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Seminar on Partial Differential Equations
Fall 2021
All talks in ZOOM, Friday at 2:00 PM
Click here for Fall 2019
| September 3 |
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| September 10 |
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| September 17 |
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| September 24 |
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| October 1 |
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| October 8 |
Dr
Benedetto Piccoli (Rutgers U)
https://piccoli.camden.rutgers.edu/
Title:
PDE models for vehicular traffic and smoothing via
autonomous vehicles
Abstract:
PDE models are used since the 60s to deal with traffic
flow. In the 90s a theory of conservation laws on graphs
was proposed for road networks, and more recently models
included ODE-PDE systems, phase transitions, and
mean-field. We present a general view on the use of PDE
models in traffic, then turn to recent applications
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| October 15 |
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| October 22 |
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| October 29 |
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| November 5 |
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| November 12 |
Dr Elena
Camacho Aguilar (Rice U)
Title:
Formalizing the Waddington landscape metaphor using
Catastrophe Theory
Abstract:
During the development of an organism, cells specialize by
transitioning between a limited set of discrete cell fates,
each defined by a distinct gene expression profile. These
transitions occur in a characteristic sequence and are
controlled by cues in the environment, such as the presence of
morphogens or signals. While quantitative models that
describe signaling pathways and gene regulatory networks in
great detail have been used to investigate cell
differentiation, these suffer from having too many parameters
to constrain with available data. Furthermore, their
complexity makes it difficult to gain intuitive understanding
or to make predictions without case-by-case simulation. A
popular and intuitive metaphor for the process of cell
differentiation is the Waddington landscape, in which a
differentiating cell is represented as a marble rolling down a
landscape of hills and valleys, encountering decision points
between different lineages, eventually settling in a valley
that defines its cell fate. We show that this metaphor can be
mathematically formalized using Catastrophe Theory, where the
landscape is defined by a potential function and the different
cell states correspond to attractors in the landscape. In this
setting, variation in the parameters of the dynamical system,
caused by changes in the signals the cell receives, alter the
landscape and give rise to bifurcations that destroy or create
attractors. Moreover, by combining this approach with
approximate Bayesian computation, we show that we can
quantitatively fit these models to large amounts of biological
data and make novel predictions. In this talk, I will show how
we took advantage of this formalism to model vulval
development in C.
elegans as
well as murine trunk development, allowing us to deeply
understand the underlying cell state transitions and to make
numerous predictions of untested experimental conditions. |
| November 19 |
Dr Konstantinos Spiliopoulos (Boston U)
http://math.bu.edu/people/kspiliop/
Title:
TBA
Abstract:
TBA |
| November 26 |
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| December 3 |
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Small changes/shifts in the dates may
be possible.
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