Slow-Pitch seminar
Purpose:
  • Provide seminars at a mathematical maturity level aimed toward graduate students, beyond seminars intended for undergraduates or non-mathematicians but not assuming professional familiarity with a specialty.
  • Introduce graduate students to the spectrum of research interests that can be pursued in the Department; allow graduate students and advisors to connect if they find common interests.
  • Provide an opportunity for specialists of one kind to learn something of a subfield other than their own.

An ideal Slow-Pitch Seminar will meet all three of these objectives; typically, the most important criterion is the first. Occasionally, visitors are invited to speak, in which case Objective 2 is necessarily attenuated.
Time and format:
    The Slow-Pitch, in semesters where it has run, has typically been a biweekly seminar scheduled for one hour during a midweek afternoon. Refreshments, usually pizza and soda, are provided by the organizer.

Examples of past seminars:
  • Sep 16, 2003
    Title:Quantum Groups And Subgroups(Or, Just What Are Those Things At 329 McAllister?)
    Speaker: Adrian Ocneanu (Penn State University)
    We describe the internal symmetry in SU(n) and its representations from a different point of view, connected to symmetries of Platonic solids.
  • Oct 14, 2003
    Title:The Rogers-Ramanujan Continued Fraction and Ramanujan's Lost Notebook
    Speaker: Prof. George Andrews (Penn State)
    For centuries we have known that the golden ratio is the value of a continued fraction: (1+5^(1/2))/2 = 1 + 1/(1 + 1/(1+ 1/(1 + 1/(...)))). This is perhaps the most well-known example of a continued fraction. Ramanujan considered a natural generalization of this continued fraction which has subsequently been called the Rogers-Ramanujan continued fraction. In Ramanujan's Lost Notebook, he states many weird and wonderful results for this fraction. We'll lead slowly up to some of the more bizarre assertions.
  • Nov 25, 2003
    Title: Integrable PDEs and Surface Water Waves
    Speaker: Diane Henderson (Penn State)
    In this talk we present a classic asymptotic method of deriving evolution equations for surface water waves. The resulting nonlinear PDEs: The Korteweg de Vries (KdV) equation and the Kadomtsev Petviashvili equation for shallow water waves; the nonlinear Schroedinger (NLS) equation and the three-wave equations for deep-water waves, are integrable by the Inverse Scattering Transform. They arise in many physical applications including optics, plasma physics and Bose-Eisnstein condensates as well as in water waves. We show an example of Inverse Scattering Theory with the KdV equation, discuss integrability versus chaos with the NLS equation, and show examples of how exact solutions of all four equations model experiments on surface water waves.
  • Oct 26, 2004
    Title: Skew and totally skew embeddings and immersions
    Speaker: Sergei Tabachnikov (Penn State)
    A skew loop is a closed smooth curve in space without parallel tangents. In the 1960s, H. Steinhaus conjectured that no skew loops existed. This proved to be false but skew loops cannot lie on quadratic surfaces. The same holds true for their multi-dimensional analogs, skew branes, submanifolds of codimension 2 in a vector space free from parallel tangent spaces. A submanifold of a vector space is called totally skew if any two lines, tangent to it at two distinct points, are neither parallel nor intersecting. Given a smooth manifold, what is the least dimension of space space that can contain it as a totally skew manifold? Even for a disk, this is a hard question, closely related to deep and hard problems of algebraic topology. I will survey old and recent results on these subjects by B. Segre, M. Ghomi, B. Solomon, J. White and myself.
  • Apr 18, 2006
    Title: K-Theory: What is it and what is it good for?
    Speaker: Paul Baum (PSU)
    Dr. Paul Baum, expert on K-theory and co-author of the famous Baum-Connes Conjecture, will give an introduction to K-theory and some of its utilisations.