This event is rescheduled untill further notice as a pre-emptive measure in view of the current Covid-19 (coronavirus) outbreak.

 

 

IISER Pune is happy to announce:

Institute Colloquium 2020

 

Lengths on Groups, RNA and Computer Proofs

 

Prof Siddhartha Gadgil, IISC, Bengaluru

(See flyer)

 

 

Date: Friday, March 27, 2020

 

Time: 5:15 pm

Abstract: 

In December 2018, Terence Tao (a leading mathematician of this age) posted on his blog a question (asked to him by Apoorva Khare) concerning so called lengths on groups. A week later, the problem was solved by an active collaboration of several mathematicians through Tao’s blog. I will discuss the proof of this result and also the process of discovery.

Groups are collections of elements with an operation combining a pair of elements to give a single one - for instance integers with the operation being addition form a group, as do rigid motions of the plane with the operation being composition (i.e., one motion followed by another). Length functions on groups are measures of the size of elements that have some natural properties. Tao's question concerned groups  where the operation on a pair of elements depends on the order (for example, composition of rigid motions). The question was whether in such cases there are length functions that behave well under scaling.

A crucial step in the discovery was the proof of an inequality that was computer generated but human readable. This was read, understood, generalized and abstracted to obtain the key step. The algorithm for finding the computer proof was based on the properties of a length function which is naturally associated to the folding of RNA.