Department of

Mathematics


Seminar Calendar
for events the day of Friday, March 20, 2015.

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Friday, March 20, 2015

4:00 pm in 241 Altgeld Hall,Friday, March 20, 2015

Equivariant operads and their algebras.

Mychael Sanchez (UIUC Math)

Abstract: An E infinity operad is an operad that encodes the idea that a multiplication operation is not strictly commutative, but commutative up to homotopy coherence. This property essentially characterizes the E infinity operad up to equivalence. However, in equivariant homotopy theory, every family of subgroups determines a distinct equivariant operad, called an N infinity operad, whose underlying topological operad is E infinity. The goal of this talk is to introduce these operads and discuss properties of their algebras.

4:00 pm in 345 Altgeld Hall,Friday, March 20, 2015

A new characterization of $\boldsymbol{\Sigma}_2^1$ sets

Aristotelis Panagiotopoulos (UIUC)

Abstract: We will go over a recent paper J.Pawlikowski in which he presents a new characterization of $\boldsymbol{\Sigma}_2^1$ sets using only classical descriptive set theory. The Ramsey space $\mathcal{R}=[\omega]^\omega$ of all infinite subsets of natural numbers is usually endowed with either the Ellentuck topology or with the Baire topology. One of the interesting aspects of this characterization is that it arises from the way these two topologies are related.

4:00 pm in 147 Altgeld Hall,Friday, March 20, 2015

Combinatorial aspects of Schubert calculus in elliptic cohomology

Cristian Lenart   [email] (SUNY Albany Math)

Abstract: Modern Schubert calculus has been mostly concerned with the study of the cohomology and $K$-theory of flag manifolds. The basic results for other cohomology theories have only been obtained recently; additional complexity is due to the dependence of the geometrically defined classes on a reduced word for the corresponding Weyl group elements. After this main theory was developed, the next step is to derive explicit combinatorial formulas. I will describe my work with K. Zainoulline in this direction, which focuses on (torus equivariant) elliptic cohomology. We generalize the formulas of Billey (in ordinary cohomology) and Graham-Willems (in $K$-theory) for the equivariant Schubert classes. Another result is concerned with defining a Schubert basis (i.e., classes independent of a reduced word), using the Kazhdan-Lusztig basis of a certain Hecke algebra.