485, Rev. Roumaine Math. Pures Appl. 70 (2025), no. 1-2, 85–105. 

-M. Pavel, M. Toma, Moduli spaces of slope semistable sheaves with reflexive Seshadri graduations, arXiv:2407.06819

-A. Neguţ, Rational, trigonometric elliptic algebras and moduli spaces of sheaves on surfaces, arXiv:2407.00522

-A. Neguţ, A. Tsymbaliuk, Fusion and specializations for type ADE shuffle algebras, arXiv:2408.02411

-M. Aprodu, A. Bruno, E. Sernesi, The second Syzygy scheme of curves of large degrees, arXiv:2409.11855

-I. Macias Tarrio, C. Spiridon, A. Stoenică, Brill-Noether loci on an Enriques surface covered by a Jacobian Kummer surface, arXiv:2408.17837, Arch. Math. (Basel) 125 (2025), no. 2, 145–156. 

-A. Neguţ, A. Marian, Derived categories of Quot schemes on smooth curves and tautological bundles, arXiv:2411.08695

-M. Kapranov, V. Schechtman, O. Schiffmann, J. Yuan, The Langlands formula and perverse sheaves, arXiv:2412.01638

-A. Neguţ, Category O for quantum loop algebras, arXiv:2501.00724

-M. Pavel, T. Tajakka, Projectivity of the moduli of higher rank PT-stable pairs on a threefold, arXiv:2502.14530

-D.-E. Diaconescu, M. Porta, F. Sala, O. Schiffmann, E. Vasserot, Cohomological Hall algebras of one-dimensional sheaves on surfaces and Yangians , arXiv:2502.19445

-J. Douçot, Simplification of exponential factors of irregular connections on P^1, arXiv:2503.16102

-A. Neguţ, Characters of quantum loop algebras, arXiv:2503.17518

-A. Boralevi, D. Faenzi, D. Frăţilă, Equivariant spaces of matrices of constant corank one, arXiv:2504.16594

-A. Stoenică , The bielliptic locus of the Hilbert scheme of canonical curves is unirational, arXiv:2504.00789

-G. Rembado, J. Douçot, D. Yamikawa, Twisted local G-wild mapping class groups , arXiv:2504.01701

-M. Aprodu, C. Spiridon,  Linear sections of Grassmannians and resonance of vector bundles. International Mathematics Research Notices, DOI:10.1093/imrn/rnaf328

-J. Douçot, New nonabelian Hodge graphs from twisted irregular connections , arXiv:2509.24861

-A. Garbali, A. Neguţ, Shuffle algebras, lattice paths and quantum toroidal $gl_{n|m}$, arxiv:2507.00538

- A. Neguţ, Quiver moduli and quantum loop algebras, arXiv:2509.20815

- A. Neguţ, Extremal monomials of $q$-characters, arXiv:2510.08103

-M. Pavel, J. Ross, M. Toma, Generalized Bogomolov inequalities, arXiv:2510.04663