Date | Speaker | Title | Abstract |
April 4, 2019 Start: 11:10 AM Location: Surge 277 |
| Planning meeting. | Planning meeting. |
Thursday, April 11, 2019 Start: 11:10 AM Location: Surge 277 |
Zhixian Zhu UC Riverside | From Bezout's theorem to intersection theory. | In this talk, we will first review the intersection theory of curves on smooth projective surfaces and state the Bezout's theorem on projective spaces. At the end, we will briefly introduce the notation of Chow groups and rational equivalence. |
Thursday, April 18, 2019 Start: 11:10 AM Location: Surge 277 |
Jose Gonzalez UC Riverside | An invitation to intersection theory. Part 1. | In this talk we will give an overview of the basics of Chow theory. |
Thursday, April 25, 2019 Start: 11:10 AM Location: Surge 277 |
Jose Gonzalez UC Riverside | An invitation to intersection theory. Part 2. | In this talk we will continue our overview of the basics of Chow theory. |
Thursday, May 2, 2019 Start: 11:10 AM Location: Surge 277 |
Ziv Ran UC Riverside | Chern Classes. Part 1. | The Chern classes of an algebraic vector bundle capture some of its topological and numerical properties, extending the correspondence between line bundles and divisors. We will discuss some basic properties and constructions for Chern classes. As time permits we will mention some of their many applications in enumerative geometry. |
Thursday, May 9, 2019 Start: 11:10 AM Location: Surge 277 |
Ziv Ran UC Riverside | Chern Classes. Part 2. | The Chern classes of an algebraic vector bundle capture some of its topological and numerical properties, extending the correspondence between line bundles and divisors. We will discuss some basic properties including Whitney sum formula, Chern roots, interpretation of top class, self-intersection formula; plus an application to enumerative geometry. |
Thursday, May 16, 2019 Start: 11:10 AM Location: Surge 277 |
Ziv Ran UC Riverside | Chern Classes. Part 2.5: 32-160+180-51=1. | How many conics are tangent to 5 given lines? Classical geometry says 1. Yet Bezout's theorem seems to give 2^5=32. We will discuss how intersection theory and Chern classes allow us to analyze the error in the Bezout number and arrive at the correct number. |
Thursday, May 23, 2019 Start: 11:10 AM Location: **Surge 284** |
Javier Gonzalez Anaya University of British Columbia | Constructing examples and non-examples of Mori Dream Spaces via a prime characteristic method. | We consider the problem of finite generation of the Cox ring for blow-ups of weighted projective planes at a generic point of the torus. By a result of Cutkosky, finite generation for these spaces is equivalent to the existence of two different curves in these varieties: (1) a “negative curve”, different from the exceptional curve, and (2) another curve disjoint from the previous one. Toric geometry converts (1) into a combinatorial problem while, by work of Kurano and Nishida, the second condition can be tested by considering the problem in positive characteristic for all primes big enough. After a brief introduction we’ll talk about the problem of finding the negative curves in (1), describe the reduction method to prime characteristic and talk about the obstructions to lift the solutions back to characteristic zero. We’ll conclude by presenting our results and some of the open problems in the area. This is joint work with J. L. Gonzalez and K. Karu. |
Thursday, May 30, 2019 Start: 11:10 AM Location: Surge 284 |
Jose Gonzalez UC Riverside | Intersection theory example: Toric varieties. | We will discuss some basic aspects of intersection theory on toric varieties including the description of the Chow ring of a smooth projective toric variety. |