Date	Speaker	Title
September 11		Planning meeting
September 18	Hunter Brook	The title of Hunter's talk was First Chern classes of holomorphic line bundles on complex tori. In this talk he showed a concrete description of first Chern classes in this setting in terms of linear algebra (more precisely, as certain alternating forms). The title of Zhixian's talk was Regular sequences and Koszul complexes, and she reviewed the definitions and basic results that we will be using in the course.
October 2	Michael Von Korff	Intersection on rational scrolls. The goal of this talk was to construct the intersection theory of divisors on surfaces and to work out in detail the intersection theory on n-fold rational scrolls.
October 9	Eugene Eisenstein and Kevin Tucker	Intersection numbers for plane curves - Herbrand Quotients . Eugene showed the uniqueness of intersection numbers for plane curves (see section 3.3 Fulton's Curves book), and Kevin covered material on Herbrand Quotients from Fulton's Intersection Theory book (see Appendix A.1 thru A.3).
October 16	Jose Gonzalez	On the topology of complex algebraic varieties. The goal of the talk was to use some topological tools to associate cohomology classes to the subvarieties of a smooth projective variety. The classes were constructed using the basic properties of Borel-Moore homology which was introduced during the talk.
October 23	Eugene Eisenstein and Mihai Fulger	This talk was devoted to some examples. Mihai showed us some explicit computations on projective bundles and Eugene discussed one well known example of a smooth surface with infinitely many rational curves of self intersection -1.
October 30	Andrew Kiluk	On the intersection theory of \overline{M_{0,n}} . In this talk Andrew reviewed some of the geometry of \overline{ M_{0,n}} and explicitly constructed some classes in the Chow ring of \overline{ M_{0,n}}. After this, he described the Chow ring of \overline{ M_{0,n}}.
November 6	Eugene Eisenstein	On the intersection theory of \overline{M_{g}} In this talk Eugene reviewed some of the geometry of \overline{M_{g}} and explicitly constructed some classes in the Chow ring of \overline{M_{g}}. Then he described the tautological ring and the Chow ring of \overline{M_{g}}.
November 13	Mihai Fulger	How many conics are tangent to 5 general conics in $\mathbb{P}^{5}$? . In this talk Mihai showed us how to answer this question from Enumerative geometry using some tools from intersection theory.
November 20	Jose Gonzalez	Flat, unramified and etale morphisms . In this talk we review the definitions and main properties of these classes of morphisms.
November 27	Thanks Giving Break
December 4	Amanda Knecht	Rationally connected varieties over $\mathbb{Q}_{p}^{nr}$. A result of Graber, Harris, and Starr shows that a rationally connected variety defined over the function field of a curve over the complex numbers always has a rational point. Similarly, a separably rationally connected variety over a finite field or the function field of a curve over any algebraically closed field has a rational point. We will discuss the case of rationally connected varieties over the maximally unramified extension of the p-adics. They `usually' have points, and we will define what `usually' means. (joint with Brad Duesler)
December 11	Jesse Kass	Intersection theory on some Jacobian bundles. In this talk Jesse explicitly described the Chow rings of some Jacobian bundles and carried out some concrete computations.