Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 7, 2017.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 7, 2017

3:00 pm in 243 Altgeld Hall,Friday, April 7, 2017

#### An introduction to quantum cohomology and the quantum product

###### Joseph Pruitt (UIUC Math)

Abstract: The quantum cohomology ring of a variety is a q-deformation of the ordinary cohomology ring. In this talk I will define the quantum cohomology ring, discuss attempts to describe the quantum cohomology rings of toric varieties via generators and relations, and I will close with some methods to actually work with the quantum product.

3:00 pm in 343 Altgeld Hall ,Friday, April 7, 2017

#### Time fractional equations and probabilistic representation

###### Zhen-Qing Chen (University of Washington)

Abstract: Time-fractional diffusion equation can be used to model the anomalous diffusions exhibiting subdiffusive behavior, due to particle sticking and trapping phenomena. In this talk, I will discuss general fractional-time derivatives and probabilistic representation of solutions of the corresponding parabolic equations in terms of the corresponding inverse subordinators with or without drifts. An explicit relation between occupation measure for Markov processes time-changed by inverse subordinator in open sets and that of the original Markov process in the open set will also be given.

4:00 pm in 241 Altgeld Hall,Friday, April 7, 2017

#### Stable Phenomena in Algebraic Topology

###### William Balderrama (UIUC Math)

Abstract: A phenomenon might be called stable if it happens the same way in every dimension. For example, if $C_\bullet$ is a chain complex, then $H_\ast C_\bullet = H_{\ast+1}C_{\bullet+1}$: taking homology'' is done the same in every dimension. In some cases, a construction might not be stable, but can be stabilized. For example, if $M$ is a smooth closed manifold, choice of distinct embeddings $i,j\colon M\rightarrow \mathbb{R}^n$ give rise to possibly nonisomorphic choices of normal bundles $N_iM$ and $N_jM$. However, we can stabilize this by adding trivial bundles: $N_iM\oplus k \simeq N_jM \oplus k$ for sufficiently large $k$, leading to the notion of the stable normal bundle. In this talk, I will introduce this notion of stability, and propose spectra, the main objects in stable homotopy theory, as a good way for dealing with it.

4:00 pm in 245 Altgeld Hall,Friday, April 7, 2017

#### Model Theory as a Geography of Mathematics

###### Lou van den Dries (UIUC)

Abstract: This is a dry run for the first talk in the Tarski lectures I am giving the week after in Berkeley. This first talk is for a rather general audience of mathematicians, logicians, and philosophers. I like to think of model theory as a {\em geography of mathematics \}, especially of its tame'' side. Here {\em tame\/} roughly corresponds to {\em geometric\/} as opposed to {\em combinatorial-arithmetic}. In this connection I will discuss Tarski's work on the real field, and the notion of o-minimality that it suggested. A structure $M$ carries its own mathematical territory with it, via interpretability: its own posets, groups, fields,and so on. Understanding this world according to $M$'' can be rewarding. Stability-like properties of $M$ forbid certain combinatorial patterns, thus providing highly intrinsic and robust information about this world.