Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, February 23, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2016          February 2016            March 2016
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2       1  2  3  4  5  6          1  2  3  4  5
3  4  5  6  7  8  9    7  8  9 10 11 12 13    6  7  8  9 10 11 12
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Tuesday, February 23, 2016

5:30 am in Altgeld Hall,Tuesday, February 23, 2016

#### Complete Network Outage

###### Math IT (Illinois Math)

Abstract: Dear colleagues, Altgeld Hall will experience a complete network outage on Tuesday, February 23rd, from 5:30AM to 7:30AM CST. During that two hour window significant parts of Altgeld Hall’s wired infrastructure will be upgraded. Please plan accordingly, as the following services will be affected: - E911 services will be unavailable: you will not be able to use Lync phones to call 911 in case of an emergency! - All wired AND wireless connections in Altgeld Hall will be down - Printing in Altgeld Hall will be unavailable - Departmental email delivery will be delayed To assure a quick restoration of services after the upgrade, it is best if everyone shuts down, or at least logs off of, any departmental computer in Altgeld Hall the night before (Monday, February 22nd). We expect that you will all be able to resume work as usual after 7:30AM. Now for the exciting part: this upgrade will assure gigabit speeds for all wired network connections in Altgeld - a 10-fold increase in speed for everyone! Math IT will work closely with Technology Services to assure a smooth upgrade and minimize any post-upgrade issues. If you have any questions or concerns, please let us know at math-it@illinois.edu.

11:00 am in 345 Altgeld Hall,Tuesday, February 23, 2016

#### An obstruction theory for producing exotic Picard elements

###### Robert Legg (Northwestern)

Abstract: Given an E_*E-comodule, for some homology theory E, can we find a spectrum whose homology is this comodule? I’ll describe an approach to answering a variant of this question using an obstruction theory and how this approach then can be used to produce elements of the K(n)-local exotic Picard group, that is, K(n)-local spectra that are invertible but which are indistinguishable from the sphere on homology.

12:00 pm in Altgeld Hall 243,Tuesday, February 23, 2016

#### Cheeger constants of arithmetic hyperbolic surfaces

###### Grant Lakeland (Eastern Illinois University)

Abstract: Given a Riemannian manifold M, the Cheeger constant, h(M), is a geometric invariant which measures the extent to which M has “bottlenecks” - roughly speaking, these are low volume, separating, codimension one submanifolds. We implement an algorithm of Benson to explicitly compute the Cheeger constant for a collection of arithmetic hyperbolic surfaces. The results have connections to arithmetic reflection groups, and to the relationship between the arithmetic and geometry of Fuchsian groups. This is joint work with Brian Benson.

1:00 pm in 345 Altgeld Hall,Tuesday, February 23, 2016

#### Compactifications of nonstandard finite cyclic groups

###### Somayeh Vojdani (Notre Dame)

Abstract: Let $H=([0,a),\ +\ mod\ a)$ be defined in a saturated elementary extension of $(\mathbb{Z},+,<)$, where $a$ is a non-standard element. Then $H^{00}$, the smallest type-definable subgroup of $H$ of bounded index, exists, and $H/H^{00}$ is a compact topological group under the logic topology. We show that the structure of $H/H^{00}$ depends only on the divisibility type of $a$, and we classify these compact groups.

2:00 pm in 347 Altgeld Hall,Tuesday, February 23, 2016

#### Functional limit laws for recurrent excited random walks.

###### Jonathon Peterson (Purdue Math)

Abstract: Excited random walks (also called cookie random walks) are model for self-interacting random motion where the transition probabilities are dependent on the local time at the current location. While self-interacting random walks are typically very difficult to study, many results for (one-dimensional) excited random walks are remarkably explicit. In particular, one can easily (by hand) calculate a parameter of the model that will determine many features of the random walk: recurrence/transience, non-zero limiting speed, limiting distributions and more. In this talk I will prove functional limit laws for one-dimensional excited random walks that are recurrent. For certain values of the parameters in the model the random walks under diffusive scaling converge to a "Brownian motion perturbed at its extremum." This was known previously for the case of excited random walks with boundedly many cookies per site, but we are able to generalize this to excited random walks with periodic cookie stacks. In this more general case, it is much less clear why perturbed Brownian motion should be the correct scaling limit. This is joint work with Elena Kosygina.

3:00 pm in 243 Altgeld Hall,Tuesday, February 23, 2016

#### Stability conditions in algebraic geometry

###### Jason Lo (UIUC)

Abstract: The area of stability conditions is a part of algebraic geometry that has been receiving a lot of attention lately. In this talk, I will give a particular example of a stability condition, explain a central problem in this area, and describe a new connection between two different types of stability.

3:00 pm in 241 Altgeld Hall,Tuesday, February 23, 2016

#### The asymptotic behavior of the correspondence chromatic number

###### Anton Bernshteyn (UIUC Math)

Abstract: Zdeněk Dvořák and Luke Postle recently introduced a new generalization of list coloring, the so-called correspondence coloring. Dvořák and Postle's motivation came from studying list colorings of planar graphs without cycles of certain lengths; correspondence coloring turned out to be exactly the right notion needed for the inductive argument to work. The correspondence chromatic number of a graph, $\chi_c(G)$, shares many properties with the list chromatic number, $\chi_\ell(G)$. However, there are also some striking dissimilarities. For instance, $\chi_c(C_n) = 3$ for any cycle $C_n$, no matter the parity of $n$. In this talk we will discuss the ways in which $\chi_c(G)$ depends on the average and maximum degrees of $G$. In particular, we will show that for a $d$-regular triangle-free $G$, the value of $d$ determines $\chi_c(G)$ up to a constant factor.

4:00 pm in 243 Altgeld Hall,Tuesday, February 23, 2016

#### Tau functions of integrable hierarchies and quivers on the Sato Grassmannian.

###### Matej Penciak (UIUC Math)

Abstract: In this talk I will briefly describe the KP Hierarchy, its $\tau$-functions, and the Sato Grassmannian. I will describe the structure of partition functions of certain matrix models in terms of the aforementioned $\tau$-functions. Motivated by this structure, I will then define a notion of a quiver on the Sato Grassmannian and describe how they can be used to study the constraints on $\tau$-functions coming from matrix models.