Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 16, 2021.

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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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1  2  3  4  5  6       1  2  3  4  5  6                1  2  3
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Tuesday, March 16, 2021

11:00 am in Zoom,Tuesday, March 16, 2021

#### An asymptotic local-global principle for integral Kleinian sphere packings

###### Edna Jones (Rutgers University)

Abstract: We will discuss an asymptotic local-global principle for certain integral Kleinian sphere packings. Examples of Kleinian sphere packings include Apollonian circle packings and Soddy sphere packings. Sometimes each sphere in a Kleinian sphere packing has a bend (1/radius) that is an integer. When all the bends are integral, which integers appear as bends? For certain Kleinian sphere packings, we expect that every sufficiently large integer locally represented as a bend of the packing is a bend of the packing. We will discuss ongoing work towards proving this for certain Kleinian sphere packings. This work uses the circle method, quadratic forms, spectral theory, and expander graphs.

For Zoom info, please email obeck@illinois.edu

2:00 pm in Zoom,Tuesday, March 16, 2021

#### Expressing graphs as symmetric differences of cliques of the complete graph

###### Puck Romback (University of Vermont)

Abstract: Any finite simple graph $G = (V,E)$ can be represented by a collection $\mathcal{C}$ of subsets of $V$ such that $uv\in E$ if and only if $u$ and $v$ appear together in an odd number of sets in $\mathcal{C}$. We are interested in the minimum cardinality of such a collection. In this talk, we will discuss properties of this invariant and its close connection to the minimum rank problem. This talk will be accessible to students. Joint work with Calum Buchanan and Christopher Purcell.