Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 2, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, October 2, 2014

10:00 am in 143 Altgeld Hall,Thursday, October 2, 2014

#### Well-Posedness Results for the Majda-Biello System

###### Erin Compaan (UIUC Math)

Abstract: The Majda-Biello system, consisting of coupled KdV-type equations, has been proposed as a model for certain long-wavelength atmospheric waves. The well-posedness of the system has been studied by Tadahiro Oh. It turns out that the system is well-posed in Sobolev spaces of sufficiently high index, where "sufficiently high" depends on the properties of the coupling parameter. This talk will discuss his results and provide a high-level overview of the proofs.

11:00 am in 241 Altgeld Hall,Thursday, October 2, 2014

#### Bounds for the logarithmic derivative of the Euler Gamma function

###### Harold Diamond   [email] (UIUC Math)

Abstract: We derive bounds for the logarithmic derivative of the Euler Gamma function. The only facts assumed are the first few terms of the asymptotic expansion and the functional equation of Gamma. The proof involves a backward induction.

12:30 pm in 464 Loomis Laboratory,Thursday, October 2, 2014

#### Scaling in Holographic Quantum Quench

###### Sumit Das (Kentucky Physics)

Abstract: In recent years the problem of quantum quench in the vicinity of critical points  has been investigated using holographic methods. This has led to an understanding of decoupling of length scales in the dynamics of slow quench  and the emergence of Kibble-Zurek scaling, and provided predictions for corrections to the leading scaling behavior. In the other limit, holographic calculations have led to the discovery of new scaling laws for fast quench, which have been subsequently shown to be generic properties of deformations  of any conformal field theory regardless of holography. This talk will discuss the salient aspects of this development.

2:00 pm in 007 Illini Hall,Thursday, October 2, 2014

#### Special Sets of Primes

###### Kyle Pratt (UIUC Math)

Abstract: We discuss special'' sets of primes in the integers, or sets of primes whose members satisfy interesting conditions. We are often interested in whether special sets of primes are infinite, but these questions are usually very difficult. We discuss how the existence of certain infinite special sets of primes would resolve a conjecture of Carmichael on the Euler totient function. We formulate similar questions for sets of primes in $\mathbb{F}_q[x]$ and discuss relevant recent joint work.

4:00 pm in 245 Altgeld Hall,Thursday, October 2, 2014

#### New methods for inferring species trees in the presence of incomplete lineage sorting

###### Tandy Warnow (Departments of Bioengineering and Computer Science, University of Illinois)

Abstract: Estimating the Tree of Life will likely involve a two-step procedure, where in the first step trees are estimated on many genes, and then the gene trees are combined into a tree on all the taxa. However, the true gene trees may not agree with with the species tree, due to biological processes such as deep coalescence, gene duplication and loss, and horizontal gene transfer. Statistically consistent methods based on the multi-species coalescent model have been developed to estimate species trees in the presence of incomplete lineage sorting; however, the relative accuracy of these methods compared to the usual "concatenation" approach is a matter of substantial debate within the systematic biology research community. In this talk, I will present results showing that coalescent-based estimation methods are impacted by gene tree estimation error, so that they can be less accurate than concatenation in many cases. I will also present new methods for estimating species trees in the presence of gene tree conflict due to ILS that are more accurate than current methods. Key to these methods is addressing gene tree estimation error more effectively. I will also present results using these techniques to estimate species tree for birds and for plants.

4:00 pm in 2 Illini Hall,Thursday, October 2, 2014

#### Down but not Out: A Cost of Capital Approach to Fair Value Risk Margins

###### John Manistre (GGY AXIS)

Abstract: The Market Cost of Capital approach is emerging as a standard for estimating risk margins for non-hedgeable risk on an insurer’s fair value balance sheet. This paper develops a conceptually rigorous formulation of the cost of capital method for estimating margins for mortality, lapse, expense and other forms of underwriting risk. For any risk situation we develop a three step modeling approach which starts with i) a best estimate model and then adds ii) a static margin for contagion risk (the risk that current experience differs from the best estimate) and iii) a dynamic margin for parameter risk (the risk that the best estimate is wrong and must be revised). We show that the solution to the parameter risk problem is fundamentally a regime switching model which can be solved by Monte Carlo simulation. The paper then goes on to develop a number of more pragmatic methods which can be thought of as short cut approximations to the first principles model. One of these short cuts is the Prospective method currently used in Europe. None of these methods require stochastic on stochastic projections to get useful results.