Title:
Additive stucture, rich lines, and exponential set-expansion
Additive stucture, rich lines, and exponential set-expansion
| dc.contributor.advisor | Croot, Ernest | |
| dc.contributor.author | Borenstein, Evan | en_US |
| dc.contributor.committeeMember | Costello, Kevin | |
| dc.contributor.committeeMember | Lyall, Neil | |
| dc.contributor.committeeMember | Tetali, Prasad | |
| dc.contributor.committeeMember | Yu, XingXing | |
| dc.contributor.department | Mathematics | en_US |
| dc.date.accessioned | 2009-08-26T17:44:00Z | |
| dc.date.available | 2009-08-26T17:44:00Z | |
| dc.date.issued | 2009-05-19 | en_US |
| dc.description.abstract | We will survey some of the major directions of research in arithmetic combinatorics and their connections to other fields. We will then discuss three new results. The first result will generalize a structural theorem from Balog and Szemerédi. The second result will establish a new tool in incidence geometry, which should prove useful in attacking combinatorial estimates. The third result evolved from the famous sum-product problem, by providing a partial categorization of bivariate polynomial set functions which induce exponential expansion on all finite sets of real numbers. | en_US |
| dc.description.degree | Ph.D. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1853/29664 | |
| dc.publisher | Georgia Institute of Technology | en_US |
| dc.subject | Arithmetic combinatorics | en_US |
| dc.subject | Additive combinatorics | en_US |
| dc.subject | Combinatorics | en_US |
| dc.subject | Incidence geometry | en_US |
| dc.subject | Sum-product inequalities | en_US |
| dc.subject | Structural theorems | en_US |
| dc.subject.lcsh | Combinatorial analysis | |
| dc.subject.lcsh | Combinatorial geometry | |
| dc.subject.lcsh | Set functions | |
| dc.title | Additive stucture, rich lines, and exponential set-expansion | en_US |
| dc.type | Text | |
| dc.type.genre | Dissertation | |
| dspace.entity.type | Publication | |
| local.contributor.advisor | Croot, Ernest | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
| relation.isAdvisorOfPublication | 12d5c098-10ae-4a65-883e-60e8f1325f62 | |
| relation.isOrgUnitOfPublication | 85042be6-2d68-4e07-b384-e1f908fae48a | |
| relation.isOrgUnitOfPublication | 84e5d930-8c17-4e24-96cc-63f5ab63da69 |
Files
Original bundle
1 - 1 of 1
- Name:
- borenstein_evan_s_200908_phd.pdf
- Size:
- 313.71 KB
- Format:
- Adobe Portable Document Format
- Description: