2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018
Current contact: Thomas Ng and Zachary Cline.
The seminar takes place on Fridays (from 1:00-2:00pm) in Room 617 on the sixth floor of Wachman Hall. Pizza and refreshments are available beforehand in the lounge next door.
Sunny Yang Xiao, Brown University
Luca Pallucchini, Temple University
Geoff Schneider
Rebekah Palmer, Temple University
In 1843, Hamilton carved "$i^2=j^2=k^2=ijk=-1$" into a bridge in Dublin after a spark of inspiration while on a walk. His original intention was to make the complex numbers $\mathbb{C}$ more complex (it worked). The restriction to $-1$ has since then been loosened in favor of generalization, known as quaternion algebras. We'll explore some introductory facts and see how these constructions occur in geometry.
Khanh Le, Temple University
Narek Hovsepyan, Temple University
It is shown that the eigenvalues of an analytic kernel on a finite interval go to zero at least as fast as $R^{ - n} $ for some fixed $R < 1$. The best possible value of R is related to the domain of analyticity of the kernel. The method is to apply the Weylâ€“Courant minimax principle to the tail of the Chebyshev expansion for the kernel. An example involving Legendre polynomials is given for which R is critical.
Reference - G. Little, J. B. Reade, Eigenvalues of analytic kernels , SIAM J. Math. Anal., 15(1), 1984, 133â€“136.
Thomas Ng, Temple University
Kathryn Lund, Temple University
Thomas Ng, Temple University
We will describe a model introduced by Bollob\'as for random finite k-regular graph. In the case when k=3, we will discuss connections with two constructions of random Riemann surfaces introduced by Buser and Brooks-Makover. Along the way, we will see a glimpse of the space of metrics on a surface (Teichmuller space) and (ideal) triangulations.
Zachary Cline, Temple University
There is a cool construction of a variant of this polynomial which is instructive and which anyone remotely interested in knot theory should see at least once in their life. I will present this construction and then explain how this polynomial invariant arises as a functor from the tangle category to the category of vector spaces over $C$.