During Spring 2017 the **UC Riverside Algebraic Geometry Seminar** will meet on Thursdays from 2:10pm to 3:00pm in Surge 268. For more information you may contact our seminar organizer Ziv Ran (ziv.ran@ucr.edu). Please find our schedule below. For information about reimbursements for our visitors click here.

Date |
Speaker |
Title |
Abstract |

Thursday, April 6, 2017 Start: 2:10 PM Location: Surge 268 |
| Planning week | No meeting this week. |

Thursday, April 13, 2017 Start: 2:10 PM Location: Surge 268 |
Daniel ChunUC Riverside | Overview of Koszul Cohomology: Applications and Current Questions | Syzygies of embedded projective varieties have historically attracted attention from many algebraists over the years. Mark Green's 1984 paper, which interprets syzygies as cohomology groups of a Koszul-type complex, made it both easier to compute them and to connect them to geometry. I will go over some applications of syzygy computations to geometric questions then introduce a current research topic about Koszul Cohomology. |

Thursday, April 20, 2017 Start: 2:10 PM Location: Surge 268 |
Omprokash DasUC Los Angeles | On the abundance problem for 3-folds in characteristic p>5 | In this talk I will explain the importance of the abundance conjecture in birational geometry, and in the classification of varieties in general. Then I will present the known cases of this conjecture in characteristic zero. Finally, I will talk about the recent advancements on this conjecture in dimension 3 and characteristic p>5. This is a joint work with Joe Waldron. |

Thursday, April 27, 2017 Start: 2:10 PM Location: Surge 268 |
Youngsu KimUC Riverside | Some commutative algebra for algebraic geometry | In this talk, we will introduce/review some commutative algebra which is often used in algebraic geometry. The primary goal of the talk is to supplement the commutative algebra part in Math 243B. If time permits, we will show that the ring C[x,y,z]/(x^2-yz) is a normal domain but not a UFD. |

Thursday, May 4, 2017 Start: 2:10 PM Location: Surge 268 |
Humberto DiazUC Riverside | Computing the class group | In this talk, I will give an overview of the basic properties of the class group of an algebraic variety, and use this to derive some tools for doing computations with the group. |

Thursday, May 11, 2017 Start: 2:10 PM Location: Surge 268 |
Youngsu KimUC Riverside | Normal rings and (discrete) valuation rings | We will continue exploring some backgrounds in algebra. This week we will revisit normal rings and then introduce (discrete) valuation rings. These rings arise often. When X is a normal k-variety, the local ring of a codimension 1 subvariety is a discrete valuation ring, DVR. |

Thursday, May 18, 2017 Start: 2:10 PM Location: Surge 268 |
Laure FlapanUC Los Angeles | Hodge Groups of Hodge Structures with Hodge Numbers (n,0,...,0,n) | One of the main tools available for proving certain cases of the Hodge conjecture for abelian varieties is to compute the Hodge groups of the weight-1 Hodge structures associated to these abelian varieties. Thus Hodge groups of abelian varieties have been extensively investigated. In this talk, we discuss generalizing these results about Hodge groups to arbitrary-weight Hodge structures with Hodge numbers (n,0,...,0,n), particularly when n is prime or twice a prime. These generalizations yield some new results about Hodge classes of 2p-dimensional abelian varieties. |

Thursday, May 25, 2017 Start: 2:10 PM Location: Surge 268 |
Fei XieUC Los Angeles | Toric surfaces over an arbitrary field | I will introduce toric varieties over arbitrary fields and classify minimal smooth projective toric surfaces. Then I will give an overview of the Merkurjev-Panin motivic category and give an explicit construction of the decomposition of toric surfaces in the motivic category into products of finite Azumaya algebras. I will explain how these Azumaya algebras determine the corresponding toric surfaces. |

Thursday, June 1, 2017 Start: 2:10 PM Location: Surge 268 |
Zhuang HeNortheastern University | New examples and non-examples of Mori Dream Spaces when blowing up toric surfaces | Mori Dream Spaces were introduced by Hu and Keel as normal, Q-factorial projective varieties whose effective cone admits a nice decomposition. As the name would indicate, Mori's minimal model program can be run for every divisor on a Mori Dream Space.
Recently there have been many studies on the question that for which integers a,b,c the blow-up of the weighted projective plane P(a,b,c) at a general point is a Mori Dream Space. In this talk, I will recall these recent work, and introduce a generalization of a result by Gonzalez and Karu in 2014. Specifically, for some toric surfaces of Picard number one, whether the blow-up is a Mori Dream Space is equivalent to countably many planar interpolation problems. I will give new examples and non-examples of Mori Dream Spaces, along with a conjecture of more non-examples, by reducing these interpolation problems. |

Thursday, June 8, 2017 Start: 2:10 PM Location: Surge 268 |
D. Blanton, T. McEldowney and A. WalkerUC Riverside | Short research presentations | Three graduate students
from our department,
working in algebraic geometry or neighboring areas,
will present the main ideas about the problems they solved or are currently working on for their theses. |