# Calendar

Jan
22
Fri
Colloquium: David R. Stoutemyer (UHM, ICS Department) @ Keller 401
Jan 22 @ 3:30 pm – 4:30 pm

Speaker: David R. Stoutemyer (UHM, ICS Department)

Title: A mathematical magic show: Demo and secrets of a prototype AskConstants website that can turn your floating-point results into the exact formulas that they want to be.”

Abstract: There are at least three existing websites that already do what the title promises:

https://isc.carma.newcastle.edu.au/

http://mrob.com/pub/ries/index.html

http://www.wolframalpha.com/

I will describe their techniques and some additional ones used in the AskConstants program. As a contest, if you email dstout at this university a floating-point constant or a float-free constant expression such as sqrt (3) / 2 + 3 * pi / 5, that I can convert to a float, then I will summarize how AskConstants and other such programs perform on that example. If you send a float, try to compute it using at least n-digit arithmetic where n is several more than the total number of digits, operators and functions in its float-free source. Good sources of ideas are calculus text definite integrals, algebraic numbers, values of special functions at rational arguments or at rational multiples of pi, constants from research literature and collections such as Steven Finch’s Encylopedia of Constants:

http://www.people.fas.harvard.edu/~sfinch/

Jan
26
Tue
Analysis Seminar – Thomas Hangelbroek @ Keller 401
Jan 26 @ 3:30 pm – 4:30 pm

Speaker: Thomas Hangelbroek, UH-Manoa

Title: Kernel approximation and PDEs (Part 1 of 2)

Abstract: Fundamental solutions to elliptic partial differential equations can serve as a useful tool for solving a variety of computational problems (e.g., data fitting, denoising, quadrature, numerical solution of differential equations). In these talks, I’ll develop some key results about meshless approximation with kernels arising as solutions to elliptic PDE — focusing primarily on analytic properties which derive directly from the differential equation, such as their approximation power and localized structure. I’ll include a number of examples on spheres, the rotation group, compact Riemannian manifolds without boundary, and Euclidean regions with boundaries.

Jan
28
Thu
Undergraduate Colloquium – Gideon Zamba (U. Iowa) @ Bilger 335
Jan 28 @ 3:00 pm – 4:00 pm

Speaker: Gideon Zamba (U. Iowa)

Title: Data-Driven Sciences: Another Way to Bring Math to the World and the World to Math

Abstract: Applied mathematics is a field of constant adaptability to the world’s contingencies. Such adaptability requires a solid training and understanding of theoretical and pure mathematical thinking—as the activity of applied thinking is vitally connected with research in pure mathematics. One such applied mathematical field is the field of statistics. As the world continues to rely more on data for decision making, statistics and associated data-driven fields have gained increased recognition. The purpose of this talk is to educate the audience about the field of statistics, about statistical involvements, and further provide examples of settings where statistical theory finds an application and where real world application calls for a new statistical development. The presentation further elaborates on Biostatistics and provides some general advice about mathematical and computational skills needed for a successful graduate degree in Biostatistics or Statistics.

The presentation is semi-technical.

Feb
2
Tue
Analysis Seminar – Thomas Hangelbroek @ Keller 401
Feb 2 @ 3:30 pm – 4:30 pm

Speaker: Thomas Hangelbroek, UH-Manoa

Title: Kernel approximation and PDEs (Part 2)

Abstract: Fundamental solutions to elliptic partial differential equations can serve as a useful tool for solving a variety of computational problems (e.g., data fitting, denoising, quadrature, numerical solution of differential equations). In these talks, I’ll develop some key results about meshless approximation with kernels arising as solutions to elliptic PDE — focusing primarily on analytic properties which derive directly from the differential equation, such as their approximation power and localized structure. I’ll include a number of examples on spheres, the rotation group, compact Riemannian manifolds without boundary, and Euclidean regions with boundaries.

Feb
4
Thu
Undergraduate Colloquium – Claude Levesque (U. Laval, Quebec) @ Bilger 335
Feb 4 @ 3:00 pm – 4:00 pm

TITLE: On Diophantine equations

ABSTRACT:

A Diophantine equation is an equation of the form F(X_1, X_2, … , X_m) = c (with a fixed c in Z) for which we look for the solutions (x_1, x_2, … , x_m) in Z^m verifying F(x_1, x_2, … , x_m) = c​. The most famous result is probably the solution of Fermat’s last theorem X^n + Y^n = Z^n found by Andrew Wiles using so-called elliptic curves. A small survey of a few results will be given and the notion of elliptic curve will be introduced. The lecture is accessible to anyone, most particularly to undergraduates.

Feb
5
Fri
Colloquium: Pamela Harris (Williams)
Feb 5 @ 3:30 pm – 4:30 pm
Feb
9
Tue
Analysis Seminar – Pat Collins @ Kelller 401
Feb 9 @ 3:30 pm – 4:30 pm

Speaker: Pat Collins, UH-Manoa
Title: Approximating with Symmetric Positive Definite Reproducing Kernels
Abstract: Symmetric positive definite kernels arise naturally as the reproducing kernels of Hilbert spaces, including certain Sobolev spaces of the form $W_{2}^{m}(Omega)$. We explore the connection between reproducing kernels and symmetric positive definite kernels, and show that the corresponding Hilbert spaces contain unique norm-minimizing solutions to interpolation problems.

Feb
10
Wed
Colloquium: David Jeffrey (U. Western Ontario)
Feb 10 @ 3:30 pm – 4:30 pm

Speaker: David Jeffrey (U. Western Ontario)

Title: Twenty years of Lambert W

Abstract: The year 2016 marks 20 years since the publication of the paper
“On the Lambert W function”. As will be pointed out, the function was
studied before 1996, but this publication has proved to be the most cited reference. The talk will review some of the decisions made in defining
the function, particularly in defining its branches.
The talk will present some of the interesting and beautiful properties
of the function, including recent work that improves on the results in
the original papers. Specifically, expressions for derivatives and
series expansions, the role of differences between branches,
the convergence of series expansions.