Feb. 14
12:201:20

Chris Fraser (IUPUI)
Cluster
varieties in geometry
Abstract [+]
I will give a historical introduction to cluster varieties, focusing on a few concrete examples (Grassmannians and spaces of decorated Glocal systems). I will end by discussing symmetries of cluster structures, emphasizing a connection with mapping class groups of surfaces and braid groups.

FEB. 21

TBD
Polyhedral
products are the central objects in the new field of
toric topology. In this talk I will give an
introduction to these combinatorial constructions in
topology, and give a few applications, including
calculations of some monodromy representations.

Feb. 28 
TBD

mar. 7


mar. 14 
Spring Break

Mar. 21

TBD

MAR. 28 
Jessie
Yang (Marian University)
Tropical geometry and NewtonOkounkov body for Grassmannian of planes
Abstract

Apr. 4 
TBD
We study the
space of group homomorphisms Hom(Z^n,G) of pairwise
commuting ntuples in a compact and connected Lie
group G, from the topological viewpoint. We will
describe a way to stabilize spaces of homomorphisms by
introducing an infinite dimensional topological space,
reminiscent of a Stiefel variety, that assembles the
spaces of commuting tuples into a single space.
HilbertPoincare series will be also described and if
time permits other properties will also be given.

ApR. 11

TBD
By the
RiemannHilbert correspondence, we have a categorical
equivalence between holomorphic connections on a
Riemann surface X (automatically flat) and
representations of the fundamental group of X. This
connects the analytic theory of ODEs with its
geometric counterpart. In this talk, we will see a
third aspect of this correspondence with a modern
algebraic flavor. Namely, any ODE of the form y' = Ay
induces an extension field called the PicardVessiot
field. Its group of differential automorphisms is a
linear algebraic group called the Galois group of the
ODE. Time permitting, we will give a classification of
regular singular and formal differential equations as
neutral tannakian categories. That is, categories of
representations for an affine group scheme G. This
extends the RiemannHilbert correspondence and
presents a unifying viewpoint between the analytical,
geometrical and algebraic theory.

APR. 18 
Peter LambertCole (IU Bloomington)

APR. 25 
TBD

Past semesters:
Fall
2016

IUPUI • Department of
Mathematical Sciences 