The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2014-09-17webmaster@math.psu.eduExistence of solutions to the transonic Pressure Gradient System in elliptic regions (continue)
http://www.math.psu.edu/seminars/meeting.php?id=22152
Speaker(s): Mingjie Li
We will describe the existence of a smooth solution in its degenerate elliptic
region in the self-similar plane to the pressure-gradient system.2014-09-18T10:00:00Hyperbolic and Mixed Type PDEs Seminarzhang_t@math.psu.eduHasse principle for generalized Kummer varieties
http://www.math.psu.edu/seminars/meeting.php?id=21882
Speaker(s): Alexei Skorobogatov
Rational points on Kummer varieties can be studied via the variation of Selmer groups of quadratic twists of the underlying abelian variety, using an idea of Swinnerton-Dyer. In joint work with Yonatan Harpaz we consider the case when the Galois action on 2-torsion has a large image. Under a mild additional assumption we prove the Hasse principle assuming the finiteness of relevant Shafarevich-Tate groups. Our approach is inspired by the work of Mazur and Rubin.2014-09-18T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.eduschwede@math.psu.edupapikian@math.psu.eduyee@math.psu.eduCommutative implies associative?
http://www.math.psu.edu/seminars/meeting.php?id=24050
Speaker(s): John Roe
By introducing the symbol i, with i<sup>2</sup>=-1, one can pass from the field of real numbers to the larger field of complex numbers. In the 19th century various attempts were made to define still larger "generalized number" fields, such as the quaternions and octonions, but all of these sacrifice some of the familiar "laws" of arithmetic: the quaternions are no longer commutative, the octonions not even associative. Notice that the commutative law apparently "dies" first. Around 1940, Heinz Hopf made an investigation of generalized number systems that were commutative but not necessarily associative, and he found that the reals and the complexes are the only examples. In other words, the commutative law implies the associative law (in the context in which he was working). Hopfs methods are topological, and are closely related to developments in topology in the latter half of the 20th century.
<b>Note: The talk starts at 1:25 p.m. </b>2014-09-18T13:15:00MASS Colloquiumvxs137@math.psu.edudunlop@math.psu.eduA Second Order Time Homogenized Model for Sediment Transport
http://www.math.psu.edu/seminars/meeting.php?id=23545
Speaker(s): Shuonan Wu
A multi-scale method for the hyperbolic systems governing sediment
transport in subcritical case is developed. The scale separation of
this problem is due to the fact that the sediment transport is much
slower than flow velocity. We first derive a zeroth-order homogenized
model, and then propose a first-order correction. It is revealed that
that the first-order correction for hyperbolic systems has to be
applied on the characteristic speed of slow variables. We develop a
second-order numerical scheme following the framework of heterogeneous
multi-scale method. The numerical results in both one and two
dimensional cases demonstrate the effectiveness and efficiency of our
method.2014-09-19T15:30:00CCMA PDEs and Numerical Methods Seminar Seriesqiao_c@math.psu.edufuw7@math.psu.eduwang_l@math.psu.eduA nonconventional local limit theorem
http://www.math.psu.edu/seminars/meeting.php?id=22058
Speaker(s): Yuri Kifer
Local limit theorems have their origin in the classical De Moivre– Laplace theorem and they study the asymptotic behavior as N → ∞ of probabilities having the form P {S_N = k} where S_N = \sum^N_{n=1} F (ξ_n ) is a sum of an integer valued function F taken on i.i.d. or Markov dependent sequence of random variables {ξ_j}. Corresponding results for lattice valued and general functions F were obtained, as well. We extend here this type of results to nonconventional sums of the form S_N = \sum^N_{n=1} F (ξ_n , ξ_{2n} , ..., ξ_{ln} ) and corresponding versions of such results can be obtained for some dynamical systems, as well. This continues the recent line of research studying various limit theorems for such expressions.2014-09-19T15:35:00Probability and Financial Mathematics Seminardenker@math.psu.edumazzucat@math.psu.eduroyer@math.psu.edunistor@math.psu.eduanovikov@math.psu.eduDynamics on Panov planes and related dynamical systems
http://www.math.psu.edu/seminars/meeting.php?id=22824
Speaker(s): Martin Schmoll
About ten years ago Dmitri Panov, then a masters student of M. Kontsevich,
discovered a linear dynamics on mildly singular complex planes
with dense orbits. His result was published 2009, just after infinite
billiards became an object of broader interest.
About the same time Phil Boyland published transitivity results for
rel-pseudo Anosov maps lifted to universal abelian covers.
Two years earlier Pollicott and Sharp showed ergodicity
in eigendirections of pseudo-Anosov maps on universal abelian covers.
Among others these results play essential role in ongoing research with Chris Johnson to
find generalizations of Panov's construction. So far we discovered relations to the periodic wind-tree model
and another physics model: Light rays in a doubly periodic pattern
of Eaton lenses. This dynamical system led to a paper with K. Fraczek (Torun).
In this paper we use a Teichmueller flow generalization of pseudo-Anosov maps to conclude dynamical
properties holding in almost every direction for the Eaton lens model.
We will talk about the dynamics on Panov planes, wind-tree models
and the periodic Eaton lens model with supporting slides showing
trajectories in eigendirection of pseudo-Anosov maps.
We will further state and discuss several dynamical results
and finally present some directions of (our) current research in the topic.2014-09-22T15:35:00Dynamical systems seminarkatok_s@math.psu.edusaz11@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduGeneric solutions of PDEs
http://www.math.psu.edu/seminars/meeting.php?id=22153
Speaker(s): Alberto Bressan
ABSTRACT: For arbitrary smooth initial data, the solution of a hyperbolic PDE can exhibit wild behavior.
However, using differential geometric methods, sometimes one can prove that "most" solutions
are in fact quite nice. In other words, if we remove a (topologically small) set of initial data leading to pathological behavior,
all the remaining solutions have a high degree of regularity.
For example, the solution to a conservation law with smooth initial data can develop countably many shocks.
But for an open dense set of C^2 initial data only finitely many shocks appear, located along smooth curves in the t - x plane,
with finitely many intersection points.
This talk will review some basic ideas and techniques in the generic theory of PDEs,
and discuss some possible future applications.2014-09-23T10:00:00Hyperbolic and Mixed Type PDEs Seminarzhang_t@math.psu.eduArithmetic Properties of Andrews' Singular Overpartitions
http://www.math.psu.edu/seminars/meeting.php?id=21917
Speaker(s): Dr. James Sellers
In a very recent work, George Andrews defined the combinatorial objects which he called singular overpartitions with the goal of presenting a general theorem for overpartitions which is analogous to theorems of Rogers--Ramanujan type for ordinary partitions with restricted successive ranks. As a small part of his work, Andrews noted two congruences modulo 3 which followed from elementary generating function manipulations. In this talk, we show that Andrews' results modulo 3 are two examples of an infinite family of congruences modulo 3 which hold for that particular function. Time permitting, we will also expand the consideration of such arithmetic properties to other functions which are part of Andrews' framework for singular overpartitions. This is joint work with Shi-Chao Chen and Michael D. Hirschhorn.2014-09-23T11:15:00Combinatorics/Partitions Seminarkatz@math.psu.edusellersj@math.psu.edusaz11@math.psu.eduandrews@math.psu.eduKeeping the beat: Homeostatic frequency control in coupled oscillators
http://www.math.psu.edu/seminars/meeting.php?id=23661
Speaker(s): Bard Ermentrout
When nonlinear oscillators are forced or coupled they will generally lock if the frequency is in a narrow enough range. However, humans and other animals such as fireflies and Snowball the dancing cockatoo are able to adjust the intrinsic frequency of their oscillators to widen the range of locking and zeroing the phase-lag. In this talk, I will start with some simple abstract circle maps and show that when the frequency is modulated by the coupling there are many possible final states and fractal basin boundaries between them. I will then turn to continuous time oscillators. Using averaging I will derive a new class of phase models and analyze their properties. I apply this to some neural models and show how the homeostatic control of the frequency greatly expands the ability to lock. Finally, I show that traveling periodic wave trains can be destabilized in the when there is frequency adjustment in rings of coupled oscillators.2014-09-23T13:00:00Theoretical Biology Seminarcpc16@math.psu.edutreluga@math.psu.eduTo be announced
http://www.math.psu.edu/seminars/meeting.php?id=22076
Speaker(s): Jake Pardo
2014-09-23T14:30:00Logic Seminarjmr71@math.psu.edusimpson@math.psu.edureimann@math.psu.eduMeasure rigidity of higher rank algebraic Z^r actions, I.
http://www.math.psu.edu/seminars/meeting.php?id=22802
Speaker(s): Zhiren Wang
As a natural extension of the long-standing Furstenberg conjecture,
it is expected that invariant measures under Z^r actions by toral
automorphisms must be of algebraic nature when r>1. To have
such rigidity phenomena, one has to exclude rank-one factors. If
one assumes in addition that there is no zero-entropy factor,
measure rigidity was first established by Katok-Spatzier for
totally non-symplectic, and then by Einsiedler-Lindenstrauss in
general. In this talk, we will sketch the Einsiedler-Lindenstrauss
approach and explain how it generalizes to Z^r actions by
nilmanifold automorphisms.2014-09-23T15:30:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.eduhertz@math.psu.edukalinin@math.psu.eduAssessing Students
http://www.math.psu.edu/seminars/meeting.php?id=23732
Speaker(s): David Zach
2014-09-23T17:45:00Teaching Seminarhalpenny@math.psu.eduDo As I Say, Not As I Do
http://www.math.psu.edu/seminars/meeting.php?id=23972
Speaker(s): Attendees
Mathematicians may profess a set of values that differs from what is inferred by their actions. This week, we discuss a paper that looks at discrepancies between what mathematicians value in proofs versus how they teach them.
<br>
Lai, Y. & Weber, K. (2014). Factors mathematicians profess to consider when presenting pedagogical proofs. <i>Educational Studies in Mathematics,</i> 85(1), 93-108.2014-09-24T15:35:00Teaching Mathematics Discussion Group Seminarjamshidi@math.psu.edu