# Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

### Beyond geometric invariant theory

**Algebraic Geometry**

Speaker: | Daniel Halpern-Leistner, Cornell University |

Related Webpage: | https://www.math.cornell.edu/m/People/bynetid/dsh233 |

Location: | 2112 MSB |

Start time: | Wed, Mar 14 2018, 11:00AM |

Geometric invariant theory is an essential tool for constructing moduli spaces in algebraic geometry. Its advantage, that the construction is very concrete and direct, is also in some sense a draw-back, because for a given moduli problem it is often intractable to explicitly describe GIT semistable objects in an intrinsic and simple way. Recently a theory has emerged which treats the results and structures of geometric invariant theory in a broader context. The theory of Theta-stability applies directly to moduli problems without the need to approximate a moduli problem as an orbit space for a reductive group on a quasi-projective scheme. I will discuss some new progress in this program: joint with Jarod Alper and Jochen Heinloth, we give a simple necessary and sufficient criterion for an algebraic stack to have a good moduli space. This leads to the construction of good moduli spaces in many new examples, such as the moduli of Bridgeland semistable objects in derived categories.