Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, April 8, 2015.

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Wednesday, April 8, 2015

2:00 pm in 2 Illini Hall,Wednesday, April 8, 2015

Cohomological Consequences of The Pattern Map

Praise Adeyemo   [email] (University of Ibadan, Nigeria)

Abstract: Billey and Braden defined maps on flag manifolds that are the geometric counterpart of permutation patterns. A section of their map is an embedding of flag manifold of a Levi subgroup into the full flag manifold. We give two expressions for the induced map on cohomology. One is in terms of generators and the other is in terms of the Schubert basis. We show that the coefficients in the second expression are naturally Schubert structure constants and therefore positive. Similar results hold for K-theory, generalizing known formulas in type A for cohomology and K-theory. This is a joint work with Frank Sottile (Texas A & M).

3:00 pm in 345 Altgeld Hall,Wednesday, April 8, 2015

Auslander-Reiten Quivers for Type A, Part II

Anna Weigandt (UIUC)

Abstract: Given a quiver, $Q$, there is a corresponding Auslander-Reiten quiver, $\Gamma_Q$, which encodes information about the building blocks of the representation theory of $Q$. When the underlying graph of $Q$ is a type A Dynkin diagram, $\Gamma_Q$ gives a complete picture. We will present two methods of constructing $\Gamma_Q$ for type A quivers, the knitting algorithm and elementary rotations of an $n+3$-gon. We will then discuss homological properties which can be derived from $\Gamma_Q$. This talk will follow section 3.1 of Representations of Quivers, by R. Schiffler. It is a continuation of last week's IRT lecture.