Department of

# Mathematics

Seminar Calendar
for Graduate Student Number Theory Seminar events the year of Wednesday, September 13, 2017.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2017           September 2017          October 2017
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5                   1  2    1  2  3  4  5  6  7
6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
27 28 29 30 31         24 25 26 27 28 29 30   29 30 31



Tuesday, January 24, 2017

2:00 pm in 241 Altgeld Hall,Tuesday, January 24, 2017

#### Poincaré sections for the horocycle flow in covers of SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$) and applications to Farey fraction statistics

###### Byron Heersink (UIUC)

Abstract: For a given finite index subgroup $H\subseteq$SL(2,$\mathbb{Z}$), we use a process developed by Fisher and Schmidt to lift a Poincaré section of the horocycle flow on SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$) found by Athreya and Cheung to the finite cover SL(2,$\mathbb{R}$)/$H$ of SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$). We then relate the properties of this section to the gaps in Farey fractions and describe how the ergodic properties of the horocycle flow can be used to obtain certain statistical properties of various subsets of Farey fractions.

Thursday, September 14, 2017

2:00 pm in 241 Altgeld Hall,Thursday, September 14, 2017

#### On the percentage of critical zeros of Riemann's zeta function

###### Kyle Pratt   [email] (UIUC)

Abstract: The Riemann hypothesis (RH) is one of the most important unsolved problems in number theory. RH asserts that all of the important zeros of the Riemann zeta function lie on a specific line, called the critical line. As we lack a solution to RH, it is natural to ask for partial results instead. One way to measure progress towards RH is to prove that some percentage of the zeros are on the critical line. I will sketch a brief history of the results about percentages of zeros on the critical line, and discuss some of the methods of proof. In the latter part of the talk I will discuss the current world record, due to Nicolas Robles and myself, and some of our ideas. The talk should be accessible to any graduate student.