Women Seminars Spring 2008 Schedule
Meeting: Tuesday 5:00 pm in 243 Altgeld Hall
- February 12, 2008
Mee Seong Im (UIUC Math)
Title:Geometric Invariants of Blow-Ups and del Pezzo
surfaces
Abstract: I will first give a brief background on
algebraic geometry and then introduce the notion of blow-ups with some
examples. I will then give some applications of blow-ups to del Pezzo
surfaces which are 2-dimensional Fano Varieties. If time allows, I will
discuss how Fano manifolds are obtained by blowing-up non Fano
manifolds.
- February 26, 2008
Supawadee Prugsapitak (UIUC Math)
Title:The Tarry-Escott problem over Z[i]
Abstract: The Tarry-Escott problem is an old problem that
asks for two different sets $\{a_1,a_2,...,a_n\}$ and
$\{b_1,b_2,...,b_n\}$ of integers such that \begin{equation} \sum_{i=1}^n
a_i^j = \sum_{i=1}^n b_i^j \quad \text{for any}~~ 1 \leq j \leq k.
\end{equation} We call $n$ the \emph{size} of solution and $k$ the
\emph{degree}. In 2006, A. Alpers and R. Tijdeman generalized the
classical Tarry-Escott problem to multinomials and they ask one to find
the solution of Tarry-Escott problem over \mathbb{Z}[i]. In this talk, I
will discuss Tarry-Escott problem over \mathbb{Z} and give a solution
degree 2 of Tarry-Escott problem over \mathbb{Z}[i].
- March 11, 2008
Merc Chasman (UIUC Math)
Title:Rayleigh Quotients and the Free Plate
Abstract: I discuss Rayleigh Quotients and how they can
be used to estimate and characterize eigenvalues of operators. I'll then
exploit this characterization to show that for a free plate, the
fundamental tone (lowest frequency of vibration) is maximal for the disk.
That is, of all metal plates vibrating at their lowest frequency, the disk
has the highest pitch.
- April 1, 2008
Chia-yen Tsai (UIUC Math)
Title:Bounds for a least pseudo-Anosov dilatation
Abstract: A current area of interest in hyperbolic
two-manifolds is understanding pseudo-Anosov homeomorphisms. First I will
explain what pseudo-Anosov dilatations mean. Since dilatations of a
surface S form a discrete set, it has a minimal element, which we call the
least pseudo-Anosov dilatation of S. I will give you known results of
bounds for some surfaces S. After that, I will state my main theorem,
bounds for a least pseudo-Anosov dilatation of a genus(>1) surface with
punctures, then I will give a proof of the upper bound.
- April 29, 2008
Melissa Dennison (UIUC Math)
Title:Purely Even Terms in the Bow Sequence
Abstract: By modifying the recursion in the Stern
sequence, we obtain a new sequence called the bow sequence. I will discuss
some properties of the bow sequence modulo 2. In particular, I will show
that 1/7 of the terms of the bow sequence are even for all sets of initial
conditions.