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Dec 14, 2012 at 21:27 comment added anon Candelas once told me that, when he asked Atiyah how to learn algebraic geometry, Atiyah responded: "You can't". At first Candelas thought Atiyah was making a statement about him personally, but what he was saying is that algebraic geometry is such a large subject that understanding it is a full-time occupation. I'm sure string theory is the same. Therein lies the problem, and it doesn't help that when mathematicians and physicists talk about the same object they often do so in very different ways.
Dec 14, 2012 at 1:26 comment added Jeff Harvey It would be fun, but would require a lot of time and dedication from both parties. I'm tempted to ask the converse, how does a physicist who knows QM, QFT and string theory learn algebraic geometry, or at least the parts that are most relevant to string theory? The standard answer seems to be to read the first few chapters of Griffiths&Harris and lecture notes by Candelas and others but I wonder if there is a better answer that doesn't involve a willing algebraic geometer.
Dec 13, 2012 at 19:58 comment added Todd Trimble Clearly the foursome should have gotten together much earlier. I'm sure there are similar blackboards with mirror symmetry on one, enumerative algebraic geometry on the other, and the two groups should somehow get together.
Dec 13, 2012 at 19:56 comment added Todd Trimble That's a really nice idea. On the covers of the IAS volumes mentioned by David Roberts, there are cartoons in four panels. The first two panels are set in the mid-60's; in one is a pair of physicists at a blackboard all excited about gauge theory, in the other is a pair of mathematicians at another blackboard all excited about Atiyah-Singer index theory. The second set of panels is set thirty years later; in the first the two physicists are staring with cartoon question marks at Atiyah-Singer index theory, and in the second the two mathematicians are likewise puzzling over gauge theory (cont.)
Dec 13, 2012 at 18:33 history answered Jeff Harvey CC BY-SA 3.0