Calendar

Apr
5
Wed
Colloquium: Caleb Shor (Western New England U.)
Apr 5 @ 3:30 pm – 4:30 pm

Speaker: Caleb Shor, Western New England University

Title: Characterization of free numerical semigroups

Abstract: Let $\mathbb{N}_0$ denote the set of nonnegative integers. A numerical semigroup $S$ is a subset of $\mathbb{N}_0$ that is closed under addition, contains 0, and has finite complement in $\mathbb{N}_0$. Such objects arise naturally in algebraic geometry and number theory. They’re also of interest to fans of postage stamps and chicken nuggets.

Given a set $G\subset\mathbb{N}_0$ with $\gcd(G)=1$, the set of nonnegative linear combinations of elements of $G$ is a numerical semigroup. It happens that every numerical semigroup arises this way, so we can think of numerical semigroups in terms of their generating sets. For example, if $G=\{3,5\}$, then $S=\{3x+5y : x,y\in\mathbb{N}_0\}=\mathbb{N}_0\setminus\{1,2,4,7\}$. In general, we will have $S=\mathbb{N}_0\setminus \textit{NR}(G)$, where $\textit{NR}(G)$ is the set of integers not representable in terms of $G$.

Numerous questions arise naturally. For instance, given a set $G$, what can we say about the cardinality, largest element, structure, and other associated objects and properties of $\textit{NR}(G)$? For a general set $G$, these can be difficult questions. In this talk, we will consider “free” numerical semigroups, which are generated by sets $G$ with certain smoothness conditions. In particular, we will see an identity which completely characterizes $\textit{NR}(G)$, and we will use that to answer some of the questions mentioned above.

Apr
6
Thu
Colloquium: Vakhtang Putkaradze (U. Alberta) @ Keller 401
Apr 6 @ 3:00 pm – 4:00 pm

Speaker: Vakhtang Putkaradze
Centennial Professor
Department of Mathematics and Statistics
Department of Chemical Engineering
PIMS Site Director at the University of Alberta

Title: Dynamics and control of flexible solar towers
Abstract:
The use of solar chimneys for energy production has been suggested more than 100 years ago. Unfortunately, this technology has not been realized on a commercial scale, in large part due to the high cost of erecting tall towers using traditional methods of construction. Recent works have suggested a radical decrease in tower cost by using an inflatable self-supported tower consisting of stacked toroidal bladders. While the statics deflections of such towers under constant wind have been investigated before, the key for further development of this technology lies in the analysis of dynamics, which is the main point of this talk. Using Lagrangian reduction by symmetry, we develop a fully three dimensional theory of motion for such towers and study the tower’s stability and dynamics. Next, we derive a geometric theory of optimal control for the tower dynamics using variable pressure inside the bladders, and perform detailed analytical and numerical studies of the control in two dimensions. Finally, we report on the results of experiments demonstrating the remarkable stability of the tower in real-life conditions, showing good agreement with theoretical results. This work has been supported by NSERC and the University of Alberta.

Apr
7
Fri
Logic seminar: Jack Yoon @ Keller 404
Apr 7 @ 2:30 pm – 3:20 pm

The Logic Seminar will meet again this Friday, usual place and time. The speaker will be Jack Yoon.

Title: Proof Mining

Abstract: Proof mining (proof unwinding) is a technique used to extract
constructive information from seemingly non-constructive proofs. We
discuss the idea behind the topic and describe the foundations which
form the basis for proof mining.

Colloquium: Pamela Harris (Williams)
Apr 7 @ 3:30 pm – 4:30 pm
Apr
13
Thu
Colloquium: Alexander Volberg (Michigan State) @ Keller 404
Apr 13 @ 3:30 pm – 4:30 pm

Title: Non-homogeneous harmonic analysis, Geometric Measure Theory and fine structures of harmonic measure

Abstract: One of the goals of harmonies analysis is to study singular integrals. Singular integrals are ubiquitous objects in PDE and in Mathematical Physics, and as it turned out recently, play an important part in Geometric Measure Theory. They have various degrees of singularity, and the simplest ones are called Calder’on–Zygmund operators. Their theory was completed in the 50′s by Zygmund and Calder’on. Or it seemed like that. The last 20 years saw the need to consider CZ operators in

very bad environment, so kernels are still very good, but the ambient set has no regularity whatsoever.

Initially such situations appeared from the wish to solve some outstanding problems in complex analysis: such as Painlev’e’s, Ahlfors’, Denjoy’s and Vitushkin’s problems.

But recently it turned out that the non-homogeneous harmonic analysis (=the analysis of CZ operators on very bad sets and measures) is also very fruitful in the part of Geometric Measure Theory that deals with rectifiability, and also helps a lot to understand the geometry of harmonic measure. The research on the geometric properties of harmonic measures was pioneered in the U. of M. in the 60-70′s by George Piranian, and came to fruition in the later works (80-90′s) by Lennart Carleson, Nikolai Makarov, Jean Bourgain, Peter Jones and Tom Wolff. But most of the results concerned the structure of harmonic measure of planar domains. As an example of the use of non-homogeneous harmonic analysis, we will show how it allows us to understand very fine property of harmonic measure of any domain in any dimension.

Apr
17
Mon
Analysis Qualifying Exam
Apr 17 @ 9:00 am – 1:00 pm
Apr
18
Tue
MFC Seminar: The Joy of FP in Haskell @ Keller 401
Apr 18 @ 3:00 pm – 4:15 pm

Title: The Joy of Functional Programming in Haskell

Speaker: Jake Fennick

Time: 3pm Tuesday April 18, 2017

Location: Keller 401

Abstract:

The goal of this talk is to convey to you the experience of pure joy
and excitement when using Haskell, and to help you actually get
started programming in Haskell. After a basic introduction to the
language, we will cover

1. The development environment and getting set up
2. More advanced language features
3. Some mathematical patterns and functional programming idioms
4. Lots of fancy demos such as plotting/visualization, LaTeX, algorithmic music generation, high performance computing, etc.
5. A little bit of theory

This will be a coding talk, so we will primarily be walking through
code and actually getting set up. The code (including installation
scripts) is at https://github.com/TypeFunc/uh-mfc I hope to cover a
lot of material, so I encourage you to check it out but it isn’t
strictly necessary.

Apr
21
Fri
Algebra Comprehensive Exam
Apr 21 @ 9:00 am – 1:00 pm