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 Fratila, Mihai Pavel (Postdoc), Andrei Stoenica (PhD student), Calin Spiridon (PhD Student).

The grant covers funding for two extra postdoctoral positions and for two PhD fellowships at the Simion Stoilow Institute of Mathematics :

Starting date : any time from May 2024

Duration : up to 20 months

Salary : from 1800 Eu/month

If you are interested, please send an email at olivier.schiffmann@gmail.com, along with a CV (and a research program for the postdoctoral positions); recommendations should be emailed directly to the same address.

Past activities :

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

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. Negut, Generators of the preprojective COHA of a quiver, arXiv:2311.07566

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

D. Mégy, M. Pavel, M. Toma, Semistability conditions defined by ample classes , arXiv:2402.07758

M. Pavel, J. Ross; M. Toma, Uniform boundedness of semistable pure sheaves on projective manifolds , arXiv:2403.12855

M. Aprodu, Y. Kim,  Resonance, syzygies, and rank-3 Ulrich bundles on the del Pezzo threefold V_5 , to appear in Crelle's Journal.