# Event № 1593

Event № 1593

Type: Seminar

Name:

Title: Seminar on Codes, Lattices and High dimensional expanders

Speaker:

Place:
Ziskind 261, Weizmann Institute of Science

*Abstract:*

------------------------------------------------------------------------------------------------- Announcement: Seminar on Codes, Lattices and High dimensional expanders ------------------------------------------------------------------------------------------------- We are planning to discuss relations between several mathematical objects central for applications in CS (Computer Science), namely error correcting codes, lattices and expander graphs. For example, it is known that expander graphs allow to construct good codes. However, in recent years there is a growing interest in robust codes (codes for which proximity of a vector to the code could be deduced super-fast - independent of the vector length). Robust codes require some rigidity and redundancy properties that expander graphs do not have. The emerging theory of high dimensional expanders exhibits expansion behavior with some inherent rigidity and redundancy, so they might shed new light on robust codes. Error correcting codes are also known to be related to lattices - many results about codes have analogues for lattices. We will try to analyze how one can use expander graphs (maybe high-dimensional expanders) to construct good lattices. In the seminar we introduce central concepts of codes, expanders and lattices, Ramanujan graphs and complexes, and try to focus on revealing some potential relations between these concepts. In particular we will discuss 1. How to measure a "goodness" of a particular object of this type (i.e. how good is some family of codes, or lattices or expanders - we are mostly interested in asymptotic bounds). 2. How one can use Ramanujan graphs and complexes to construct good (potentially robust) codes and good lattices. We would like to formulate precise mathematical conjectures about Ramanujan graphs and complexes that should lead to objects with very good bounds. 3. We will discuss comparison of parameters of these objects with parameters of "random" objects Some of the concepts we discuss (like Ramanujan graphs and complexes) arise in representation and number theory. Other concepts (like robust codes) are at the heart of the theory of computation. So one of main aims of the seminar is to get together people from different communities (CS, Math, Eng, etc) to talk about these fascinating objects. In the seminar we will try to describe these objects from the point of view of the disciplines from which they arise, with the focus on finding potential relations between them. This should be interesting for people from all these communities. The seminar will feature talks of external experts as well as talks by some of the participants. The seminar is organized by Prof. Joseph Bernstein and Tali Kaufman. We will be glad to have your comments and suggestions about possible topics to discuss in the seminar. The seminar is scheduled for Wednesdays at 3-4:30pm @ Weizmann (starting Wednesday Oct 28; room 261). No prior knowledge in any of the mentioned concepts is assumed.

SubmittedBy:
Tali Kaufman , kaufmant@mit.edu

EventLink: Event № 1593