The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2015-08-30webmaster@math.psu.eduSlow entropy for smooth flows on surfaces
http://www.math.psu.edu/seminars/meeting.php?id=27208
Speaker(s): Adam Kanigowski
We will discuss slow entropy in the class of mixing smooth flows on surfaces. As a consequence we will find countably many non-isomorphic (disjoint) smooth flows. Moreover, we will show that they don't have finite rank.2015-08-31T15:35:00Dynamical systems seminarkatok_s@math.psu.edusaz11@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduA Combinatorial Proof of a Relationship Between Maximal (2k-1,2k+1)-cores and (2k-1,2k,2k+1)-cores
http://www.math.psu.edu/seminars/meeting.php?id=26943
Speaker(s): James Sellers
Integer partitions which are simultaneously t-cores for distinct values of t have attracted significant interest in recent years. When s and t are relatively prime, Olsson and Stanton have determined the size of the maximal (s,t)-core. When k > 1, a conjecture of Amdeberhan on the maximal (2k-1,2k,2k+1)-core has also recently been verified by numerous authors.
In this work, we analyze the relationship between maximal (2k-1,2k+1)-cores and maximal (2k-1,2k,2k+1)-cores. In previous work, Nath noted that, for all k > 0, the size of the maximal (2k-1,2k+1)-core is exactly four times the size of the maximal (2k-1,2k,2k+1)-core and requested a combinatorial interpretation of this unexpected identity. Here, using the theory of abaci, partition dissection, and elementary results relating triangular numbers and squares, we provide such a combinatorial proof. This is joint work with Rishi Nath.2015-09-01T11:15:00Combinatorics/Partitions Seminarsellersj@math.psu.edukatz@math.psu.edusaz11@math.psu.eduandrews@math.psu.eduNote special time: *Thursday* at 12:20pm
http://www.math.psu.edu/seminars/meeting.php?id=27464
Speaker(s): Igor Aronson
2015-09-01T13:30:00Theoretical Biology Seminarcpc16@math.psu.edutreluga@math.psu.eduDegrees of unsolvability. Part 1: introduction
http://www.math.psu.edu/seminars/meeting.php?id=27015
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. An important 20th century discovery is that there are algorithmically unsolvable problems in virtually every branch of mathematics. Degrees of unsolvability are an attempt to measure the "amount" or "extent" of the unsolvability of such problems. They are based on the idea of "reducibility" of one problem to another. In this introductory talk we define and discuss two particular degree structures: the Turing degrees, and the Muchnik degrees. We point out that the Muchnik degrees are the completion of the Turing degrees, similarly to how the real numbers are the completion of the rational numbers. We discuss specific examples of Turing degrees, and we give at least one specific example of a Muchnik degree which is not a Turing degree. (There are many more such examples, and we shall discuss some of them in later talks in this series.) We point out how the Muchnik degrees provide a rigorous implementation of Kolmogorov's calculus of problems.2015-09-01T14:30:00Logic Seminarsimpson@math.psu.edujmr71@math.psu.edureimann@math.psu.eduYang-Baxter and reflection equations: unifying structures behind quantum and classical integrable systems
http://www.math.psu.edu/seminars/meeting.php?id=27016
Speaker(s): Vincent Caudrelier
The Yang-Baxter equation (YBE) is central in the theory of quantum integrable systems. For decades, together with its companion for problems with boundaries (the quantum reflection equation), it has been studied and used in the quantum realm, leading to the area of quantum groups. But it was suggested by Drinfeld in 1990 that the general study of the so-called «set-theoretical YBE » is also important. This can be understood as the problem of finding nonlinear representations of the braid group on arbitrary sets. It turns out that classical integrable PDEs provide a means to construct certain types of such representations, called Yang-Baxter maps, by looking at soliton collisions. I will use the vector nonlinear Schrödinger (NLS) equation as the main example to illustrate the idea. It has its origin in the physics of wave phenomena in fluid dynamics, nonlinear optics, plasma physics or quantum cold gases. After reviewing this, I will show how the new concept of set-theoretical reflection equation naturally emerges by studying solitons in integrable PDEs with a boundary. As before, the problem of finding solutions to this equation can be understood as the question of finding nonlinear representations of the finite Coxeter group of type BCn. I will show how to construct such representations using solitons.2015-09-01T14:30:00GAP Seminareus25@math.psu.eduping@math.psu.edustienon@math.psu.eduhigson@math.psu.eduSome Open Problems Arising from my Recent Finite Field Research
http://www.math.psu.edu/seminars/meeting.php?id=26944
Speaker(s): Gary Mullen
We will discuss a number of my favorite open problems and
conjectures which have arisen in my recent research related
to finite fields. These discussions will focus on a variety
of areas including some theoretical topics as well as some
topics from combinatorics and coding theory.2015-09-03T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.edupapikian@math.psu.eduyee@math.psu.edueisentra@math.psu.eduComputational model of cell motility
http://www.math.psu.edu/seminars/meeting.php?id=28707
Speaker(s): Igor Aronson
Cell motility and collective migration are among the most important themes in cell biology, mathematical biology, and bioengineering, and are crucial for morphogenesis, wound healing, and immune response in eukaryotic organisms. It is also relevant for the development of effective treatment strategies for diseases such as cancer, and for the design of bioactive surfaces for cell sorting and manipulation. Substrate-based cell motility is, however, a very complex process as both regulatory pathways and physical force generation mechanisms are intertwined.
To understand the interplay between adhesion, force generation and motility, we develop a computational model based on the phase field method, which is especially suited to treat the moving and deformable boundaries involved in both individual and collective cell motility. The resulting system of coupled PDEs with the non-local volume-conservation constraint is solved by the quasi-spectral method in a periodic two-dimensional square domain. The model captures all essential phenomenology exhibited by moving cells, including the abrupt onset of motion and the response to external stimuli. We investigate by the means of large-scale GPU computations how cells navigate on substrates with patterned adhesion properties and modulated stiffness of substrate. Such substrates are currently under technological development to collect and sort cells. For multiple cells, the generalized multiphase-field model is able to predict that collective cell migration emerges spontaneously as a result of inelastic collision-type interactions of cells.2015-09-03T12:20:00Center for Interdisciplinary Mathematics Seminarbressan@math.psu.eduberlyand@math.psu.eduA tour of Pritchard Lab
http://www.math.psu.edu/seminars/meeting.php?id=28189
Speaker(s): Diane Henderson
The MASS students will be introduced to the Pritchard Fluids Lab, a physics that is a part of the Mathematics Department.2015-09-03T13:25:00MASS Colloquiumtabachni@math.psu.edusaz11@math.psu.eduNoncommutative Geometry 102: Asymptotics and spectral theory
http://www.math.psu.edu/seminars/meeting.php?id=27119
Speaker(s): Nigel Higson
I shall give two lectures introducing some of the ideas that appear in the research of Penn State's noncommutative geometry group. In the first I shall discuss differential and Hilbert space operators, and various sorts of "symbols" that can be attached to them. In the second I shall examine how the general theory applies to Sturm-Liouville operators on a half-line, following some remarkable early work Hermann Weyl that has proved to be very influential in representation theory.2015-09-03T14:30:00Noncommutative Geometry Seminarroe@math.psu.eduhigson@math.psu.edusaz11@math.psu.eduDepartmental Reception
http://www.math.psu.edu/seminars/meeting.php?id=25672
Speaker(s): Departmental Reception
2015-09-03T15:30:00Department of Mathematics Colloquiumsaz11@math.psu.eduliu@math.psu.eduAlgorithmic Stability in Adaptive Data Analysis
http://www.math.psu.edu/seminars/meeting.php?id=26945
Speaker(s): Adam Smith
Adaptivity is an important feature of modern data analysis—often, the
choice of questions asked about a dataset depends on previous
interactions with the same dataset. Adaptivity can arise in a single
study (say, when a researcher choses which model to fit based on some
exploratory data analysis) or, more subtly, when data sets are shared
and re-used across multiple studies. Unfortunately, most of the
statistical inference theory used in empirical sciences to control
false discovery rates, and in machine learning to avoid overfitting,
assumes that the analyses to be performed are selected independently
of the data. If the set of analyses run is itself a function of the
data, much of this theory becomes invalid.
Specifically, suppose there is an unknown distribution P and a set of
n independent samples x is drawn from P. We seek an algorithm that,
given x as input, “accurately” answers a sequence of adaptively chosen
“queries” about the unknown distribution P. How many samples n must we
draw from the distribution, as a function of the type of queries, the
number of queries, and the desired level of accuracy?
In this work we make two new contributions towards resolving this question:
1. We give upper bounds on the number of samples n that are needed to
answer "statistical queries" that improve over the bounds in the
recent work of Dwork et al. (2015).
2. We prove the first upper bounds on the number of samples required
to answer more
general families of queries. These include arbitrary low-sensitivity
queries and convex risk minimization queries.
Our algorithms are based on a connection between generalization error
and a distributional stability condition on inference algorithms,
called "differential privacy".
The talk will be self-contained.
Based on joint work with Raef Bassily, Kobbi Nissim, Thomas Steinke,
Uri Stemmer and Jon Ullman. http://arxiv.org/abs/1503.04843
For some nontechnical background reading, see
Gelman and Lokem, "The Garden of Forking Paths".
http://www.stat.columbia.edu/~gelman/research/unpublished/p_hacking.pdf2015-09-04T15:35:00Probability and Financial Mathematics Seminaranovikov@math.psu.edudenker@math.psu.edumazzucat@math.psu.eduroyer@math.psu.edunistor@math.psu.edu