Distinguished Visiting Professor Talk Series: Nicolas Sirolli, Universidad de Buenos Aires, Febuary 11th @4pm in Olin 372

Z3s7Ej6GTitle: From Congruent Numbers to Modular Forms

Abstract: A positive integer is called a congruent number if it is the area of a
right triangle with rational sides. The problem of giving a criterion for
deciding if a number is congruent has been open for hundreds of years. The
best answer known was given by Tunnell in 1983, using many deep results
from modern Number Theory. His work will give a completely satisfactory
answer, once the Birch and Swinnerton-Dyer conjecture gets proved.

In this talk we will introduce, in a way as friendly as possible, the main
ingredients needed to understand Tunnell’s result: elliptic curves,
modular forms, and some deep theorems concerning them.

Student Talk Series: John Klobusicky, Geisinger Health Systems, February 5th, Olin 268 @ noon


Title: Piecewise Deterministic Markov Processes and Metal Grain Coarsening

Abstract: In material science, individual metal grains obey surprisingly simple rules.  However, geometric considerations can create difficulties when attempting to analyze the bulk properties of metals.  In this talk, we’ll describe a mean field model using piecewise deterministic Markov processes which converts the geometric problem of grain evolution to one of analysis and stochastic processes.  In particular, we’ll show that densities of grains approach a law of large numbers described by a partial differential equation.

Joint Talk with Management: Anne Robinson and John Williamson, Verizon Wireless, February 5th, Rooke CHEM 116 @ 3pm


Title: How Analytics Professionals Make the World Go Round


It’s hard to open a business magazine, walk through an airport or even participate in an executive meeting and NOT see or hear reference to analytics. Recognized as the currency of business, mathematics or analytics are empowering decision-making at new levels. A trend that started with CIOs is spreading throughout the C-Suite – Everyone wants ANALYTICS!


What exactly are these analytics professionals doing? What types of real-world problems are they solving? Are they actually applying the math, statistics and operations research tools they learned in their courses? What other skills or certifications do they have?  What opportunities are there for graduate studies in analytics?
Hear from Anne Robinson and John Williamson of Verizon Wireless.  Anne Robinson holds a Ph.D. in Industrial Engineering from Stanford University and served as President of INFORMS, the largest professional organization for both practitioners and academics in the field of Analytics/Operations Research.  John Williamson holds a M.B.A. in Supply Chain Management from Penn State University.  There will be an opportunity to speak with the presenters following the talk.

Student Talk Series: Tracy Sweet, University of Maryland, January 22nd, Olin 268 @ noon


Title: Hierarchical Social Network Models with Applications in the Social Sciences

Abstract: The term “social network analysis” includes most quantitative methods for analyzing relational data and these methods are both exploratory and inferential. For inference, there are a variety of social network statistical models to represent the stochastic nature of network relationships.  In this talk, I will present social network models that are written as Hierarchical Bayes models and describe how these generative models can be used in the social sciences which often involve multiple partially exchangeable networks.

Distinguished Visiting Professor Talk Series: Sergi Elizalde, Dartmouth College, November 24th @4pm in Olin 372

Title: Consecutive patterns in permutations


Abstract: An occurrence of a consecutive pattern sigma in a permutation pi
is a subsequence of adjacent entries of pi in the same relative
order as the entries of sigma. For example, occurrences of the
consecutive pattern 21 are descents, and alternating permutations
are those that avoid the consecutive patterns 123 and 321. The
systematic study of consecutive patterns in permutations started over
a decade ago.  More recently, consecutive patterns have become
relevant in the study of one-dimensional dynamical systems, and they
are useful in creating tests to distinguish random from deterministic
time series.

We show that the number of permutations avoiding the consecutive
pattern 12…m —that is, containing no m adjacent entries in
increasing order— is asymptotically larger than the number of
permutations avoiding any other consecutive pattern of length m. At
the other end of the spectrum, the number of permutations avoiding
12… (m-2)m(m-1) is asymptotically smaller than for any other
consecutive pattern.

Student Talk Series: Sergi Elizalde, Dartmouth College, November 20th, Olin 268 @ noon

Title: Lattice paths between two boundaries

Abstract: Dyck paths are lattice paths with steps N=(0,1) and E=(0,1) starting
at (0,0), ending at (n,n), and never going below the diagonal y=x.
Among the many interesting facts known about Dyck paths, one is that
the parameters ‘number of E steps at the end’ and ‘number of returns
to the diagonal’ have a symmetric joint distribution, meaning that to
each Dyck path we can bijectively associate another one where these
parameters are interchanged.

I will show that this symmetry property applies not only to Dyck
paths, but more generally to lattice paths with N and E steps that lie
between any two fixed boundaries. Finally, I will discuss how these
lattice paths are related to other objects in combinatorics, such as
matroids, semistandard Young tableaux and k-triangulations.

This is joint work with Martin Rubey.

Distinguished Visiting Professor Talk Series: Paola Sztajn, North Carolina State University, November 4, @ 4pm in Olin 372

Title: Learning from systematic descriptions of mathematics professional development

Abstract:  In this talk I present emerging results from a systematic
review of publications on mathematics professional development. The
research team reviewed over 170 papers published between 1992 and 2010
to address the following research questions: What do we know about the
design and conduct of mathematics PD being studied by researchers and
how are these PD characterized in research reports? The conceptual
framework included six elements: theory, context, goals, content,
format, and activities.

Problem of the Week Instructions and This Week’s Problem

Try the Math Department Problem of the Week!

New Problems every Tuesday at 1pm!

How it Works:

  1. Pick up a problem sheet in the Math Department on the third floor of Olin Science
  2. Do the problem!
  3. Turn in your solution in the Math Dept. Office in Olin 380 before 5pm the following Monday.
  4. Every correct solution over the course of the semester gives you a chance to win a $50 Amazon Gift Card.
  5. Keep doing the Problem of the Week! Each correct solution adds your name to the drawing at the end of the semester!

2 correct solutions = 2 tickets in the drawing!


Problem of the Week #4:



Distinguished Visiting Professor Talk Series: Eva A. Gallardo Gutierrez, Universidad Complutense de Madrid, October 23rd @ 4pm in Olin 372


Title: Rota’s Universal Operators

Abstract: The Invariant Subspace Problem for Hilbert spaces is a long-standing question and the use of universal operators in the sense of Rota has been one tool for studying the problem. The best known universal operators have been adjoints of analytic Toeplitz operators or unitarily equivalent to them. We present many examples of Toeplitz operators whose adjoints are universal operators and exhibit some of their common properties. Some ways in which the invariant subspaces of these universal operators interact with operators in their commutants are given. Special attention is given to the closed subalgebra, not always the zero algebra, of compact operators in their commutants.



Algebra etc. Seminar: Shelby Kilmer, October 16 @ 4pm in Olin 372

Title: Random Groups at Density 1/2

Abstract: Random groups in the density model (with density 0<d<1) have
presentations with a random set of (2m-1)^{dk} relators of length k on
m generators. The classic theorem in the density model states that for
d>1/2, random groups are asymptotically almost surely trivial or
isomorphic to Z/2Z, while for d<1/2, random groups are asymptotically
almost surely infinite hyperbolic. This summer our research group
studied random groups at d=1/2 and found both infinite hyperbolic
groups and trivial groups are generic, depending on how we tuned
certain parameters.