Dependent random choice, statistical physics, and the local rank of tensors
- Series
- Other Talks
- Time
- Friday, November 15, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Daniel Zhu – Princeton
We present a lemma, inspired by dependent random choice and sampling procedures from statistical physics, for finding dense structure in arbitrary $d$-partite $d$-uniform hypergraphs. We will then discuss how this lemma leads to the concept of local rank, a notion of tensor rank which is instrumental in proving a "structure vs. randomness" result for tensors (and by extension, polynomials): namely, a relation between the partition and analytic ranks of tensors over finite fields. This is joint work with Guy Moshkovitz.