Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, January 25, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2017           January 2018          February 2018
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1  2       1  2  3  4  5  6                1  2  3
3  4  5  6  7  8  9    7  8  9 10 11 12 13    4  5  6  7  8  9 10
10 11 12 13 14 15 16   14 15 16 17 18 19 20   11 12 13 14 15 16 17
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Thursday, January 25, 2018

11:00 am in 243 Altgeld Hall,Thursday, January 25, 2018

#### The convolution square root of 1 and application to the prime number theorem.

###### Harold Diamond (University of Illinois)

Abstract: We explain what this arithmetic function is and show how the PNT can be deduced from knowledge of its summatory function.

2:00 pm in 241 Altgeld Hall,Thursday, January 25, 2018

#### Decomposition results and the sum product phenomenon

###### George Shakan   [email] (UIUC)

Abstract: Balog and Wooley in 2015 showed that any set can be decomposed into two sets, one that is not additively structured and one that is not multiplicatively structured. I'll talk about some recent progress in the area. As an application, I'll show a bound for the difference-quotient problem as well as mention an application to a character sum.

4:00 pm in 245 Altgeld Hall,Thursday, January 25, 2018

#### Garden of Eden Theorems for dynamical systems: old and new

###### Tullio Ceccherini-Silberstein (Universita' del Sannio (Benevento))

Abstract: In this talk, completely self-contained, I would like to survey the classical Garden of Eden Theorem for cellular automata with finite alphabet over the group Z^d, originally establisehd by E.F. Moore and J. Myhill in the early 1960', and its more recent generalizations (with other alphabet sets and over larger classes of groups) as well as some extensions to other dynamical systems of algebraic origin, obtained in collaboration with Michel Coornaert.