**SMS scnews item created by John Enyang at Tue 18 Jun 2013 0906**

Type: Seminar

Distribution: World

Expiry: 21 Jun 2013

**Calendar1: 21 Jun 2013 1205-1255**

**CalLoc1: Carslaw 375**

Auth: enyang@penyang.pc (assumed)

### Algebra Seminar

# The topology of the affine Grassmannian and the Mirkovic-Vilonen conjecture

### Achar

###### Friday 21st June, 12:05-12:55pm, Carslaw 375

###### Speaker:

Pramod Achar (Louisiana State University)

###### Title:

The topology of the affine Grassmannian and the Mirkovic-Vilonen conjecture

###### Abstract:

Given a complex reductive group \(G\), one can form its "affine Grassmannian" (or "loop Grassmannian"), a certain infinite-dimensional space that in many ways resembles ordinary (finite-dimensional) flag manifolds or Grassmannians. A deep result of Mirkovic-Vilonen (building on earlier work of Ginzburg and Lusztig) asserts that the algebraic topology of the affine Grassmannian encodes the representation theory of the dual group to \(G\) over any field. More precisely, certain intersection cohomology groups with coefficients in a field \(k\) realize the irreducible representations of the dual group over \(k\). This result raises the possibility of using the "universal coefficient theorem" of topology to compare representations over different fields. With that in mind, Mirkovic and Vilonen conjectured in the late 1990's that the local intersection cohomology of the affine Grassmannian with integer coefficients is torsion-free. I will try to explain these ideas with examples, and I will discuss the recent proof of (a slight modification of) the Mirkovic-Vilonen conjecture. This is joint work with Laura Rider.

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We will take the speaker to lunch after the talk.

See the Algebra Seminar web page for information about other seminars in the series.

John Enyang John.Enyang@sydney.edu.au

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