**Seminars and Colloquiums**

for the week of November 30, 2015

for the week of November 30, 2015

*SPEAKER:*

Elise Weir, UTK, Monday

Antoine Choffrut, Warwick, UK, Wednesday

*TEA TIME*

3:00 – 3:30 pm, Ayres 401

Monday, Tuesday, & Wednesday

Hosted by Alan and Chris

3:00 – 3:30 pm, Ayres 401

Monday, Tuesday, & Wednesday

Hosted by Alan and Chris

**Monday, November 30th **

GEOMETRY AND TOPOLOGY SEMINAR

TITLE: Complex Hyperbolic Geometry

SPEAKER: Elise Weir, UTK

TIME: 2:30-3:30

ROOM: Ayres 114

Real hyperbolic spaces are a familiar concept for many, but how can those ideas be extended into a complex vector space? We'll begin by reviewing some models for real hyperbolic space, and then define complex hyperbolic space in terms of non-degenerate Hermitian forms. We'll see how different choices of Hermitian forms correspond to different analogues of the real models, and discuss a proof by D.B.A. Epstein that uses these forms to give an explicit formula for distance in complex hyperbolic space.

**Wednesday December 2nd **

JOINT SEMINAR

DIFFERENTIAL EQUATIONS SEMINAR

& COMPUTATIONAL & APPLIED MATHEMATICS

TITLE: Rayleigh-B´enard Convection: physically relevant a priori estimates

SPEAKER: Antoine Choffrut, Warwick, UK

TIME: 3:30-4:30 pm

ROOM: Ayres 112

A fluid contained between two horizontal plates is heated from below and cooled from above. Heat transfer is effected via two mechanisms: (1) thermal conduction, at the microscopic level; and (2) thermal convection, where lighter, warmer particles carry their internal energy to the top. On the other hand, fluid motion is resisted by inner friction due to viscosity.

The governing equations are those of the Boussinesq approximation. The average upward heat flux relative to pure conduction is measured by the Nusselt number (Nu). The temperature gradient is measured by the Rayleigh number (Ra). The relative strength of viscosity over inertia is measured by the Prandtl number (Pr).

In this talk I will present near optimal scaling laws for Nu as a function of Ra for two regimes of Pr, whereas previous work, pioneered by Constantin and Doering, with contributions from many others, assumed infinite Pr. The proof relies on maximal regularity estimates for the (linear) Stokes system in L1- and L1-type spaces, the latter with a borderline failing Muckenhoupt weight.

This is joint work with Camilla Nobili and Felix Otto.

*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 colloquium AT math DOT utk DOT edu *