Sunflowers and friends

Shachar Lovett
University of California San Diego
November 5, 2018
The Erdos-Rado sunflower conjecture is one of the tantalizing open problems in combinatorics. In my talk, I will describe several attempts on how to get improved bounds for it. These will lead to surprising connections with several other combinatorial structures, such as randomness extractors, intersecting families and DNFs.

Based on joint works with Xin Li, Noam Solomon and Jiapeng Zhang.

On the NP-hardness of 2-to-2 Games

Dor Minzer
Member, School of Mathematics
October 30, 2018

The Unique-Games Conjecture is a central open problem in the field of PCP’s (Probabilistically Checkable Proofs) and hardness of approximation, implying tight inapproximability results for wide class of optimization problems. 

We will discuss PCPs, the Unique-Games Conjecture and some recent progress. (no familiarity with PCPs or with last week's talk are needed).

 

The Zilber-Pink conjecture

Jonathan Pila
University of Oxford
October 26, 2018

The Zilber-Pink conjecture is a far reaching finiteness conjecture in diophantine geometry, unifying and extending Mordell-Lang and Andre-Oort. This lecture will state the conjecture, illustrate its varied faces, and indicate how the point-counting strategy can be applied to parts of it.