Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, January 29, 2015.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, January 29, 2015

11:00 am in 241 Altgeld Hall,Thursday, January 29, 2015

#### When is the multiplicative group of a field indecomposable?

###### Sunil Chebolu   [email] (Illinois State University)

Abstract: Recall that an abelian group is said to be indecomposable if it cannot be written as a direct sum of two non-trivial subgroups. Let F be a field and let F^* denote the multiplicative group of F. The problem we investigate is the following. When is F^* an indecomposable abelian group? We will solve this problem when the characteristic of F is not equal to 2. The answer involves Mersenne and Fermat primes, and one solution to this problem involves the famous Catalan's conjecture. We also have some partial results when the characteristic of the field is 2. I will discuss these results which are in joint work (arXiv:1407.3481) with Keir Lockridge.

1:00 pm in Altgeld Hall 243,Thursday, January 29, 2015

#### Certifying the Thurston norm via twisted homology

###### Nathan Dunfield (UIUC Math)

Abstract: From the very beginning of 3-manifold topology, a fundamental task has been to find the simplest surface in a given 2-dimensional homology class, e.g. the Seifert genus of a knot in the 3-sphere. The behavior of the minimal topological complexity as the homology class varies is encapsulated in the Thurston norm. In this talk, I will discuss tools for proving that a particular surface has minimal genus. These are generalizations of the classical Alexander polynomial, but are defined using homology with coefficients twisted by some finite-dimensional representation of the fundamental group of the manifold. I will discuss recent work with Ian Agol on situations where using representations coming from hyperbolic geometry suffices to provide such certificates. If time permits, I will sketch how all of this relates to fundamental questions about the computational complexity of finding the Thurston norm. Only basic facts about manifolds and homology will be assumed. View lecture at http://youtu.be/b7a-WXpNLAQ

2:00 pm in 140 Henry Administration Bldg,Thursday, January 29, 2015

#### Open problems in Number Theory, I

###### Bruce Berndt (UIUC Math)

2:00 pm in 243 Altgeld Hall,Thursday, January 29, 2015

#### Sub-Riemannian isoperimetric inequalities on totally geodesic foliations

###### Fabrice Baudoin (Purdue University)

Abstract: In this talk I will present some joint works with Bumsik Kim concerning isoperimetric inequalities on sub-Riemannian manifolds that come from a totally geodesic Riemannian foliation.

3:00 pm in 243 Altgeld Hall,Thursday, January 29, 2015

#### Organizational Meeting

4:00 pm in 245 Altgeld Hall,Thursday, January 29, 2015