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Algebra and lattices in Hawaii 2018

Pictured: Pondering the smallest lattice not yet known to be a congruence lattice of any finite algebra.

Three Legends of Universal Algebra and Lattice Theory,

worked most of their careers at the University of Hawai’i at Manoa.

They all will be approximately 70 years old in May 2018, and a conference, ALH-2018, is being organized by PhD alumnus William DeMeo and others to celebrate their achievements.


Nonstandard analysis (Spring 2018)

MATH 649B Nonstandard Analysis 

Spring 2018

Day and Time: MWF 1:30-2:20, Keller 314
Professor: David Ross, PSB 319,

Nonstandard analysis is the art of making infinite sets finite by ex-
tending them.

– Michael Richter

Nonstandard analysis is an area of mathematics which lives at the interface of mathematical logic (especially model theory) and classical mathematics. Originally introduced as a way to make it possible to work with infinitesimals in a rigorous fashion, it has developed into a powerful methodology with applications in many areas of mathematics. It is especially useful when the concept of limit is central, or when an infinitary or continuous situation has a natural discrete or combinatorial intuition.

This course will be an introduction to the subject, with an eye to getting into ‘real’ applications as quickly as possible. The choice of applications will depend a bit on the background and interests of the students in the class, and might include a bit of topology, probability, measure theory, geometric groups, and additive number theory.

The course will be entirely self-contained, though mathematical training and experience at the early graduate level is assumed. In particular, some background in the applications areas won’t hurt.

The course will mainly be out of lecture notes.


Real geometry (Spring 2018)

Real geometry, from algebraic to subanalytic and beyond.
MATH 649K, Spring 2018

We will study real algebraic sets (with emphasis on geometry over algebra), semialgebraic sets (sets
defined by polynomial equalities and inequalities) , and subanalytic sets. We will consider the basic
properties of these sets, study of appropriate classes of functions on them, topology, applications.
We may get into further classes of “tame geometry” such as o-minimal geometries.
There are no particular prerequisites, just a certain level of mathematical maturity; undergraduate
mathematical analysis and topology should be enough.

Instructor: Les Wilson