**Seminars and Colloquiums**

for the week of October 15, 2018

for the week of October 15, 2018

*SPEAKERS*

** Tuesday**

Mat Langford, University of Tennessee

**Wednesday**

Remus Nicoara, University of Tennessee

Simon Praetorius, Technische Universität Dresden

**Thursday**

Marco Mendez, University of Chicago

**Friday**

Shelby Scott, University of Tennessee (EEB graduate student)

Chris Anderson, University of California, Los Angeles

**TEA TIME**

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**

**MINIMAL SURFACES SEMINAR**

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**

**ANALYSIS SEMINAR**

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.

**COMPUTATIONAL and APPLIED MATHEMATICS (CAM) SEMINAR**

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**

**JR. COLLOQUIUM**

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.

**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**

**MATH BIOLOGY SEMINAR**

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

**COLLOQUIUM**

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:**