The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2015-10-08webmaster@math.psu.eduDetermining continuum quantities from Molecular dynamics models
http://www.math.psu.edu/seminars/meeting.php?id=27535
Speaker(s): Xiaojie Wu
Even though Molecular dynamics (MD) models continuum mechanics are
widely used in the same areas, the connection between MD models and
continuum mechanics is not clear. This talk will review the definition
of virial stress and Hardy's theory. More generalized definitions of
continuum quantities will be presented in both Eulerian and Lagrangian
specification. Some techniques are also involved to improve the
accuracies of these quantities. The techniques are verified by
numerical simulations. This talk will end up with the definition of
traction for many-body potentials.2015-10-09T14:30:00CCMA PDEs and Numerical Methods Seminar Seriesma_y@math.psu.edusaz11@math.psu.edufuw7@math.psu.edusxw58@math.psu.eduDiffusion on social networks
http://www.math.psu.edu/seminars/meeting.php?id=26960
Speaker(s): Kalyan Chatterjee
This presentation will discuss two papers in which individual agents interact on given social networks. In the first model, the agents behave according to simple rules or heuristics in reacting to their neighbours’ choices and outcomes. In the second, players rationally decide whether to pass on messages they receive. The first model studies the extent of diffusion on the line; the second also investigates characteristics of the network that could lead to desirable outcomes.2015-10-09T15:35:00Probability and Financial Mathematics Seminaranovikov@math.psu.edumazzucat@math.psu.edudenker@math.psu.eduNCG Seminar
http://www.math.psu.edu/seminars/meeting.php?id=30164
Speaker(s): Damien Broka
2015-10-10T14:00:00Student Geometric Functional Analysis Seminarbakshi@math.psu.eduIntroduction to FEM
http://www.math.psu.edu/seminars/meeting.php?id=27314
Speaker(s): Serge Nicaise
2015-10-12T12:20:00CCMA Luncheon Seminarxli@math.psu.edusaz11@math.psu.edumsm37@math.psu.eduliu@math.psu.edushaffer@math.psu.eduFrom a priori error estimates to a posteriori error estimates for the finite element approximations of boundary value problems with singularities
http://www.math.psu.edu/seminars/meeting.php?id=27315
Speaker(s): Serge Nicaise (Host: A Mazzucato)
2015-10-12T14:30:00Computational and Applied Mathematics Colloquiumxli@math.psu.edusaz11@math.psu.edushaffer@math.psu.eduliu@math.psu.edufuw7@math.psu.eduSolving differential games by PDE methods
http://www.math.psu.edu/seminars/meeting.php?id=27396
Speaker(s): Alberto Bressan
Non-cooperative differential games are commonly used in economics and management science, to model competitive interactions between two or more agents, in continuous time.
For such games, one usually looks for a Nash equilibrium, where the strategy adopted by each player is a best reply to the strategies implemented by all other players. Nash equilibrium in feedback form can be found by solving a system of Hamilton-Jacobi PDEs, describing the value functions for the various players.
In this introductory talk, I shall explain how to derive these PDEs, and what are the main difficulties toward their solution. In particular, I shall review the standard way to solve LQ games (with linear dynamics and quadratic costs) and discuss their stability w.r.t. nonlinear perturbations.2015-10-13T10:00:00Hyperbolic and Mixed Type PDEs Seminarzhang_t@math.psu.edusaz11@math.psu.edujpr223@math.psu.eduyzheng@math.psu.eduImmmersions of the circle in the sphere and in higher Riemann surfaces
http://www.math.psu.edu/seminars/meeting.php?id=27039
Speaker(s): Robert Coquereaux
We encode circle immersions with n crossings in terms of orbits of the centraliser of a special element of the symmetric groups S(2n) or S(4n) acting by conjugation on particular subsets, or in terms of appropriate double cosets. The details depend on the various orientability hypothesis made on the source (the circle) and on the target (a surface of genus g), and also on a possible constraint of bi-colariability that one can furthermore impose.
We count and tabulate non-equivalent images of spherical immersions up to 10 crossings therefore recovering and extending results by Arnold (5 crossings) and followers (7 crossings), we also obtain the corresponding classifications for genus higher than 0. In the latter case we introduce the notion of bicolourability and determine the first terms (up to 9 crossings) of the corresponding sequences.
This presentation summarizes recent work done in collaboration with with J.-B. Zuber.2015-10-13T14:30:00GAP Seminareus25@math.psu.edustienon@math.psu.eduping@math.psu.eduhigson@math.psu.eduDegrees of unsolvability. Part 3: Muchnik degrees of effectively closed sets
http://www.math.psu.edu/seminars/meeting.php?id=27040
Speaker(s): Stephen G. Simpson
This series of talks is based on my recent 3-hour tutorial at the Computability in Europe conference in Bucharest. The lattice of all Muchnik degrees is large and complicated, but in this talk I discuss two sublattices which are smaller and hopefully more manageable. Namely, let E_w and S_w be the sublattices consisting of the Muchnik degrees of nonempty, effectively closed sets in the Cantor space and the Baire space respectively. I prove that E_w is an initial segment of S_w, and I use this fact to obtain many specific, natural examples of degrees in E_w. I note that there is a strong analogy between E_w and E_T, the upper semilattice of recursively enumerable Turing degrees. I argue that E_w is more interesting than E_T, because E_T contains no specific, natural examples of degrees other than the top and bottom degrees, 0' and 0.2015-10-13T14:30:00Logic Seminarsimpson@math.psu.edujmr71@math.psu.edureimann@math.psu.eduRigidity of topological entropy on manifolds carrying a metric of constant negative curvature, after Besson-Courtois-Gallot
http://www.math.psu.edu/seminars/meeting.php?id=27166
Speaker(s): Alena Erchenko
2015-10-13T15:30:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.edusaz11@math.psu.edukatok_s@math.psu.eduhertz@math.psu.edukalinin@math.psu.eduAmple divisors on Hilbert schemes of points
http://www.math.psu.edu/seminars/meeting.php?id=26962
Speaker(s): Jack Huizenga
I will give a gentle introduction to the minimal model program for Hilbert schemes of points, Bridgeland stability conditions, and the positivity lemma of Bayer and Macri. I will then explain how this theory leads to a computation of the cone of ample divisors on the Hilbert scheme of points of a surface.2015-10-15T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.edupapikian@math.psu.eduyee@math.psu.edueisentra@math.psu.eduMono-monostatic bodies: the story of the Gömböc
http://www.math.psu.edu/seminars/meeting.php?id=28195
Speaker(s): Gábor Domokos
In 1995, V.I. Arnold conjectured that convex, homogeneous solids with just two static balance points (so-called mono-monostatic bodies) may exist. Ten years later, based on a constructive proof, the first such object (dubbed "Gömböc") was built.
The newly discovered objects show various interesting features. We will point out that mono-monostatic bodies are neither flat, nor thin, they are not similar to typical objects with more equilibria and they are hard to approximate by polyhedra. Despite these "negative" traits, there seems to be strong indication that these forms appear in the living Nature due to their special mechanical properties: some turtle species evolved special shell geometries close to the Gömböc to facilitate self-righting.
The first numbered Gömböc (Gömböc 001) was given to V.I. Arnold on the occasion of his 70th birthday in Moscow. Here Arnold proposed that the Gömböc may play a role in explaining the geometric evolution of pebbles. I will discuss some mathematical and geophysical aspects of this conjecture in the Department Colloquium.2015-10-15T13:25:00MASS Colloquiumtabachni@math.psu.edusaz11@math.psu.eduDeterminants in K-theory and operator algebras
http://www.math.psu.edu/seminars/meeting.php?id=27125
Speaker(s): Joe Migler
A determinant in algebraic K-theory is associated to any two Fredholm operators that commute modulo the trace ideal. One can also calculate a homological invariant known as joint torsion. In this talk I will discuss recent work on these invariants and some applications.2015-10-15T14:30:00Noncommutative Geometry Seminarroe@math.psu.eduhigson@math.psu.edusaz11@math.psu.eduArnold's problem, the Gömböc and the evolution of pebble shapes
http://www.math.psu.edu/seminars/meeting.php?id=25684
Speaker(s): Gábor Domokos - Joint MASS Speaker (Host: Sergei Tabachnikov)
The best known mathematical models for the abrasion of sedimentary particles are curvature-driven flows, a special class of nonlinear partial differential equations defining the evolution of a surface Sigma by the speed v in the direction of its surface normal, and v is a function of the principal curvatures kappa, lambda of Sigma: v=v(kappa, lambda).
In 1987 Grayson proved that if Sigma is given as a distance function from a fixed reference O then the number N(t) of spatial critical points (extrema of the distance) is decreasing monotonically under the planar v=kappa flow. We will show that there is mounting evidence that similar, though weaker (generic, stochastic) statements are true for static balance points on 3D solids evolving under the above equation.
Our model predicts that the expected value of the number of static balance points on abrading solids will decrease monotonically. Laboratory and field data show a remarkable match with the proposed Markov process. We will also discuss why Gömböc shapes, with minimal number of balance points,
are almost never found in Nature. Rather, as physicist Sir Michael Berry expressed it,``they exist in Nature only as a dream".
I will speak on the discovery of the Gömböc in the MASS colloquium.2015-10-15T15:35:00Department of Mathematics Colloquiumtabachni@math.psu.edusaz11@math.psu.eduliu@math.psu.edu