Bumsig Kim (KIAS)

- TItle: Hochschild Homology of GLSM

- Abstract: A Landau-Ginzburg model is a smooth DM stack X with a regular function w or more generally, a section w of a line bundle on X.  There is a notion of  factorizations for w which plays the role of complexes of sheaves. When the Landau-Ginzburg model is a gauged linear sigma model, we compute Hochschild homology. This is based on joint work with I. Ciocan-Fontanine, D. Favero, J. Guere, and M. Shoemaker.

Marian Aprodu (University of Bucharest)

- TItle: Koszul modules and syzygies of rational cuspidal canonical curves

- Abstract: Koszul modules originate in geometric group theory in relations with the Chen ranks of a finitely generated group. I will discuss a vanishing result for Koszul modules and its applications to syzygy theory. The talk is based on joint works with G. Farkas, C. Raicu, S. Papadima and J. Weyman.

Zhang De-Qi (National University of Singapore)

- Title: Characterizations of Toric Varieties via Polarized Endomorphisms

- Abstract: Let X be a normal projective variety and f: X to X a non-isomorphic polarized endomorphism. We give two characterizations for X to be atoric variety.

First we show that if X is Q-factorial and G-almost homogeneous for some linear algebraic group G such that f is G-equivariant, then X is atoric variety.

Next we give a geometric characterization: if X is ofFano type and smooth in codimension 2 and if there is an f^{-1}-invariant reduced divisor D such that f|_{XD} is quasi-etale and K_X+D is Q-Cartier, then X admits a quasi-etale cover X’ such that X’ is atoric variety and f lifts to X’. In particular, if X is further assumed to be smooth, then X is atoric variety. This is a joint work with Sheng Meng.

Edoardo Sernesi (Rome III)

- Title: Explicit Brill-Noether-Petri general curves.

- Abstract: The purpose of my talk is to explain the construction of a concrete class of integral plane curves of arbitrary geometric genus whose normalization is Brill-Noether-Petri general, following a recent paper by Arbarello-Bruno-Farkas-Sacc?.