Intersections from various perspectives: A tourist guide
Duration: 33 mins 2 secs
Share this media item:
Embed this media item:
Embed this media item:
About this item
| Description: |
Algebraic Geometry - Recorded 16/04/09 3:30-4:00pm, MR2
Speaker: Oliver Braeunling |
|---|
| Created: | 2009-06-11 13:02 |
|---|---|
| Collection: | Beyond Part III - Young Researchers in Mathematics 2009 |
| Publisher: | University of Cambridge |
| Copyright: | A.C. Cullum Hanshaw |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 4:3 |
| Screencast: | No |
| Bumper: | not set |
| Trailer: | not set |
| Abstract: | The notion of an 'intersection multiplicity' may be approached from various directions. We may start with a real oriented surface (as a manifold) and by drawing a few pictures one is led quite naturally to an intersection theory for oriented compact manifolds. We focus on the de Rham picture (neglecting torsion) and here intersecting two suitable submanifolds comes down to computing the wedge product of forms in de Rham cohomology (this is a graded anti-commutative product). For a regular variety (for example in positive characteristic) many of the manifold techniques do not have an immediate counterpart in "algebraic" algebraic geometry, and we no longer have the flexibility of smooth functions/forms. Nonetheless one may construct an intersection theory, this time living in a commutative ring called CH* (as opposed to the anticommutative wedge product). At first sight this may seem incompatible, but the situation is clarified by looking at complex manifolds, where complex submanifolds live in the even degree parts of de Rham cohomology. Moreover, if they intersect transversally, they do so with multiplicity +1. The talk will not contain anything new. Instead it intends to present an example of approaching the same problem from totally different directions.
|
|---|---|
Available Formats
| Format | Quality | Bitrate | Size | |||
|---|---|---|---|---|---|---|
| Flash Video | 480x360 | 800.95 kbits/sec | 193.79 MB | View | Download | |
| Flash Video | 320x240 | 435.33 kbits/sec | 105.33 MB | View | Download | |
| iPod Video | 320x240 | 504.37 kbits/sec | 122.03 MB | View | Download | |
| QuickTime (for download) | 480x360 | 506.29 kbits/sec | 122.49 MB | View | Download | |
| QuickTime (for streaming) | 480x360 | 913.32 kbits/sec | 220.97 MB | View | Download | |
| MP3 | 44100 Hz | 125.0 kbits/sec | 30.05 MB | Listen | Download | |
| RealAudio | 257.2 kbits/sec | 61.82 MB | View | Download | Stream | |
| RealMedia | 876.27 kbits/sec | 212.01 MB | View | Download | Stream | |
| Windows Media Video (for download) | 477.02 kbits/sec | 115.41 MB | View | Download | ||
| Windows Media Video (for streaming) | 476.76 kbits/sec | 115.35 MB | View | Download | Stream | |
| Auto * | (Allows browser to choose a format it supports) | |||||