Sasaki-Einstein manifolds and AdS/CFT correspondence

Speaker: 

Dan Xie

Institution: 

Tsinghua University

Time: 

Monday, February 11, 2019 - 4:00pm

Location: 

RH 340P

Sasakian manifolds are odd dimensional analog of Kahler manifolds,
and it is an interesting question to determine when
a Sasakian manifold admits an Einstein metric. Five dimensional
Sasaki-Einstein (SE)  manifolds play an important role in AdS/CFT
correspondence, which relates a string theory and a quantum field theory. I
will discuss the existence of SE manifolds and its geometric properties
which will be of great interest to AdS/CFT correspondence.

Solving the Twisted Rabbit Problem using trees

Speaker: 

Rebecca Winarski

Institution: 

University of Michigan

Time: 

Monday, January 28, 2019 - 4:00pm to 5:00pm

Host: 

Location: 

RH 340P

The twisted rabbit problem is a celebrated problem in complex dynamics. Work of Thurston proves that up to equivalence, there are exactly three branched coverings of the sphere to itself satisfying certain conditions. When one of these branched coverings is modified by a mapping class, a map equivalent to one of the three coverings results. Which one?

After remaining open for 25 years, this problem was solved by Bartholdi-Nekyrashevych using iterated monodromy groups. In joint work with Belk, Lanier, and Margalit, we present an alternate solution using topology and geometric group theory that allows us to solve a more general problem.

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