Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, September 20, 2016.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, September 20, 2016

11:00 am in 345 Altgeld Hall,Tuesday, September 20, 2016

#### From motivic to equivariant homotopy groups - a worked example

###### Bert Guillou (University of Kentucky)

Abstract: The realization of a motivic space defined over the reals inherits an action of Z/2Z, the Galois group. This realization functor allows for information to pass back and forth between the motivic and equivariant worlds. I will discuss one example: an equivariant Adams spectral sequence computation for ko, taking the simpler motivic computation as input. This is joint work with M. Hill, D. Isaksen, and D. Ravenel.

12:00 pm in 243 Altgeld Hall,Tuesday, September 20, 2016

#### Dynamics of free group automorphisms and a subgroup alternative for Out(F_N)

###### Caglar Uyanik (Illinois Math)

Abstract: The study of outer automorphism group of a free group is closely related to the study of mapping class groups of hyperbolic surfaces. In this talk, I will draw analogies between these two groups, and deduce several structural results about subgroups of Out(F_N) by proving several north-south dynamics type results. Part of this talk is based on joint work with Matt Clay.

1:00 pm in 345 Altgeld Hall,Tuesday, September 20, 2016

#### A metric interpretation of reflexivity for Banach spaces

###### Pavlos Motakis (Texas A&M)

Abstract: This lecture mainly concerns the question as to whether the property of a separable Banach space to be reflexive can be characterized metrically. Broadly speaking, a metric characterization of a property of Banach spaces is an equivalent formulation of this property that refers only to the metric structure of the space and not to its linear structure. On each Schreier family $\mathcal{S}_\alpha$, $\alpha<\omega_1$ we define two metrics $d_{\infty,\alpha}$ and $d_{1,\alpha}$ and we study the separable Banach spaces $X$ for which there exists a map $\Phi:\mathcal{S}_\alpha\to X$ and two positive constants $c$, $C$ so that for all $A,B\in\mathcal{S}_\alpha$ $$cd_{\infty,\alpha}(A,B)\leqslant \|\Phi(A)-\Phi(B)\|\leqslant C d_{1,\alpha}(A,B).$$ As it turns out, such maps can always be constructed on non-reflexive Banach spaces. However, within the class of separable reflexive Banach spaces the existence of a map with the above property is closely linked to the Szlenk index of that space, an index measuring the size'' of the space's dual. We draw two main conclusions. The first one concerns a metric interpretation of reflexivity, namely the following: a separable Banach space is reflexive if and only if for every $\alpha<\omega_1$ there exists a map satisfying the above property. The second one concerns a metric characterization of the Szlenk index of a reflexive Banach space. More precisely, for countable ordinal numbers $\alpha$ with the property $\alpha = \omega^\alpha$ it follows that for a separable reflexive Banach space $X$, $(\mathcal{S}_\alpha,d_{1,\alpha})$ bi-Lipschitzly embeds into $X$ if and only if $\max\{\mathrm{Sz}(X),\mathrm{Sz}(X^*)\}>\alpha$. This is joint work with Thomas Schlumprecht.

1:00 pm in 7 Illini Hall,Tuesday, September 20, 2016

#### Quasiconformal mappings on the Grushin plane

###### Matthew Romney   [email] (UIUC Math)

Abstract: Recent research in geometric analysis studies the problem of deciding when a metric space can be parametrized by a well known model space such as Euclidean space under a quasiconformal mapping. There are several competing definitions of quasiconformality between metric spaces or metric measure spaces, so it becomes an interesting problem to determine how these relate to each other in general metric space settings. We will investigate these questions for the case of the Grushin plane, a classical example of a sub-Riemannian manifold. We prove an appropriate equivalence of definitions of quasiconformality in the Grushin plane, and we discuss limitations of this equivalence. This is joint work with C. Gartland and D. Jung.

2:00 pm in 241 Altgeld Hall ,Tuesday, September 20, 2016

#### Sieve methods and Fouvry-Iwaniec primes

###### Kyle Pratt   [email] (UIUC )

Abstract: Sieve methods were invented in order to find prime numbers in various sequences. In their original incarnation sieves are, unfortunately, incapable of fulfilling their intended purpose, due to a fundamental obstruction known as the "parity problem.'' However, with additional analytic input it is sometimes possible to break the parity barrier and find primes in interesting sequences. In this talk, the second of two lectures, we continue our exploration of the result of Fouvry and Iwaniec that there are infinitely many primes of the form $p = x^2+\ell^2$, with $\ell$ a prime. We focus on the parity-breaking features of the proof, which requires finding cancellation in a bilinear form involving the $M\ddot{o}bius$ function.

3:00 pm in 243 Altgeld Hall,Tuesday, September 20, 2016

#### Sums of powers of linear and quadratic forms

###### Bruce Reznick (UIUC)

Abstract: Various results on this topic will be discussed from a "first principles" approach, with lots of historical remarks. Particular attention will be paid to writing binary sextic forms as a sum of two (or three) cubes of binary quadratic forms.

3:00 pm in 241 Altgeld Hall,Tuesday, September 20, 2016

#### The Kelmans-Seymour Conjecture

###### Yan Wang (Georgia Institute of Technology)

Abstract: Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of $K_5$. This conjecture was proved by Ma and Yu for graphs containing $K_4^-$. Recently, we proved this entire Kelmans-Seymour conjecture. In this talk, I will give a sketch of our proof, and discuss related problems. This is joint work with Dawei He and Xingxing Yu.

4:00 pm in 1 Illini Hall,Tuesday, September 20, 2016

#### Coherent mortality forecasts for dependent populations: a Bayesian approach

###### Anastasios Bardoutsos (University of Groningen)

Abstract: Underestimating the future improvement of mortality rates translates into higher than expected pay-out-ratios for pensions funds and insurance companies and therefore implies a risk, the so-called longevity risk. The solvency of pension systems and annuity providers in the presence of longevity risk is a major point of concern. Quantification of the longevity risk with appropriate stochastic mortality models is key. Recent studies propose multi-population stochastic mortality models as a strategy for achieving robust and coherent projections of mortality rates. This paper presents a Bayesian analysis of two coherent multi-population models of log-bilinear type, designed for two or more populations, while allowing for dependence between these populations. The first model is inspired by Cairns et al. (2011) and Enchev et al. (2016), and the second is the well known Li & Lee model, proposed by Li and Lee (2005). For both models we identify the parameters through appropriate constraints and we avoid the multi-step calibration strategy that is currently used in the literature. We assume a Poisson distribution for the number of deaths at a certain age and in a certain period and include full dependency between the period effects. As such, we extend earlier work where period effects are considered independent. Moreover, we utilize the Kannisto parametric mortality law to close the generated mortality scenarios for higher ages and provide projections of important demographic markers, such as period and cohort life expectancy. We develop the technicalities necessary for Markov Chain Monte Carlo ([MCMC]) simulations and provide software implementation (in R) for the models discussed in the paper. We finally present a case study using five European countries which are geographically close and share similar socio-economic characteristics.