Department of

Mathematics


Seminar Calendar
for events the day of Friday, February 28, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, February 28, 2014

3:00 pm in 343 Altgeld Hall,Friday, February 28, 2014

0-Hecke algebra actions on coinvariants, flags, and Stanley-Reisner rings

Jia Huang (U. Minnesota)

Abstract: The 0-Hecke algebra is a deformation of the group algebra of the symmetric group. In this talk I will first review some interesting results regarding the symmetric group actions on coinvariants, finite flags, and Stanley-Reisner rings, and then present analogous results that I obtained for the 0-Hecke algebra actions on these objects.

4:00 pm in 243 Altgeld Hall,Friday, February 28, 2014

There is life on L^p: Examples of operator algebras on L^p spaces

Chris Phillips (University of Oregon)

Abstract: Banach space theorists will certainly tell you many interesting things about L^p spaces ("there is life _in_ L^p"). We exhibit what we believe to be interesting examples of operator algebras _on_ L^p spaces. We will concentrate on L^p analogs of Cuntz algebras and UHF algebras. (There is also work on reduced group L^p operator algebras, crossed products, and L^p analogs of irrational rotation algebras.) The basic properties of the C*-algebras carry over: for the L^p analogs of Cuntz algebras, simplicity, uniqueness, pure infiniteness, amenability, and the K-theory; for the L^p analogs of UHF algebras, simplicity, unique tracial state, and, for fixed p, classification in terms of K-theory. Sometimes the proofs are harder; occasionally, they are completely different (and do not work for p = 2). There are also new phemonena: none of these algebras for one value of p can ever be isomorphic to any such algebra for any other value of p.

4:00 pm in 241 Altgeld Hall,Friday, February 28, 2014

Automorphisms of free groups and Outer Space

Caglar Uyanik (UIUC Math)

Abstract: The study of outer automorphism group of a free group $F_N$ has greatly benefited from its analogy with the mapping class group. In this talk we will talk about the analogs of the Teichmuller space of a surface in the free group setting and show how one can retract information about the individual elements in $Out(F_N)$ by analyzing their action on various spaces. In particular, we will define Outer Space and space of geodesic currents and show some pictures.

4:00 pm in 345 Altgeld Hall,Friday, February 28, 2014

Measuring definable sets in o-minimal fields

Jana Marikova (Western Illinois)

Abstract: Let R be an o-minimal field. We propose a measure on the R-definable sets contained in the finite part of R^n. While this measure is not real-valued, it does take values in an ordered semiring and has various desirable properties, such as assigning a positive value to precisely the measurable sets with non-empty interior and satisfying a change of variables formula. This is joint work with Masahiro Shiota.