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## Seminars, Colloquia, and Conferences
Calendars |
## Seminars, Colloquia, and Conferences## Colloquia## Fall 2019September 13, 2019Jehanzeb Chaudhry, University of New Mexico (Host: James Adler) Time: 3:00pmLocation: Bromfield-Pearson 101Reception: 4:00pmTitle: Efficient Distribution Estimation and Uncertainty
Quantification for Elliptic Problems on Domains with Stochastic
BoundariesAbstract: We study the problem of uncertainty quantification for the
numerical solution of elliptic partial differential equation
boundary value problems posed on domains with stochastically varying
boundaries. We introduce simple transformations that map a family of
domains with stochastic boundaries to a fixed reference domain. We
exploit the transformations to carry out a priori and a posteriori
error analyses and to derive an efficient Monte Carlo sampling
procedure. Time permitting, we'll also talk about error estimation
for non-overlapping and overlapping domain decomposition methods.October 25, 2019Norbert Wiener Lecture, Mary Wheeler, Professor, The University of Texas at Austin Time: 3:00pmLocation: Bromfield-Pearson 101Reception: 4:00pmTitle: Phase Field Modeling for Diffusive Networks and Stimulation
in Porous MediaAbstract: The phase field method has emerged in recent years as a
powerful variational approach to model crack propagation in elastic
porous media. The most important feature of this method lies in the
fact that it can handle fracture nucleation, propagation, merging,
branching, kinking and curvilinear paths without any post-processing
or additional computations; these complex fracture paths arise
naturally as part of the numerical solution of an underlying partial
differential equation. Unlike other computational fracture mechanics
approaches, the phase field method does not require modeling the
discontinuities in the medium or tracking the crack tip Instead, it
introduces a diffusive zone that interpolates between the fracture
zone and the intact material. This smears out the sharp crack
interfaces that typically introduce singularities in the numerical
computations.In this presentation, a novel computational framework is introduced for simulation of multiphase flow, geomechanics, and fracture propagation in porous media based on Biot's model for poroelasticity. Here, state-of-the-art numerical modeling of natural and hydraulic fractures using a diffusive adaptive finite element phase field approach is employed. Since realistic porous media contains many natural fractures, not only is it important to stimulate hydraulic fractures but also to study the interaction between natural and hydraulic fractures. The enriched Galerkin finite element methods (EG) are employed to model multiphase flow with local mass conservation and dynamic mesh adaptivity. Geomechanics approximated by a continuous Galerkin finite element method is coupled to multiphase flow by applying an iteratively coupled scheme. Numerical examples are presented that demonstrate the effectiveness of this framework for different propagation scenarios, by varying the degrees of physics, and the capabilities to perform high-fidelity simulations on complex fracture networks. November 1, 2019Ming-Jun Lai, University of Georgia (Host: Xiaozhe Hu) Time: 3:00pmLocation: Bromfield-Pearson 101Reception: 4:00pmTitle: Recent Development on Matrix CompletionAbstract: Starting from the Netflex problem in 2006, I will
survey the development of matrix completion in theory and
computation. In particular, I will explain a few negative and a
positive results on when a given incomplete matrix M can be uniquely
completed. Also, I will show that the completion of a matrix is not
only dependent on the number of entries, but also dependent on the
values of entries. Next I shall explain several algorithms to
complete matrices and present a comparison of their performance.
November 12, 2019Giovanni Gallavotti, Universita` degli Studi di Roma "La Sapienza" (Host: Boris Hasselblatt) Time: 3:00pmLocation: Bromfield-Pearson 007Reception: 4:00pmTitle: Reversibility and nonequilibrium ensembles in stationary
Navier Stokes equationAbstract: In the '70s Ruelle proposed that "generically" chaotic motions would
generate a uniquely determined statistics, i.e., a unique
probability distribution on the possible states of the system,
provided initial data were chosen with probability 1 with respect to
(any) absolutely continuous measure. This means assigning to each
measurable set in phase space the frequency of visit to it, hence a
stationary probability distribution. After recalling the proposal
and pointing out that in the case of equilibrium states of isolated
mechanical systems it is a bold generalization of the ergodic
hypothesis the natural question is whether the impressive
developments that followed since Boltzmann and Maxwell in the last
century the new proposal could lead to a deeper understanding of
nonequilibrium phenomena and to a formulation of a theory of
ensembles analogous to that for the equilibrium ensembles (e.g.,
canonical or microcanonical ensembles) to describe the stationary
states out of equilibrium, which led and still leads also to
impressive mathematical results. Since Ruelle's initial motivation
was turbulence theory it seems appropriate here to analyze the
example of the Navier–Stokes equation. The Navier–Stokes equation
will be considered for an incompressible fluid in a periodic box and
subject to a stirring force constant in time and acting at large
scale (that is, at the scale of the container): the simplest
geometry. Stationary states depend (therefore) ona single parameter
R=Reynolds number=inverse of viscosity and form a family E of
probability distributions on the velocity fields. The possibility
will be discussed of existence of other equations whose stationary
states have exactly the same distributions through a homogeneization
mechanismanalogous to that for the equivalence of equilibrium states
of different ensembles (and will be proposed to be similar to the
equivalence in the thermodynamic limit which, in the Navier–Stokes
case, will correspond to the ultraviolet regularization N →
[infinity].November 22, 2019Robert Kropholler Time: 3:00pmLocation: Bromfield-Pearson 101Reception: 4:00pmTitle: Fibering and incoherence for free-by-free groups.
Abstract: We will survey recent results on virtual fibering
of groups and discuss recent work on free-by-free groups and more
generally finitely generated-by-free groups. This is joint work with
Genevieve Walsh. December 4, 2019Kelly Delp, Cornell and ICERM, (Host: Genevieve Walsh)Time: 3:00pmLocation: Bromfield-Pearson 007Reception: 4:00pmTitle: Playing with Surfaces: Spheres, Monkey Pants, and
ZippergonsAbstract: In the Spring of 2010 I began a collaboration
with William Thurston, which was inspired by clothing design, and
involved building smooth surfaces from flat, rigid material. This
project was an application of the following fact, which clothing
makers regularly apply: the Gaussian curvature of a singular surface
can be defined as a signed measure via the Gauss-Bonnet Theorem.
I'll describe an explicit example of how to make well-fitting
clothing for a sphere, based on an octahedral pattern, and report on
my current adventures in making patterns for surfaces with long
meandering seams. This talk will be accessible to a wide
mathematical audience, including undergraduates. December 10, 2019Kim Ruane, Tufts University Time: 4:00pmLocation: Nelson Auditorium (Anderson, 112)Reception: 5:00pm, Burden LoungeAbstract: I will discuss my experience teaching a math
course through the Tufts University Prison Initiative Program
(TUPIT). I taught a quantitative reasoning course at MCI Concord to
26 incarcerated men in the Spring/Summer of 2019. I will begin by
describing the structure and material of the course. I will discuss
the many pedagogical challenges I faced as a teacher in an unusual
environment with an incredibly diverse group of students. It was
simultaneously the most difficult yet rewarding challenge of my
teaching career. I will also give an overview of the activities and
mission of TUPIT because this is an amazing program. I prefer for
this to be a discussion rather than a lecture so I am happy to
answer any questions you might have.Co-Sponsored by the Center for the Enhancement of Learning and
Teaching, Tufts Department of Education, Tufts Math Society, and
Tufts Prison Initiative of Tisch College |
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