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Seminars and Colloquiums
for the week of October 15, 2018


Mat Langford, University of Tennessee
Remus Nicoara, University of Tennessee
Simon Praetorius, Technische Universität Dresden
Marco Mendez, University of Chicago
Shelby Scott, University of Tennessee (EEB graduate student)
Chris Anderson, University of California, Los Angeles

3:00 PM – 3:30 PM
Monday, Tuesday, & Wednesday
Rooms: Ayres 404 (Monday), Ayres 401 (Tuesday & Wednesday)
Hosted by: Anna Sisk & Wencel Valega
Topics: Pros and cons of academia and industry positions/how to decide; tips for job searching; internships and summer opportunities.

Tuesday, 10/16

TITLE: Colding and Minicozzi paper I section II: Estimates for stable annuli with slits
SPEAKER: Mat Langford, University of Tennessee
TIME: 4:00 PM-5:30 PM
ROOM: Ayres 121
This and next week, we will show that certain stable minimal disks which are multivalued graphs can be extended 'horizontally'.

Wednesday, 10/17

TITLE: Spin model commuting squares and intermediate subfactors, part II.
SPEAKER: Remus Nicoara, University of Tennessee
TIME: 2:30 PM-3:20 PM
ROOM: Ayres 113
We discuss a class of spin model commuting squares which yield subfactors (inclusions of von Neumann algebras) with intermediate subfactors.

TITLE: From individual motion to collective cell migration
SPEAKER: Simon Praetorius, Technische Universität Dresden
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 113
The motion of living cells plays an important role in many important processes, like in wound healing, as part of the immune system, and in tissue development. Modeling the migration of cells thereby involves the study of the motion of a single cell and on collective behavior of many cells.

Various different mechanisms have been proposed and studied to describe motility of a single cell in different situations. We study the motility mechanisms of eukaryotic cells by polymerization and depolymerization of and contractile stresses between cytoskeletal actin filaments. A (hydrodynamic) active polar gel model is presented with the polarity as mean alignment of actin fibres in the cytoskeleton. Modeling the fibre network as a field of polar liquid crystals, i.e. rod-like particles with polar order, a spontaneous symmetry breaking in the alignment leads to cell motility. Shape changes and an internal flow of actin push the cell forward. The model combines a Helfrich-Navier-Stokes model with surface tension and an active polar gel theory in a diffuse-interface setting.

While the mechanics, dynamics, and motility of individual cells have received considerable attention, the understanding of collective behavior of cells, the interaction and influence of their motion, remains challenging. We consider a continuum model for collective cell movement. Each cell is modeled by a phase field, driven by an active polar gel model and the cells interact via steric interactions. The collision dynamics of two cells is studied in detail and the collective behavior of about 1000 cells in a crowded environment is considered. This process is computational challenging due to the high number of individuals, their local resolution and individual motion driven by principles shown before. This leads to a highly parallelized multi-phase field model.

Figure 1: Interaction of 48 cells in a periodic environment. Shown is the cell membrane as contour plot, with direction of motion indicated by an arrow. Deformation and cell-cell interaction may eventually lead to a collective motion in a common direction.

Thursday, 10/18

TITLE: Old analogies in the Calculus of Variations - The Brachistochrone
SPEAKER: Marco Mendez, University of Chicago
TIME: 3:40 PM-4:35 PM
ROOM: Ayres 405
I will tell the story of the Brachistochrone problem. This is one of the oldest variational problems and can be solved only using elementary calculus. I will present in detail Johann Bernoulli's clever solution, which is based on Fermat's principle and a variational analogy between mechanics and optics. If time permits, I will briefly discuss a more recent analogy between the theory of phase transitions and minimal hypersurfaces, which will be the subject of my talk in the Geometric Analysis Seminar.

TITLE: The Allen-Cahn equation and the theory of minimal surfaces
SPEAKER: Marco Mendez, University of Chicago
TIME: 5:00 PM-6:00 PM (note change)
ROOM: Ayres 121
The Allen-Cahn equation behaves as a desingularization of the area functional. This allows for a purely PDE approach to the construction of minimal hypersurfaces in closed Riemannian manifolds. After presenting an overview of the subject, I will discuss recent results regarding a Weyl Law and its consequences for the density of minimal hypersurfaces in generic metrics. This is joint work with P. Gaspar.

Friday, 10/19

TITLE: Handguns and Hotspots: Spatio-Temporal Modeling of Gun Crime in Chicago, IL
SPEAKER: Shelby Scott, University of Tennessee (EEB graduate student)
TIME: 10:10 AM-11:00 AM
ROOM: Ayres 401

TITLE: The Solution of Schroedinger's Equation and Quantum Dots
SPEAKER: Chris Anderson, University of California, Los Angeles
TIME: 3:35 PM-4:35 PM
ROOM: Ayres 405
There's been increased interest in the development of devices that exploit quantum mechanical behavior, e.g. devices for quantum sensors, devices for quantum cryptography, and controllable gates for quantum computers. The need for computational simulation to support this development has led to the need to solve a myriad of mathematical problems associated with the creation of approximate solutions of the N-particle Schroedinger equation. In this talk I will outline a general algorithmic strategy that's used to create approximate solutions of Schroedinger's equation and discuss the solution of some of the mathematical problems that arise. The example of computing the solution of Schroedinger's equation to model the behavior of electrostatially confined quantum dots will be used as the context for the topics discussed. This talk is intended for a general mathematics audience, and should be accessible to any advanced undergraduate or beginning graduate student.

If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar.

If you have questions, or a date you would like to confirm, please contact mlangfo5 AT utk DOT edu

Past notices:

Oct. 8, 2018

Oct. 1, 2018

Sept. 24, 2018

Sept. 17, 2018

Sept. 10, 2018

Sept. 3, 2018

Aug. 27, 2018



last updated: October 2018

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