Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, January 26, 2021.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 26, 2021

11:00 am in Via Zoom,Tuesday, January 26, 2021

#### Models of Lubin-Tate spectra via Real bordism theory

###### XiaoLin "Danny" Shi (University of Chicago)

Abstract: In this talk, we will present Real-oriented models of Lubin-Tate theories at p=2 and arbitrary heights. For these models, we give explicit formulas for the action of certain finite subgroups of the Morava stabilizer groups on the coefficient rings. This is an input necessary for future computations. The construction utilizes equivariant formal group laws associated with the norms of the Real bordism theory. As a consequence, we will describe how we can use these models to prove periodicity theorems for Lubin-Tate theories and set up an inductive approach to prove differentials in their slice spectral sequences. This talk is based on several joint projects with Agnès Beaudry, Jeremy Hahn, Mike Hill, Guchuan Li, Lennart Meier, Guozhen Wang, Zhouli Xu, and Mingcong Zeng.

Abstract: A sequence ${a_1, a_2,\dots, a_k}$ of integers is called a $B_2$ sequence if all the sums $a_i + a_j$, $1 \leq i \leq j \leq k$, are different. Let $F_2(n)$ be the maximum number of elements that can be selected from the set ${1,2,\dots,n}$ so as to form a $B_2$ sequence. Among others we give a new elementary proof for the result of Erdos and Turan (1941) that $F_2(n)= \sqrt{n} + O(n^{1/4})$.