#### Hall 123

#### Homological Algebra of Ideals Related to Finite Simple Graphs

#### Arindam Banerjee

##### Purdue University

*Given any finite simple graph, one can naturally associate two quadratic homogeneous ideals: the edge ideal and the binomial edge ideal. The interplay between the homological algebra of these ideals along with their various powers and quotients, with the combinatorics of the underlying graphs has been an active area of research in last few decades. In this talk we shall discuss the relation between homological invariants like regularity , depth etc with various combinatorial structures in the graph. Some new techinues and results will be introduced and some open problems for future research will be discussed. Various connections with other areas of homological commutative algebra, like local cohomology, Stanley-Reisner theory etc shall also be mentioned.*

Done