The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2015-03-02webmaster@math.psu.eduProperties of a Restricted Binary Partition Function a la Andrews and Lewis
http://www.math.psu.edu/seminars/meeting.php?id=24749
Speaker(s): James Sellers
In 2001, Andrews and Lewis utilized an identity of F. H. Jackson to derive some new partition generating functions as well as identities involving some of the corresponding partition functions. At the end of their paper, they define a family of functions $W_1(S_1, S_2;n)$ to be the number of partitions of $n$ into parts from $S_1 \cup S_2$ which do not contain both $a_j$ and $b_j$ as parts (where $S_1 = \left\{ a_1, a_2, a_3, \dots\right\}$ and $S_2 = \left\{ b_1, b_2, b_3, \dots\right\}$ and $S_1 \cap S_2 = \phi$). This definition is motivated by the main results of their paper; in that case, $S_1$ and $S_2$ contain elements in arithmetic progression with the same ``skip value'' $k$. Our goal in this work is to consider more general examples of such partition functions where $S_1$ and $S_2$ satisfy the requirements mentioned above but do not simply contain elements in an arithmetic progression. In particular, we consider the situation where $S_1$ and $S_2$ contain specific powers of $2.$ We then prove a number of arithmetic properties satisfied by this function using elementary generating function manipulations and classic results from the theory of partitions. This work was completed in collaboration with my undergraduate student Bin Lan.2015-03-03T11:15:00Combinatorics/Partitions Seminarsellersj@math.psu.edukatz@math.psu.edusaz11@math.psu.eduandrews@math.psu.eduStochastic modeling of carcinogenesis
http://www.math.psu.edu/seminars/meeting.php?id=24697
Speaker(s): Rafael Meza
Carcinogenesis is the transformation of normal cells into cancer cells. This
process has been shown to be of a multistage nature, with stem cells that go
through a series of (stochastic) genetic and epigenetic changes that
eventually lead to a malignancy. Since the origins of the multistage theory
in the 1950s, mathematical modeling has played a prominent role in the
investigation of the mechanisms of carcinogenesis. In particular, two
stochastic (mechanistic) models, the Armitage-Doll and the two-stage clonal
expansion (TSCE) model, have been widely used in the past for cancer risk
assessment and for the analysis of cancer population and experimental data.
In this talk, I will introduce some of the biological and mathematical
concepts behind the theory of multistage carcinogenesis, and discuss in
detail the use of these models in cancer epidemiology. Recent applications
of multistage models in lung and colon cancer will be reviewed.2015-03-03T13:00:00Theoretical Biology Seminartreluga@math.psu.educpc16@math.psu.eduKolmogorov Random Graphs
http://www.math.psu.edu/seminars/meeting.php?id=24906
Speaker(s): John Pardo
We will discuss several properties of Kolmogorov random graphs using deficiency functions, i.e. functions that bound how far away a graph is from maximum complexity, and relate these properties back to the usual notion of randomness for binary strings as well as connect them to the property of quasirandomness.2015-03-03T14:30:00Logic Seminarjmr71@math.psu.edusimpson@math.psu.edureimann@math.psu.eduIntroduction to KAM (Kolmogorov-Arnold-Moser) theory, IV
http://www.math.psu.edu/seminars/meeting.php?id=25361
Speaker(s): Alena Erchenko
2015-03-03T15:30:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.edusaz11@math.psu.eduhertz@math.psu.edukalinin@math.psu.eduANTHROPOMORPHIC IMAGE RECONSTRUCTION VIA OPTIMAL CONTROL AND HYPOELLIPTIC DIFFUSION
http://www.math.psu.edu/seminars/meeting.php?id=25332
Speaker(s): Ugo Boscain
In this talk I will present a model of geometry of vision due to Petitot, Citti, Sarti, and our research group. One of the main features of this model is that the primary visual cortex V1 lifts an image from R^2 to the bundle of directions of the plane. Neurons are grouped into orientation columns, each of them corresponding to a point of this bundle.
In this model a corrupted image is reconstructed by minimizing the energy necessary for the activation of the orientation columns corresponding to regions in which the image is corrupted. The minimization process intrinsically defines an hypoelliptic heat equation on the bundle of directions of the plane.
The numerical integration of this equation is difficult and require techniques of non-commutative Fourier analysis.
The purpose of this research is to validate the biological model and to obtain an algorithm of image inpainting going beyond the state of the art.
[1] U. Boscain, J. Duplaix, J.P. Gauthier, F. Rossi, “Anthropomorphic image reconstruction via hypoelliptic diffusion”. SIAM J. CONTROL OPTIM.Vol. 50, No. 3, pp. 1309–1336, 2012.
http://arxiv.org/abs/1006.3735
[2] U. Boscain, R. Chertovskih, J.P. Gauthier, A. Remizov. Hypoelliptic diffusion and human vision: a semi-discrete new twist. SIAM Journal on Imaging Sciences 2014, Vol. 7, No. 2, pp. 669-695.
http://arxiv.org/abs/1304.20622015-03-03T16:00:00Applied Analysis Seminaranovikov@math.psu.edusaz11@math.psu.edulevi@math.psu.eduberlyand@math.psu.edupesin@math.psu.eduGeodesics on the convex surfaces.
http://www.math.psu.edu/seminars/meeting.php?id=25469
Speaker(s): Anton Petrunin
We give a universal bound for the variation of turn of minimizing geodesics on convex surfaces. This is a joint work with Nina Lebedeva.2015-03-04T12:05:00Geometry Luncheon Seminarburago@math.psu.edusaz11@math.psu.eduThe dynamic boundary condition and Dirichlet to Neumann map
http://www.math.psu.edu/seminars/meeting.php?id=25333
Speaker(s): Chun Liu
2015-03-04T15:30:00Complex Fluids Seminartxh35@math.psu.edufuy3@math.psu.edu“Studies on the weak convergence of partial sums in Gibbs-Markov dynamical systems”
http://www.math.psu.edu/seminars/meeting.php?id=27462
Speaker(s): Xuan Zhang, Adviser: Manfred Denker
We investigates distributional limit theorems of partial sums of the form $f_{n,1}+f_{n,2}\circ T_n+\cdots+f_{n,n}\circ T_n^{n-1}$ for Gibbs-Markov dynamical systems $(X_n, \mathscr B_n, T_n,\mu_n,\alpha_n)$ and an array of functions $f_{n,m}: X_n\to \mathbb R$ of certain classes. We show a Central Limit Theorem (CLT) for this array, a CLT of Lindeberg type (with uniformly bounded functions) and we also investigate the Poisson limit case. We relate the Poisson limit theorem to escape rates of sweep-out sets and the CLT is applied in various situations, in particular to some statistical functions.2015-03-05T08:30:00Ph.D. Thesis Defensehalpenny@math.psu.eduZeros of Dirichlet series
http://www.math.psu.edu/seminars/meeting.php?id=24847
Speaker(s): Robert Vaughan
We are concerned here with Dirichlet series
f(s) = 1 +\sum_{n=2}^{\infty} \frac{c(n)}{n^s}
which satisfy a function equation similar to that of the Riemann zeta function, typically of the form
f(s) = \epsilon 2^s q^{1/2-s} \pi^{s-1} \Gamma(1-s) \big(\sin\textstyle\frac{\pi}{2}(s+\kappa)\big) f(1-s),
but for which the Riemann hypothesis is false.2015-03-05T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.edupapikian@math.psu.eduyee@math.psu.edueisentra@math.psu.edu" A Complete Set of Invariants for Density Operators Under Local Conjugation"
http://www.math.psu.edu/seminars/meeting.php?id=27419
Speaker(s): Jacob Turner, Adviser: Jason Morton
A density operator of is a trace one, positive semi-definite matrix in the tensor product of the spaces End (V_i) for i=1,...,n. These are used in physics to represent a quantum system of n particles, the ith of which has dim (V_i) spins. One of the most important questions about a density operator is the entanglement of the state it represents. Almost every notion of entanglement is invariant under conjuagation by the affine cone over the Segre product of the unitary groups over each V_i. Using techniques from algebraic geometry and representation theory, we determine a finite set of invariant polynomials that completely seperate orbits of density operators.2015-03-05T12:30:00Ph.D. Thesis Defensehalpenny@math.psu.eduIntermediate C*-norms
http://www.math.psu.edu/seminars/meeting.php?id=25489
Speaker(s): Matthew Wiersma
It is known that C*-algebras admit unique C*-norms, but this is not true in general for dense *-subalgebras of C*-algebras. For example, if G is a discrete group, then its group ring algebra may admit more than one C*-norm. Similarly, the algebraic tensor product of two C*-algebras may admit multiple C*-norms. Each of these examples admits two canonical C*-norms. During this talk, we will investigate C*-norms which fall between these canonical constructions.2015-03-05T14:30:00Noncommutative Geometry Seminarhigson@math.psu.edusaz11@math.psu.eduTechniques and concepts of amenability of discrete groups
http://www.math.psu.edu/seminars/meeting.php?id=24924
Speaker(s): Kate Juschenko (Nate Brown)
The subject of amenability essentially begins in 1900's with Lebesgue.
He asked whether the properties of his integral are really fundamental
and follow from more familiar integral axioms. This led to the study of
positive, finitely additive and translation invariant measure on
different spaces. In particular the study of isometry-invariant measure
led to the Banach-Tarski decomposition theorem in 1924. The class of
amenable groups was introduced and studied by von Neumann in 1929 and
he explained why the paradox appeared only in dimensions greater or
equal to three. In 1940's and 1950's a major contribution was made by M.
Day in his paper on amenable semigroups. We will give an introductory to
amenability talk, and explain more recent developments in this field.2015-03-05T15:30:00Department of Mathematics Colloquiumsaz11@math.psu.eduliu@math.psu.edu