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Seminars and Colloquiums
for the week of November 2, 2015


Jerzy Dydak, UTK, Monday
Josephine Yu, Georgia Tech, Monday
Kody J.H. Law, ORNL, Tuesday
Kevin Sonnanburg, UTK, Wednesday
Brian Allen, UTK, Thursday
Kokum Rekha DeSilva, UTK, Thursday
Remus Nicoara, UTK, Thursday
Christopher Peterson, UTK, Friday
Jochen Denzler, UTK, Friday

Tea Time, Monday - Wednesday, 3:00 pm
Cancelled for this week

Monday, November 2nd

TITLE: Quest to create happy endings for the Greek tragedy known as teaching geometry
SPEAKER: Jerzy Dydak, UTK
TIME: 2:30-3:20pm
ROOM: Ayres 114
The aim of the talk is to outline a new axiomatization of planar geometry by reinterpreting the original axioms of Euclid. The basic concept is still that of a line segment but its equivalent notion of betweenness is viewed as a topological, not a metric concept. That leads quickly to the notion of connectedness without any need to dwell on the definition of topology. In our approach line segments must be connected. Lines and planes are unified via the concept of separation: lines are separated into two components by each point, planes contain lines that separate them into two components as well. We add a subgroup of bijections preserving line segments and establishing unique isomorphism of basic geometrical sets, and the axiomatic structure is complete. Of fundamental importance is the Fixed Point Theorem that allows for creation of the concepts of length and congruency of line segments.

The resulting structure is much more in sync with modern science than other axiomatic approaches to planar geometry. For instance, it leads naturally to the Erlangen Program in geometry. Our Conditions of Homogeneity and Rigidity have two interpretations. In physics, they correspond to the basic tenet that independent observers should arrive at the same measurement and are related to boosts in special relativity. In geometry, they mean uniqueness of congruence for certain geometrical figures.
Euclid implicitly assumes the concepts of length and angle measure in his axioms. Our approach is to let both of them emerge from axioms. Euclid obfuscates the fact that to compare lengths of line segments one needs rigid motions beforehand. Our system of axioms of planar geometry rectifies that defect of all current axiomatic approaches to planar geometry (of Hilbert and Tarski).

Another thread of the talk is the introduction of boundary at infinity, an important concept of modern mathematics, and linking of Pasch Axiom to endowing boundaries at infinity with a natural relation of betweenness. That way spherical geometry can be viewed as geometry of boundaries at infinity.

TITLE: Generic Sparse Polynomials
SPEAKER: Josephine Yu, Georgia Tech
TIME: 3:35-4:25
ROOM: Ayres 114
Let us fix the monomial supports of a few multivariate polynomials and choose coefficients "randomly" from an algebraically closed field. Do these polynomials generate a prime ideal for "most" choices of coefficients? We will give a complete combinatorial characterization of the supports for which the answer is yes.

Tuesday November 3rd

TITLE: Multilevel sequential Monte Carlo samplers
TIME: 2:10 – 3:10pm
ROOM: Ayres 405
Partial differential equations (PDEs) modeling physical phenomena are often defined only up to some unknown parameters, which may be high-dimensional or even function-valued. Given some observed data, one would like to invert for those parameters. It is natural to formulate the inverse problem probabilistically. Due to the cost of solving the PDE and the high-dimensional space, or in principle function-space, over which the probability distribution is defined, this is a computationally challenging problem.

This talk will review the probabilistic formulation of the inverse problem, the sequential Monte Carlo (SMC) sampling framework, and the standard multilevel Monte Carlo (MLMC) framework. These ideas will coalesce into the MLSMC sampling algorithm for Bayesian inverse problems. A numerical example of permeability inversion through an elliptic PDE given observations of pressure will illustrate the theoretical results.

Wednesday November 4th

SPEAKER: Kevin Sonnanburg, UTK
TIME: 9:05-9:55am
LOCATION: Ayres 405
I would like to start with some research I did in medical imaging in undergrad that got me interested in geometry.  This interest has evolved into work in mean curvature flow, and now relies heavily on theory from dynamical systems.  I will discuss my research, but also I will leave room for discussion since so many topics are involved.  Additionally, I plan to share some recent new ideas for applications.

Thursday November 5th

TITLE: Inverse Mean Curvature Flow of Graphs over Cylinders and Cigars
SPEAKER: Brian Allen, UTK
TIME: 2:10–3:25pm
ROOM: Ayres 114
Inverse Mean Curvature Flow (IMCF) is an important geometric evolution equation that has been used to prove interesting geometric inequalities, most notably the Riemannian Penrose Inequality from General Relativity. In this talk we will discuss my result of long time existence of IMCF for bounded graphs over cylinders and cigars and mention the asymptotic properties we expect for the flow.

TITLE: Investigating advection control in competitive PDE systems and environmental transmission in Johne’s Disease ODE models
SPEAKER: Kokum Rekha DeSilva, UTK
TIME: 3:30 pm
ROOM: Ayres 112
Her committee consists of Professors: Lenhart (Chair), Day, Phan, and Eda (Forestry, Wildlife & Fisheries).

TITLE: Hadamard matrices, gossip, music and goats
SPEAKER: Remus Nicoara, UTK
TIME: 3:40pm - 4:30pm
ROOM: Ayres 405
Do you want to build a concert hall with great acoustics? Spread gossip in your own error-correcting code? Quantum-teleport your goats to a different cabbage patch? The solutions to these problems, and many others, involve Hadamard matrices.

Friday November 6th

SPEAKER: Christopher Peterson, UTK
TIME: 10:10-11am
ROOM: Ayres 405

Cancelled this week.

TITLE: Asymptotics of Fast Diffusion by Dynamical Systems Methods
SPEAKER: Jochen Denzler
TIME: 3:00 snacks, 3:35 -4:25pm
ROOM: Ayres 405
The asymptotic analysis of the fast diffusion equation to higher order in time leads to an interesting interplay between spatial decay and convergence rates to the self-similar solution. At the same time, a non-euclidean Riemannian metric on R^n determines the proper scale of weights in the function spaces that establishes uniformity of estimates in an inherently non-uniformly parabolic equation.

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



last updated: May 2018

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