Department of

Mathematics


Seminar Calendar
for events the day of Thursday, September 8, 2016.

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Thursday, September 8, 2016

11:00 am in 241 Altgeld Hall,Thursday, September 8, 2016

Galois actions on the homology of Fermat curves, and applications

Vesna Stojanoska (Illinois Math)

Abstract: In the late 80ties, Anderson gave a method for describing the Galois action on the singular homology of Fermat curves. In this talk, I will concentrate on Fermat curves of prime exponent p, and the singular homology will have mod p coefficients. I will describe how to explicitly determine the Galois action using Andersonís work, and then proceed to compute some Galois cohomology groups, which naturally appear when studying certain obstructions to the existence of rational points. This is all joint work in progress with R. Davis, R. Pries, and K. Wickelgren.

12:00 pm in 243 Altgeld Hall,Thursday, September 8, 2016

Floer homology, group orders, and taut foliations of hyperbolic 3-manifolds

Nathan Dunfield (U of I Math)

Abstract: A bold conjecture of Boyer-Gorden-Watson and others posit that for any irreducible rational homology 3-sphere M the following three conditions are equivalent: (1) the fundamental group of M is left-orderable, (2) M has non-minimal Heegaard Floer homology, and (3) M admits a co-orientable taut foliation. Very recently, this conjecture was established for all graph manifolds by the combined work of Boyer-Clay and Hanselman-Rasmussen-Rasmussen-Watson. I will discuss a computational survey of these properties involving several hundred thousand hyperbolic 3-manifolds.

4:00 pm in 245 Altgeld Hall,Thursday, September 8, 2016

Geometric paradoxes and definability

Andrew Marks (UCLA)

Abstract: The well-known Banach-Tarski paradox states that the unit ball in $\mathbb{R}^3$ can be partitioned into finitely many pieces that can be rearranged by rotations and translations to form two unit balls. More than simply a curiosity, this type of paradox is intimately tied to the important group-theoretic notion of amenability. It also has applications in measure theory, for example, as part of Drinfeld, Margulis, and Sullivan's theorem that Lebesgue measure is the unique finitely additive rotation-invariant measure on the Lebesgue measurable subsets of the $n$-sphere, for $n > 1$. I will discuss some recent developments in descriptive graph combinatorics which have applications to the problem of how pathological the pieces in these paradoxes must be.