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Seminar on Partial Differential Equations
Spring 2024
Friday at 2:00 PM in PGH 646
| February 2 |
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| February 9 |
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| February 16 |
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| February 23 |
Dr. Soumia Touhami (Mid Sweden University)
Canceled
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| March 1 |
Dr. Alexandria Volkening (Purdue University)
Title: Modeling and topological data analysis of biological pattern formation
Abstract:
Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Here I will focus on the specific example of pattern formation in zebrafish, which are named for the dark and light stripes that appear on their bodies and fins. Mutant zebrafish, on the other hand, feature different skin patterns, including spots and labyrinth curves. All of these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells. The longterm motivation for my work is to help identify the alterations to cell interactions that lead to mutant patterns. Toward this goal, I will overview our work using agent-based models to simulate pattern formation and make experimentally testable predictions. Because stochastic, microscopic models are not analytically tractable using traditional techniques, I will discuss the topological methods that we have developed to quantify cell-based patterns and describe ongoing work on quantitatively linking agent-based and continuum (integro-differential equation) models.
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| March 8 |
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| March 15 |
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| March 22 |
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| March 29 |
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| April 5 |
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| April 12 |
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| April 19 |
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| April 26 |
Dr. Soumia Touhami (Mid Sweden University)
Title: Functional Characterizations of Trace Spaces in Lipschitz Domains
Abstract:
Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces H^s(\partial \Omega) involving a family of positive self- adjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary \partial \Omega of a bounded Lipschitz domain \Omega \subset R^d and applying Moore-Penrose pseudoinverse properties together with a special inner product on H^1(\Omega). We also establish generalized results of the Moore- Penrose pseudoinverse.
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Small changes/shifts in the dates may
be possible.
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