Proof of the Geometric Langlands

(artwork by Elliot Kienzle)

Indeed, May has been an exciting month with posted preprints of the geometric Langlands conjecture:

Proof of the geometric Langlands conjecture I: construction of the functor

The bulk of the proof is found in parts II and III, and all parts are available here:

https://people.mpim-bonn.mpg.de/gaitsgde/GLC/

M-theory (and F-theory) from D=27+3

As the M-theory and Mathematics conference takes place in Abu-Dhabi, it’s great time to reflect on talks from last year.  In D=26+1 the M-theory superalgebra permits a 10-brane, with D=10+1 worldvolume signature.  This gives a worldvolume interpretation of 11D M-theory in 27-dimensions.  However, to include F-theory as well one is required to have at least a D=11+3 worldvolume theory, whose superalgebra takes the form specified by Sezgin et al. in hep-th/9711127.  Such a worldvolume exists in D=27+3, where an 11-brane sweeps out an (11,3) signature worldvolume.  Here string dualities are related to the various geometric reductions of this 11-brane worldvolume theory.

The State of String Theory

Brian Greene hosted a discussion with Edward Witten, Andrew Strominger and David Gross to discuss the state of string theory.  Topics were covered from black holes to AdS/CFT, as well as a historical discussion of string theory since the late 60s.  It would have been nice to hear more about M-theory and F-theory models, but alas strings were center stage in this gathering.

Coding the Cosmos: Stephen Wolfram

Stephen Wolfram discusses his computational approach to fundamental physics which utilizes multiway graphs and branchial networks.

M-theory & Math 2023

 

The M-theory and Mathematics workshop (2023) at NYUAD was a great success.  The quality of talks was excellent, especially with further progress on mysterious duality, K-theory and Cohomotopy (given hypothesis H).

Cheers to the organizers H. Sati, U. Schreiber and the Center for Quantum and Topological Systems.  Indeed, the quest for the underlying mathematics of M-theory continues.

Strings 2022

 

Ooguri gives an overview talk, mentioning wormholes, quantum chaos and compact Calabi-Yau spaces.  He ends with details of the organizational details of string conferences, including costs.  It is remarkable that during the pandemic, virtual conferences costed only 2k and 3k and enjoyed over 2,300 participants in 2020 and 2021.

Strings 2021

 

Continuing with a virtual format, talks included excellent reviews by Green, Schwarz and Witten.  The importance of understanding dualities was emphasized.  Indeed, string dualities require one to go beyond M-theory and F-theory in D=11 and D=12.

Strings 2020

A nice overview of Strings 2020, given by David Gross.  Fuzzballs and replica wormholes took center stage.