| Colloquium | Seminars | Clec Lectures | Public Lectures | Distinguished Lectures |
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| Friday, January 25, 3-4pm, MP3314 | meeting | |
| Friday, February 1st, 3-4pm, MP3314 | Richard Ball, University of Denver | P-spaces and P-frames |
| Friday, February 8, 3-4pm, MP3314 | cancelled | |
| Thursday, February 14, 3-4pm, MP3314 | Matt Blair, University of Rochester |
Nonlinear wave equations on exterior domains |
| Friday, February 22, 3-4pm, MP3314 | Gabor Luckacs, University of Manitoba (Canada) | Pontryagin duality and number theory |
| Friday, February 29, 3-4pm, MP3314 | Shijun
Zheng, Georgia Southern University |
Spectral calculus, Besov spaces and Dispersive equations |
| Friday, March 7, 3-4pm, MP3314 | Xingping Sun, Missouri State University | Approximation of Equilibrium Measures via Radial Basis Functions |
| Friday, March 14, 3-4pm, MP3314 | Willard Miller, University of Minnesota | Truth and beauty in science. A celestial mechanics case study. |
| Spring Break | ||
| Friday, March 28, 3-4pm, MP3314 | Shanshuang Yang, Emory University | Rigidity of conformal embeddings |
| Monday, March 31st, 5-6pm, MP3314 | George Andrews, Pennsylvania State | Old and New Thoughts on the Rogers-Ramanujan Identities |
| Tuesday, April 1st, 6-7pm, IT 1004 | DISTINGUISHED
LECTURE: George Andrews, Pennsylvania State |
Euler and the beginning of the theory of partitions |
| Friday, April 4th, 3-4pm, MP3314 | Gavin Seal, Georgia Southern University |
Galois connections and the filter monad |
| Friday, April 11, 3-4pm, MP3314 | Ed Enochs, University of Kentucky | Covers and Envelopes |
| Friday, April 18, 3-4pm, MP3314 | Chris Heil, Georgia Tech | Music, Time-Frequency Shifts, and Linear Independence |
| Monday, April 21, 5pm-6pm, MP3314 | Homeira Pajoohesh, Medgar Evers College (CUNY) | |
| Friday, April 25, 2pm-3pm, MP3314 | Ramona Anton, John Hopkins University | Non-linear Schrödinger equations on domains with boundary |
| Friday, April 25, 3-4pm, MP3314 | Grillakis, University of Maryland | Impurity and quaternions in
nonrelativistic scattering from quantum memory |
| Monday, April 28, 5pm-6pm, MP3314 | Dirk Hofmann, University of Aveiro (Portugal) | Triquotient maps via ultrafilter convergence |
| Friday, May 2nd, 3-4pm, MP3314 | Shao, UCLA | The Restriction Conjecture |
Details of Spring 2008 lectures
Friday, February 1st, 3pm-4pm, MP 3314
Speaker: Richard Ball, University of DenverAbstract:
A space is called
“pseudo discrete,” or more commonly, a P-space,
provided that every real-valued function is constant in a neighborhood
of every point. Since we assume all spaces Tychanov, i.e.,
Hausdorff and completely regular, there are plenty of non-constant
real-valued functions, enough to separate the points. Thus it
might appear that these spaces are exotic and remote from daily
mathematical existence. In fact, they play a central role in
general topology since they carry the epicomplete objects in the most
natural categories which axiomatize C(X), the ring of continuous
functions on the space X. We will sketch some of the
classical characterizations of P-spaces at the beginning of the talk.
But the story gets more interesting when we consider the point-free analog, namely a P-frame. Here the spatial theory carries over for the most part, but diverges for considerations involving subspaces, i.e., quotient frames. The true objective of this talk is to pose a problem we have been unable to resolve.
Thursday, February 14st, 3pm-4pm, MP 3314
Speaker: Matt Blair, Rochester UniversityAbstract:
We consider certain semilinear wave equations posed on an exterior domain. While basic questions such as existence, uniqueness, and scattering of solutions have been answered in the Euclidean case, less is known in the case of an exterior domain. Here the presence of Dirichlet or Neumann boundary conditions can affect the flow of energy, complicating these issues considerably. We discuss recent progress in the area, including the development and applications of space-time integrability estimates for the wave equation ("Strichartz estimates"). This is a joint work with H. Smith and C. Sogge.Fourier
series provide a way of writing almost any signal as a
superposition of pure tones, or musical notes. But this
representation
is not local, and does not reflect the way that music is actually
generated
by instruments playing individual notes at different times.
We will discuss
Fourier series, and then present time-frequency representations, which
are a type of local Fourier representation of signals. This
gives us a
mathematical model for representing music. While the model is
crude for
music, it is in fact a powerful mathematical representation that has
appeared widely throughout mathematics (e.g., partial differential
equations),
physics (e.g., quantum mechanics), and engineering (e.g., time-varying
filtering). We ask one very basic question: are the notes in
this
representation linearly independent? This seemingly trivial
question
leads to surprising mathematical difficulties.
Abstract: (joint work by R. Kopperman, S. Matthews, and H. Pajoohesh)
In this paper we investigate some notions of completion of partial metric spaces, including the bicompletion, to some extent the Smyth completion, and a new ``spherical completion". Given an auxiliary relation, we find a partial metric that gives rise to it and whose spherical completion is its round ideal completion. A partial metric induces an order; with respect to this order we give an example of a partial metric space which is a continuous dcpo but its bicompletion and Smyth completion are not continuous posets, and an example of a continuous poset whose spherical completion is not a continuous poset.Abstract:
Models in quantum computing rely on transformations of states of
quantum memory. We study mathematical aspects of a model proposed
by Wu in which the memory state is changed via scattering of incoming
particles. This operation causes the memory content to deviate from a
pure state, i.e. induces impurity. For nonrelativistic particles
scattered
from a two-state memory and sufficiently general interaction potentials
in 1 + 1 dimensions, we express impurity in terms of quaternionic
commutators.
I this context, pure memory states correspond to null hyperbolic
quaternions. In the case of point interactions, the scattering process
amounts to appropriate rotations of quaternions in the frequency domain.
This point of view complements a previous analysis by Margetis and Myers
(2006 J. Phys. A 39 11567-11581) and is in collaboration with D.
Margetis.
Abstract: See pdf file.
Please direct questions or comments regarding the colloquium to Frederic Mynard