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K-State Today

February 19, 2013

Mathematics Colloquium today

By Reta McDermott

Christopher Brav from the Mathematical Institute at the University of Oxford will present "Ping-Pong and Thin Monodromy" at 2:30 p.m. today in 122 Cardwell Hall. 

Abstract: Monodromy groups of low order hypergeometric differential equations have been well understood since the 19th century, with the examples arising in algebraic geometry typically being "arithmetic." While some general results about monodromy groups of higher order equations have been known for over 20 years, many basic questions remain open.

Brav will discuss joint work with Hugh Thomas that gives the first examples of nonarithmetic or "thin" monodromy groups of higher rank arising in algebraic geometry. More precisely, Brav and Thomas use the ping-pong lemma of Fricke and Klein to show that the monodromy groups of certain one-parameter families of Calabi-Yau manifolds split as free products and then apply a cohomological criterion to deduce that the groups are not arithmetic.