KAVLI IPMU NEWS | ISSUE #28 | DECEMBER 2014

ROUND TABLE TALK : CONVERSATION WITH EDWARD WITTEN | 17 PAGE PDF

|| EXCERPT 1 | KYOTO PRIZE & 4TH VISIT TO KYOTO ||

OOGURI : First I would like to congratulate Edward on your Kyoto Prize . In every four years , the Kyoto Prize goes in the field of mathematical sciences , and this is the first prize in this category awarded to a physicist .

WITTEN : Well , I can tell you I am deeply honored to receive this prize .

OOGURI : It is wonderful that your work in the area at the interface of mathematics and physics has been recognized as one of the most important progress in mathematics as well as in physics .

For those of us working in this area , this is also very gratifying .

As Yuji Tachikawa said at the workshop yesterday , you are like sunshine for all of us in this area of research .

WITTEN : Actually in my acceptance speech a couple of days ago , I remarked that I regard it also as a recognition of the field , not just of me .

|| EXCERPT 2 | LANGLANDS CORRESPONDENCE & GAUGE THEORY DUALITIES ||

WITTEN : For that year , I felt like someone who had discovered the meaning of life and could not explain it to anybody else . And in a sense , I still feel that way for the following reason .

Physicists with a background in string theory or gauge theory dualities can understand my paper with Kapustin on geometric Langlands but for most physicists this topic is too detailed to be really exciting .

On the other hand , it is an exciting topic for mathematicians , but difficult to understand because too much of the quantum field theory and string theory background is unfamiliar ( and difficult to formulate rigorously ) .

That paper with Kapustin may unfortunately remain mysterious to mathematicians for quite some time .

YAMAZAKI : Maybe that means that we have to wait an extra 10 or 15 years before . . .

WITTEN : We indeed may have to . I think it is actually very difficult to see what advance in the near term could make the gauge theory interpretation of geometric Langlands accessible for mathematicians .

That is actually one reason why I am excited about Khovanov homology .

My approaches to Khovanov homology and to geometric Langlands use many of the same ingredients , but in the case of Khovanov homology , I think it is quite feasible that mathematicians could understand this approach in the near future if they get excited about it . I believe it will be more accessible .

|| EXCERPT 3 | MESSAGE TO YOUNG STUDENTS ||

WITTEN : In the last 20 years , not only has this interaction of math and physics continued to be very rich but it has developed in such diversity that very frequently exciting things are done which I myself am able to understand embarrassingly little about , because the field is expanding in so many directions .

I am sure that this is going to continue and I believe the reason it will continue is that quantum field theory and string theory , I believe , somehow have rich mathematical secrets .

When some of these secrets come to the surface , they often come as surprises to physicists because we do not really understand string theory properly as physics — we do not understand the core ideas behind it .

At an even more basic level , the mathematicians are still not able to fully come to grips with quantum field theory and therefore things coming from it are surprises .

So for both of those reasons , I think that the physics and math ideas generated are going to be surprising for a long time .

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