| Spring 2007 | This spring, the working geometry seminar will focus on the study of lines on projective varieties and more generally minimal degree rational curves on Fano varieties. The goal is to keep the presentations as elementary as possible while giving the participants (including graduate students) tools to work on open questions regarding lines and rational curves, in particular questions relating the the Hwang-Mok program. Here are surveys by Hwang, Mok, and Landsberg that are relevant to the seminar. |
| Jan 16: | J.M. Landsberg, Introduction to lines on projective varieties and minimal degree rational curves. I'll give an overview of the Hwang-Mok program and explain some conjectures on lines, e.g. the Debarre-deJong conjecture. |
| Jan 26: [Fri] |
J.M. Landsberg, Lines on homogeneous varieties.
I'll describe the varieties of lines on a Grassmannian, and the variety of lines through a point of a Grassmannian. I'll then show how to find the corresponding varieties on an arbitrary homogeneous variety using a pictorial recipe with Dynkin diagrams. This talk will be logically independent from last week's talk, so newcomers are still welcome! |
| Feb 6: [Tue] |
J. M. Landsberg, Proof of the Debarre-deJong conjecture?
I was just sent a preprint to go over, with a possible proof of the Debarre--de Jong conjecture. I'll discuss what I understand of this exciting development. Paper copies of the preprint available upon request. |
| Feb 23: [Fri] |
J.M. Landsberg, Lines in projective varieties and their
deformations. After covering some backround material on line bundles I'll begin studying lines, loosely following the survey lectures of Hwang and Mok you can obtain by clicking the links above. |
| Feb 27: [Tue] |
P. Stiller, Vector bundles on projective space. |
| Mar 7: [Wed] |
Milner 317, 4:00--5:30. J. Dilles, The Beheshti lemma on lines on low degree hypersurfaces. |
| Mar 13: | No seminar - Spring Break |
| Mar 23: [Fri] |
Colleen Robles,
The linear span of tangents to minimal rational curves on Fano
manifolds, Part 1. When is the distribution integrable? References include S.4 of the Hwang--Mok paper Rigidity of irreducible Hermitian symmetric spaces of the compact type under Kähler deformation; S.2 of Hwang's survey (above); and p.32--36 of Mok's lecture slides (above). |
| Mar 30: [Fri] |
Colleen Robles,
The linear span of tangents to minimal rational curves on Fano
manifolds, Part 2. Q: When is the distribution integrable? Q: What can we say about the variety of tangents to minimal rational curves when the picard number of M is 1? |
| Apr 3: [Tues, 2:30] |
Colleen Robles,
The linear span of tangents to minimal rational curves on Fano
manifolds, Part 3. Milner 317 Q: What can we say about the variety of tangents to minimal rational curves when the picard number of M is 1? |
| May 8: | Tues, 3 o'clock, Milner 216. |
| Jimmy Dilles (TAMU), Moduli of stable bundles and minimal rational tangents, following Hwang. | |
| Fall 2006 | Chapters 4-6 of Joyce's book Compact manifolds with special holonomy. This will included an introduction to Kahler geometry and Calabi-Yau manifolds. Our focus will be on the Calabi conjecture and Calabi-Yau manifolds. In addition to Joyce's book, we will use this short note by Blocki on the key estimate and this set of lectures on the Calabi conjecture by Blocki. |
| Nov 28: | Mustata Fest. |
| Nov 21: | Thanksgiving. |
| Nov 14: | J. Dilles, Everything you always wanted to know about
Calabi-yau manifolds, but were afraid to ask. |
| Oct 24 & 31, Nov 6: | No meetings do to the extra Geometry Seminars. |
| Oct 17: | J. Dilles, A gentle introduction to Calabi-Yau manifolds. |
| Oct 10: | E. Straub, Proof of the Calabi conjecture, Part 3. |
| Oct 3: | No meeting. |
| Sep 26: | E. Straub, Proof of the Calabi conjecture, Part 2. |
| Sep 19: | E. Straub, Proof of the Calabi conjecture -- after Z. Blocki, Part 1. |
| Sep 12: | C. Robles, Kahler geometry and the Calabi conjecture, Part 2. |
| Sep 5: | C. Robles, Kahler geometry and the Calabi conjecture, Part 1. |
| Aug 29: | J.M. Landsberg, What is a Kahler manifold and why should you care? |
| Summer 2006 | As a special end of summer treat, we will first go through Kostant's classic paper "Lie algebra cohomology and the generalized Borel-Weil" theorem. |
| Aug 22: | J.M. Landsberg, Lie algebra cohomology and the Bott-Borel-Weil Theorem. |
| Aug 15: | J.M. Landsberg, Introduction to Lie algebra chohomology. |