Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 20, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2014            March 2014             April 2014
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1                      1          1  2  3  4  5
2  3  4  5  6  7  8    2  3  4  5  6  7  8    6  7  8  9 10 11 12
9 10 11 12 13 14 15    9 10 11 12 13 14 15   13 14 15 16 17 18 19
16 17 18 19 20 21 22   16 17 18 19 20 21 22   20 21 22 23 24 25 26
23 24 25 26 27 28      23 24 25 26 27 28 29   27 28 29 30
30 31


Thursday, March 20, 2014

11:00 am in 241 Altgeld Hall,Thursday, March 20, 2014

#### Zeros of the Riemann zeta-function on the critical line

###### Alexandru Zaharescu (UIUC Math)

Abstract: We discuss some very recent progress on the above problem. This is joint work with Nicolas Robles (University of Zurich) and Arindam Roy (UIUC).

2:00 pm in 241 Altgeld Hall,Thursday, March 20, 2014

#### An application of cointegration techniques to cause-specific mortality in USA, Japan, England & Wales and Australia

###### Severine Arnold (University of Lausanne (HEC Lausanne), Actuarial Science)

Abstract: Non-stationary time series have been widely studied by economists over the past decades. One interesting feature of non-stationary vari- ables is that we can distinguish between long-run relations, that are stationary, and short-run adjustments towards these. These long-run relations are known as cointegrating relations and represent long-run equilibriums. Since mortality rates are non-stationary variables, the theory developed for economic variables can also be used to gain in- sights into the long-run relations that may exist between mortality rates for different causes of death. In this work, cointegration is de- veloped for cause-of-death mortality. We analyze the five main causes of death across four major countries, including USA, Japan, England & Wales and Australia. Our analysis identifies long-run equilibrium relationships between the five main causes of death, providing new insights into the dependence structure that exists between competing risks. We show how male and female mortality trends by cause have been similar, although these differ across countries.

2:00 pm in 243 Altgeld Hall,Thursday, March 20, 2014

#### Gap distribution of Farey fractions determined by subgroups of SL(2,$\mathbb{Z}$)
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 the limiting gap distribution of various subsets of Farey fractions.