Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, January 28, 2020.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2019           January 2020          February 2020
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  6  7             1  2  3  4                      1
8  9 10 11 12 13 14    5  6  7  8  9 10 11    2  3  4  5  6  7  8
15 16 17 18 19 20 21   12 13 14 15 16 17 18    9 10 11 12 13 14 15
22 23 24 25 26 27 28   19 20 21 22 23 24 25   16 17 18 19 20 21 22
29 30 31               26 27 28 29 30 31      23 24 25 26 27 28 29



Tuesday, January 28, 2020

1:00 pm in 241 Altgeld Hall,Tuesday, January 28, 2020

#### Organizational Meeting and Introduction

###### Dakota Ihli/Alexi Block Gorman (UIUC)

Abstract: We will decide on the permanent time and location for the seminar in this meeting. We will also discuss what we plan to cover for the next few weeks, and who will lead the seminar for those dates. We will state a few of the basic definitions for computability theory and discuss them briefly. All levels of experience with logic/computability are welcome!

2:00 pm in 243 Altgeld Hall,Tuesday, January 28, 2020

#### Ramsey upper density of infinite graphs

###### Ander Lamaison (Freie U. Berlin)

Abstract: Let $H$ be an infinite graph. In a two-coloring of the edges of the complete graph on the natural numbers, what is the densest monochromatic subgraph isomorphic to $H$ that we are guaranteed to find? We measure the density of a subgraph by the upper density of its vertex set. This question, in the particular case of the infinite path, was introduced by Erdős and Galvin. Following a recent result for the infinite path, we present bounds on the maximum density for other choices of $H$, including exact values for a wide class of bipartite graphs.

3:00 pm in 245 Altgeld Hall,Tuesday, January 28, 2020

#### Insuring longevity risk and long-term care: Bequest, housing and liquidity

###### Mengyi Xu (University of New South Wales)

Abstract: The demand for life annuities and long-term care insurance (LTCI) varies among retirees with different preferences and financial profiles. This paper shows that bequest motives can enhance the demand for LTCI unless the opportunity cost of self-insurance through precautionary savings is low. This typically occurs when retirees have sufficient liquid wealth. If retirees tend to liquidate housing assets in the event of becoming disabled that requires sizeable costs, housing wealth is likely to enhance the demand for annuities and to crowd out the demand for LTCI. Cash-poor-asset-rich retirees show little interest in annuities, but they may purchase LTCI to preserve their bequests.