The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2016-02-10webmaster@math.psu.eduConnections Between Path Partitions and Restricted m-ary Partitions
http://www.math.psu.edu/seminars/meeting.php?id=29227
Speaker(s): James Sellers
In this talk, we will describe unique path partitions (whose motivation comes from representation theory of the symmetric group). Once this introduction is complete, we will discuss an explicit characterization of the unique path partitions of n (or up-partitions for short) in terms of partitions we call strongly decreasing (and which are closely related to the non-squashing partitions of Sloane and JAS). We then discuss numerous connections between up-partitions and certain types of binary partitions. Thanks to such connections with binary partitions, we conjecture and prove various arithmetic properties of u(n), the number of unique path partitions of n. We will close the talk with a discussion of generalizations to certain types of m-ary partitions as well as very recent work on arithmetic properties satisfied by such m-ary partition functions. This talk will touch on joint works of Christine Bessenrodt, Jorn Olsson, and JAS; George Andrews, Aviezri Fraenkel, and JAS; and George Andrews, Eduardo Brietzke, Oystein Rodseth, and JAS.2016-02-11T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.edupapikian@math.psu.eduyee@math.psu.edueisentra@math.psu.eduNumerical Modeling of Ice Sheets
http://www.math.psu.edu/seminars/meeting.php?id=30637
Speaker(s): David Pollard
A brief overview of continental-sized ice sheets will be given, both for today (Greenland and Antarctica) and the past (North American and Eurasian). Basic physical processes and the equations describing ice-sheet variations through time will be described. The numerical techniques used to solve for the slow flow of ice deforming under its own weight will be outlined, focusing on the sparse-matrix solution of the horizontal stretching equations. The performance of the sparse-matrix solver used in our model will be assessed, and advice sought on how to improve on this performance.2016-02-11T14:30:00CCMA PDEs and Numerical Methods Seminar Seriessxw58@math.psu.edufuw7@math.psu.eduma_y@math.psu.eduFirst-passage percolation
http://www.math.psu.edu/seminars/meeting.php?id=30199
Speaker(s): Arjun Krishnan
First-passage percolation is a random growth model on the cubic lattice Z^d. It models, for example, the spread of fluid in a random porous medium. This talk is about the asymptotic behavior of the first-passage time T(x), which represents the time it takes for a fluid particle released at the origin to reach a point x on the lattice.
The first-order asymptotic --- the law of large numbers --- for T(x) as x goes to infinity in a particular direction u, is given by a deterministic function of u called the time-constant. The first part of the talk will focus on a new variational formula for the time-constant, which results from a connection between first-passage percolation and stochastic homogenization for discrete Hamilton-Jacobi-Bellman equations.
The second-order asymptotic of the first-passage time describes its fluctuations; i.e., the analog of the central limit theorem for T(x). In two dimensions, the fluctuations are (conjectured to be) in the Kardar-Parisi-Zhang (KPZ) or random matrix universality class. We will present some new results (with J. Quastel) in the direction of the KPZ universality conjecture.
The analysis of this problem will involve tools and ideas from probability, PDEs, and ergodic theory.2016-02-11T15:35:00Department of Mathematics Colloquiumsaz11@math.psu.eduliu@math.psu.eduauh243@math.psu.eduPostive loops - on a question by Eliashberg-Polterovich and a contact systolic inequality
http://www.math.psu.edu/seminars/meeting.php?id=30063
Speaker(s): Peter Albers
In 2000 Eliashberg-Polterovich introduced the concept of positivity in contact geometry. The notion of a positive loop of contactomorphisms is central. A question of Eliashberg-Polterovich ist whether C^0-small positive loops exist. We give a negative answer to this question. Moreover we give sharp lower bounds for the size which, in turn, gives rise to a L^\infty-contact systolic inequality. This should be contrasted with a recent result by Abbondandolo et. al. that on the standard contact 3-sphere no L^2-contact systolic inequality exists. The choice of L^2 is motivated by systolic inequalities in Riemannian geometry. This is joint work with U. Fuchs and W. Merry.2016-02-15T15:35:00Dynamical systems seminarkatok_s@math.psu.edusaz11@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduJordan Groups, Abelian Varieties and Conic Bundles
http://www.math.psu.edu/seminars/meeting.php?id=29253
Speaker(s): Yuri Zarhin
A classical theorem of Jordan asserts that each finite subgroup of the complex general linear group GL(n) is ``almost commutative": it contains a commutative normal subgroup
with index bounded by a universal constant that depends only on n.
We discuss an analogue of this property for the groups of birational (and biregular) automorphisms of complex algebraic varieties and the groups of diffeomorphisms of real manifolds.
This is a report on a joint work with Tatiana Bandman (Bar-Ilan).2016-02-16T14:30:00GAP Seminareus25@math.psu.eduhigson@math.psu.eduping@math.psu.edustienon@math.psu.eduroyer@math.psu.eduFine Structure Theory and Algorithmic Randomness (II)
http://www.math.psu.edu/seminars/meeting.php?id=29285
Speaker(s): Jan Reimann
2016-02-16T14:30:00Logic Seminarreimann@math.psu.edusimpson@math.psu.edujmr71@math.psu.eduErgodic theory of C^1 generic conservative diffeomorphisms: II.
http://www.math.psu.edu/seminars/meeting.php?id=30042
Speaker(s): Jairo Bochi
In this pair of talks, I'll survey what is known about the ergodic theory of C^1-generic volume-preserving and symplectic diffeomorphisms, and what are the various perturbation techniques used to prove those results. In the first part, I'll explain a statement of Mañé (generic area-preserving diffeomorphisms either have zero Lyapunov exponents a.e. or are Anosov), and its higher-dimensional generalizations. In the second part, I'll explain more recent results, culminating with the following theorem of Avila, Crovisier, and Wilkinson: C^1-generic volume-preserving diffeomorphisms either have zero Lyapunov exponents a.e. or the volume measure is ergodic, hyperbolic, and moreover the splitting into stable and unstable spaces is globally uniformly dominated.2016-02-16T15:32:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.edusaz11@math.psu.edukatok_s@math.psu.eduhertz@math.psu.eduSL(2,R) seminar
http://www.math.psu.edu/seminars/meeting.php?id=31130
Speaker(s): Various
This seminar will example aspects of the representation theory of SL(2,R)2016-02-16T16:15:00Special Eventhigson@math.psu.edu