# Special Quantum PCP and/or Quantum Codes: Simplicial Complexes and Locally Testable CodesDay

### room B-220, 2nd floor, Rothberg B Building

On Thursday, the 24th of July we will host a SC-LTC (simplicial complexes and classical and quantum locally testable codes) at the Hebrew university, Rothberg building B room 202 (second floor) in the Givat Ram campus. Please join us, we are hoping for a fruitful and enjoyable day, with lots of interactions. Coffee and refreshments will be provided throughout the day, as well as free “tickets” for lunch on campus
There is no registration fee, but please email dorit.aharonov@gmail.com preferably by next Tuesday if there is a reasonable probability that you attend –  so that we have some estimation regarding the number of people, for food planning

Program:SC-LTC day – simplicial complexes and locally testable classical and quantum codes –Rothberg building B202
9:00 gathering: coffee and refreshments

9:30 Irit Dinur: Locally testable codes, a bird’s eye view

10:15: coffee break

10:45 Tali Kaufman, High dimensional expanders and property testing

11:30 15 minutes break

11:45 Dorit Aharonov, quantum codes and local testability

12:30 lunch break

2:00 Alex Lubotzky: Ramanujan complexes

2:50 coffee break

3:15 Lior Eldar: Open questions about quantum locally testable codes and quantum entanglement

3:45 Guy Kindler: direct sum testing and relations to simplicial complexes ( Based on David, Dinur, Goldenberg, Kindler, and Shinkar, 2014)

4:15-5 free discussion, fruit and coffee

# Helly’s Theorem, “Hypertrees”, and Strange Enumeration I

### 1. Helly’s theorem and Cayley’s formula

Helly’s theorem asserts: For a family of n convex sets in $R^d$, n > d, if every d+1 sets in the family have a point in common then all members in the family have a point in common.

Cayley’s formula asserts: The number of  trees on n labelled vertices is $n ^{n-2}$.

In this post (in two parts) we will see how an extension of Helly’s theorem has led to high dimensional analogs of Cayley’s theorem.

left: Helly’s theorem demonstrated in the Stanford Encyclopedia of Philosophy (!), right: a tree

### 2. Background

This post is based on my lecture at Marburg. The conference there was a celebration of new doctoral theses Continue reading