Department of

Mathematics


Seminar Calendar
for events the day of Monday, October 26, 2015.

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Monday, October 26, 2015

4:00 pm in 141 Altgeld Hall,Monday, October 26, 2015

Forcing and Baire category: an introduction (Part V)

Anton Bernshteyn (UIUC Math)

Abstract: We continue the series of talks introducing the method of forcing and its interpretation through the lens of Baire category. Previously we discussed how, using a countable model $M$ of ZFC, one can define objects that are "generic" relative to $M$. Now we are going to learn how to adjoin such objects to $M$ in order to construct models of ZFC with certain desirable properties (for instance, models satisfying the Continuum Hypothesis or its negation).

4:00 pm in 245 Altgeld Hall,Monday, October 26, 2015

Algebro-geometric methods in algebraic topology

Matthew Ando (Department of Mathematics, University of Illinois)

Abstract: One of the most productive areas of research in algebraic topology has been the used the algebra and geometry of one-dimensional algebraic groups, such as the multiplicative group and elliptic curves. Iíll indicate the origins of this in Quillenís theorem about complex cobordism, and Iíll also talk about K-theory and elliptic cohomology. In the case of elliptic cohomology, I hope I can mention a fascinating still evolving relationship with physics. From the point of view of algebraic topology, these are examples of the chromatic program in stable homotopy theory, and Iíll try to give an idea of what that is.

4:00 pm in 145 Altgeld Hall,Monday, October 26, 2015

Smoothness of Hilbert schemes of points on surfaces

Mi Young Jang (UIUC Math)

Abstract: In general, Hilbert schemes are highly non-smooth even for simple cases. Through this talk, however, we will see that Hilbert schemes of n points on smooth surfaces have nice smooth structure of dimension $2n$, and the Hilbert-Chow morphism from the Hilbert scheme of n points $Hilb^n(S)$ on a surface $S$ to the symmetric product $Sym^n(S)$ is a resolution of singularities.

5:00 pm in 241 Altgeld Hall,Monday, October 26, 2015

Continued Fractions and Operator Algebras

Florin Boca (UIUC Math)