Alumnae and Alumni

Alex James Bene
Project Researcher (from 2009/09/01 to 2010/08/31)
Current Affiliation
Math Department, Santa Monica College


Last Update 2024/05/20

In my research, I study Riemann surfaces, their moduli spaces, and their mapping class groups. The main tool I employ is a type of Feynman diagrams called a fatgraph which essentially gives a combinatorial representative of such surfaces. With this combinatorial perspective, one can use QFT techniques to study the cohomological aspects of moduli of Riemann surfaces and mapping class groups. More recently, I have used this combinatorial approach to study representations of mapping class groups, the classical Johnson homomorphisms, and finite type invariants of 3-manifolds. This last topic is interesting as it has a different QFT interpretations, and many of these finite type invariants also can be described in terms of similar Feynman diagrams.

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