Department of

Mathematics


Seminar Calendar
for events the day of Friday, February 26, 2016.

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Friday, February 26, 2016

2:00 pm in 445 Altgeld Hall,Friday, February 26, 2016

Extremal Quasiconformal Mappings

Chris Gartland (UIUC Math)

Abstract: Given an orientation preserving homeomorphism between two Riemann surfaces, the classical Teichmuller problem asks to find a quasiconformal mapping in the same homotopy class with minimal distortion. In the same spirit, we'll investigate the problem of finding a quasiconformal mapping within a given class of mappings with minimal distortion. The class of mappings we consider are orientation preserving homeomorphisms of an annulus to itself with prescribed behavior on the boundary.

4:00 pm in 241 Altgeld Hall,Friday, February 26, 2016

$\alpha$-continued Fractions

Claire Merriman (UIUC Math)

Abstract: Continued fractions are one way to represent positive real numbers as a sequence of integers with connections to number theory, geometry, and dynamics. Nakada’s $\alpha$-continued fraction expansions are a family of continued fraction expansions corresponding to the regular continued fraction expansion when $\alpha=1$. I will review the regular continued fraction representation, as well as introducing the Gauss map and its invariant measure. Most of the talk will focus on Nakada’s work constructing an invariant measure for the $\alpha$-Gauss map and its natural extension when $1/2\leq \alpha\leq 1$.

4:00 pm in 345 Altgeld Hall,Friday, February 26, 2016

To be announced

Iván Ongay Valverde (UW-Madison Math)

4:00 pm in 347 Altgeld Hall,Friday, February 26, 2016

Combinatorial formulas for type A quiver orbit closures

Ryan Kinser   [email] (University of Iowa)

Abstract: This talk is based on joint work with Allen Knutson and Jenna Rajchgot. Orbit closures of quivers come up in several of areas of mathematics, for example: representations of finite-dimensional algebras, Lusztig's construction of the canonical basis, generalizations of determinantal varieties, and degeneracy loci for maps of vector bundles. This talk is most related to the last one, where "formulas" for orbit closures means their equivariant K-classes and cohomology classes. Previous work of many people produced such formulas in the case where all arrows of the quiver point the same direction, often having positive structure constants in some particular basis. We generalize some of these formulas to Type A quivers of arbitrary orientation. The main ingredient is the bipartite Zelevinsky map constructed in previous work of Rajchgot and mine, which identifies orbit closures with intersections of Schubert varieties and opposite Schubert cells in a partial flag variety.