Standard graded Hilbert functions and generic initial ideals

Speaker: 

Kristina Crona

Institution: 

UCI

Time: 

Tuesday, October 26, 2004 - 2:00pm

Location: 

MSTB 254

Macaulay's Theorem and theorems by Gotzmann will be discussed in this introduction to standard graded Hilbert functions. My presentation will rely on Gr\"obner bases theory, in particular generic initial ideals and lexsegment ideals. The talk requires no special background, and may be useful for my next talk about multigraded Hilbert functions.

Light transport in two-layer tissues

Speaker: 

Prof. Arnold Kim

Institution: 

UC Merced

Time: 

Monday, October 18, 2004 - 4:00pm

Location: 

MSTB 254

Light propagation in tissues is governed by the theory of radiative transport. The radiative transport equation takes into account absorption and scattering due to inhomogeneities. A two-layer medium is a useful model for tissues because it accounts for the differences in optical properties between the superficial and deep regions of tissues. We are interested in probing only the superficial layer because most pre-cancerous tissues develop there. To do this we introduce an alternate boundary condition that allows for the removal of the bottom layer from the problem. For the case when the top layer is thin, we compute an asymptotic solution. We validate our results by comparing them with numerical solutions.

Pages

Subscribe to UCI Mathematics RSS