High dimensional expanders, topological overlapping and property testing
Event details
| Date | 11.06.2015 |
| Hour | 11:15 › 12:15 |
| Speaker | Alex Lubotzky [Jerusalem] |
| Location |
MA A3 30
|
| Category | Conferences - Seminars |
Expander graphs in general, and Ramanujan graphs in particular, have played an important role in computer science and pure mathematics in the last 4 decades.
In recent years the area of high dimensional expanders (i.e. simplical complexes with properties generalizing those of expanding graphs) and Ramanujan complexes is starting to emerge.
It appears naturally (so far) in 3 topics:
a) Linial-Meshulam theory of random complexes generalizing the Erdos-Renyi random graphs,
b) Gromov's overlapping properties (these are far reaching extensions of the following result: for every N points set P in the plane, there is a point z which is covered by at least 2/9 of the (N choose 3) triangles determined by P.)
c) Testability properties in computer science.
We will survey these developments and present some new results and open problems.
Our works on these topics are joint with subsets of { Tali Kaufman, David Kazhdan, Roy Meshulam, Beth Samuels, Uzi Vishne }.
In recent years the area of high dimensional expanders (i.e. simplical complexes with properties generalizing those of expanding graphs) and Ramanujan complexes is starting to emerge.
It appears naturally (so far) in 3 topics:
a) Linial-Meshulam theory of random complexes generalizing the Erdos-Renyi random graphs,
b) Gromov's overlapping properties (these are far reaching extensions of the following result: for every N points set P in the plane, there is a point z which is covered by at least 2/9 of the (N choose 3) triangles determined by P.)
c) Testability properties in computer science.
We will survey these developments and present some new results and open problems.
Our works on these topics are joint with subsets of { Tali Kaufman, David Kazhdan, Roy Meshulam, Beth Samuels, Uzi Vishne }.
Practical information
- General public
- Free
Contact
- Jacques Thévenaz