The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department
20141125
webmaster@math.psu.edu

No meeting
http://www.math.psu.edu/seminars/meeting.php?id=21892
Speaker(s): Mr Turkey
20141127T11:15:00
Algebra and Number Theory Seminar
rvaughan@math.psu.edu
schwede@math.psu.edu
papikian@math.psu.edu
yee@math.psu.edu

Thanksgiving Break
http://www.math.psu.edu/seminars/meeting.php?id=22017
Speaker(s): Thanksgiving Break
20141127T15:30:00
Department of Mathematics Colloquium
saz11@math.psu.edu
liu@math.psu.edu

Uncertainty quantification and geophysical hazard mapping
http://www.math.psu.edu/seminars/meeting.php?id=22722
Speaker(s): Elaine Spiller
PDE models of granular flows are invaluable tools for developing probabilistic hazards maps for volcanic landslides, but they are far from perfect. First, any probabilistic hazard map is conditioned on assumptions about the aleatoric uncertainty  how mother nature rolls the dice  and is hence tied to the choice of probability distributions describing various scenarios (e.g. initial and/or boundary conditions). Thus new data, differing expert opinion, or emergent scenarios may suggest that the original assumptions were invalid and thus the hazard map made under those assumptions is not terribly useful. Epistemic uncertainty  uncertainty due to a lack of model refinement  arises through assumptions made in physical models, numerical approximation, and imperfect statistical models. In the context of geophysical hazard mapping, we propose a surrogatebased methodology which efficiently assesses the impact of various uncertainties enabling a quick yet methodical comparison of the effects of uncertainty and error on computer model output.
20141201T14:30:00
Computational and Applied Mathematics Colloquium
shaffer@math.psu.edu
liu@math.psu.edu

An avalanche principle for dynamical systems
http://www.math.psu.edu/seminars/meeting.php?id=22834
Speaker(s): Manfred Denker
Consider a product transformation $S=S_1\times S_2\times...S_N$ of $N$ transformations. Given sets $U_i$ in the domain of $S_i$, one can define a new transformation: whenever a coordinate falls into $U_i$ a transformation $T$ is applied as many times as this happens until such a process stops. Otherwise apply $S$ at each time step. The talk will make this construction precise and discuss the case when $T=S$ and the case when $T$ and $S$ are product transformations on $[0,1]^N$ given by two rotations.
The results are on basic properties of such transformations, as topological transitivity, stationary measures, ergodicity.
20141201T15:35:00
Dynamical systems seminar
katok_s@math.psu.edu
saz11@math.psu.edu
katok_a@math.psu.edu
hertz@math.psu.edu

Uniqueness of conservative solutions to a variational wave equation
http://www.math.psu.edu/seminars/meeting.php?id=22173
Speaker(s): Alberto Bressan
An interesting class of variational wave equations take the form
u_tt  c(u)(c(u)u_x)_x = 0,
where c(u) > 0 is the wave speed. It is well known that solutions
remain uniformly Holder continuous, but their gradient can blow up in
finite time. When this happens, multiple solutions can be constructed.
Uniqueness can be achieved by further imposing that the total energy
remains constant in time.
The uniqueness proof relies on a refined analysis of characteristics,
which in this case satisfy an ODE with Holder continuous right hand side.
The talk will present the main ideas in the construction, and review some earlier results on uniqueness for ODEs with possibly discontinuous right
hand side.
20141202T10:00:00
Hyperbolic and Mixed Type PDEs Seminar
yzheng@math.psu.edu
zhang_t@math.psu.edu

Infinitely Many Congruences Modulo 5 for 4Colored Frobenius Partitions
http://www.math.psu.edu/seminars/meeting.php?id=21927
Speaker(s): James Sellers
In his 1984 AMS Memoir, Andrews introduced the family of functions c\phi_k(n), which denotes the number of generalized Frobenius partitions of n into k colors. Recently, Baruah and Sarmah, Lin, Sellers, and Xia established several Ramanujanlike congruences for c\phi_4(n) relative to different moduli. In this paper, which is joint work with Michael D. Hirschhorn of UNSW, we employ classical results in qseries, the wellknown theta functions of Ramanujan, and elementary generating function manipulations to prove a characterization of c\phi_4(10n+1) modulo 5 which leads to an infinite set of Ramanujanlike congruences modulo 5 satisfied by c\phi_4. This work greatly extends the recent work of Xia on c\phi_4 modulo 5.
20141202T11:15:00
Combinatorics/Partitions Seminar
sellersj@math.psu.edu
saz11@math.psu.edu
katz@math.psu.edu
andrews@math.psu.edu

Properties of networks with partially structured and partially random connectivity
http://www.math.psu.edu/seminars/meeting.php?id=23671
Speaker(s): Yashar Ahmadian
Networks studied in many disciplines, including neuroscience, have connectivity that may be stochastic about some underlying mean connectivity represented by a nonnormal matrix. Furthermore the stochasticity may not be i.i.d. across elements of the connectivity matrix. More generally, the problem of understanding the behavior of stochastic matrices with nontrivial mean structure and correlations arises in many settings. We address this by characterizing large random $N\times N$ matrices of the form $A = M + LJR$, where $M$, $L$ and $R$ are arbitrary deterministic matrices and $J$ is a random matrix of zeromean independent and identically distributed elements. $M$ can be nonnormal, and $L$ and $R$ allow correlations that have separable dependence on row and column indices. We first provide a general formula for the eigenvalue density of $A$. For $A$ nonnormal, the eigenvalues do not suffice to specify the dynamics induced by $A$, so we also provide general formulae for the transient evolution of the magnitude of activity and frequency power spectrum in an $N$dimensional linear dynamical system with a coupling matrix given by $A$. These quantities can also be thought of as characterizing the stability and the magnitude of the linear response of a nonlinear network to small perturbations about a fixed point. We derive these formulae and work them out analytically for some examples of $M$, $L$ and $R$ motivated by neurobiological models. We also argue that the persistence as $N\rightarrow\infty$ of a finite number of randomly distributed outlying eigenvalues outside the support of the eigenvalue density of $A$, as previously observed, arises in regions of the complex plane $\Omega$ where there are nonzero singular values of $L^{1} (z\one  M) R^{1}$ (for $z\in\Omega$) that vanish as $N\rightarrow\infty$. When such singular values do not exist and $L$ and $R$ are equal to the identity, there is a correspondence in the normalized Frobenius norm (but not in the operator norm) between the support of the spectrum of $A$ for $J$ of norm $\sigma$ and the $\sigma$pseudospectrum of $M$.
20141202T13:00:00
Theoretical Biology Seminar
cpc16@math.psu.edu
treluga@math.psu.edu

Gelfand duality and Ramsey theory
http://www.math.psu.edu/seminars/meeting.php?id=22086
Speaker(s): Willem FouchÃ©
In this talk, I want to discuss recent developments arising from the paper [1] (1987). In this paper, Andreas Blass introduced the idea of, what he called, a Ramsey action of a group on a discrete space in the context of understanding the tension, in set theory, between the Axiom of Choice and the Prime Ideal Theorem for Boolean algebras.
In this talk, I will discuss this very tension, with the benefit of hindsight, as to what has happened to his viewpoint as viewed from the world of the dynamical aspects of structural Ramsey theory. Some recent links with Gelfand duality of commutative Câˆ— algebras will be discussed.
20141202T14:30:00
Logic Seminar
reimann@math.psu.edu
simpson@math.psu.edu
jmr71@math.psu.edu

Free Products as Topological Groups in Dynamics, II
http://www.math.psu.edu/seminars/meeting.php?id=22812
Speaker(s): Kurt Vinhage
In the study of partially hyperbolic homogeneous systems, the Lyapunov manifolds become cosets of unipotent subgroups and their free product appears as a natural object of study. At best, the natural topology of such a free product can be described as unpleasant, with key properties like local compactness and first countability failing. In these talks, we will see how dynamical and topological arguments can be used to tame these complexities, leading to a local rigidity result. In particular, we will see two powerful and classical theorems on topological groups appear (one of MontgomeryZippin and another of GleasonPalais), and prove one of them. Timepermitting, we will see how free products may also appear in a nonhomogeneous setting.
20141202T15:30:00
Working Seminar: Dynamics and its Working Tools
katok_a@math.psu.edu
hertz@math.psu.edu
kalinin@math.psu.edu