| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Research Abstract |
In this research, I developed a theory that describes a surprising new relation between Heegaard Floer homology and the Homfly polynomial. The connection is well understood in the case of special alternating links, with partial results toward a generalization to all oriented links. It uses a theory in algebraic combinatorics (on hypertrees, polymatroids, and their interior polynomials) that I developed and which is very interesting in its own right. In joint work with Juhasz and Rasmussen, we related these notions to Heegaard Floer homology, and in joint work with Murakami, we described their connection to quantum invariants. All these works were presented at conferences both inside and outside of Japan, and with the exception of the joint work with Murakami, they were published in refereed journals.
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