Category Archives: People

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Alumnae update

It is time for a quick update on some graduates.

MA program

  • Malihe Alikhani is now an Assistant Professor at University of Pittsburgh where she among other things advises a team of doctoral students that is one of 10 finalists in Amazon’s second Alexa Prize TaskBot Challenge.
  • Corrisa Heyes is now a PhD Candidate at UHM in Mechanical Engineering, and has been awarded the Department of Defense Science, Mathematics, and Research for Transformation Scholarship.
Press release from the SMART Scholarship program

This award provides students with full tuition for up to five years, mentorship, summer internships, a stipend and full-time employment with the Department of Defense after graduation. This unique opportunity offers students hands-on experience at one of over 200 innovative laboratories across the Army, Navy, Air Force and larger Department of Defense.
During summer internships, SMART scholars work directly with an experienced mentor, gaining valuable technical skills. After graduation Heyes will work at Naval Surface Warfare Center – Carderock Division in West Bethesda, MD.

Heyes is currently studying Mechanical Engineering, with a focus in Materials Science. Heyes said, “Sponsorship as a SMART scholar is the opportunity of a lifetime to leverage my education and experience with colleagues and mentors who work on the cutting edge of advancement in my field” about the award.
The Department of Defense is committed to developing the Nation’s STEM talent and is the largest employer of federal scientists and engineers with nearly 150,000 civilian STEM employees working across the Department. DoD STEM activities support this mission by providing authentic learning experiences through a variety of education and outreach initiatives, such as the SMART Scholarship-for-Service Program. For over a decade, SMART has trained a highly skilled STEM workforce that competes with the evolving trends of industry to support the next generation of science and technology for our nation.
For more information on the SMART Program or to learn how students can apply, please visit www.smartscholarship.org. The application is open annually from August through December.

Math major

Winnie Lau has been accepted to an REU (research experience undergraduates) in computational chemistry with Prof. Xiaosong Li at University of Washington.

Aloha Winnie!winnielau.min

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In memoriam William Lampe

Emeritus faculty member William (Bill) Austyn Lampe died on January 8th 2023, surrounded by family.

Except for a one year post doc at Colorado and a two year stay at the Institute for Advanced Study, he spent his whole career at UH. He came here in 1972, was chair 1983-1986, and retired in 2011.
He will be missed.

Mathematical research

A major theme of Bill’s work was congruence lattice representations, that is, the problem of finding an algebra whose family of congruence relations is isomorphic to a given lattice. For example, the three-element lattice $\mathbf{0}<\mathbf{1}<\mathbf{2}$ arises as the congruence lattice of the symmetric group $S_3$.

Grätzer and Schmidt in 1963 bridged lattice theory and universal algebra by showing that every compactly generated lattice has such a representation. Simplifications were found by Lampe (1973) and Pudlak (1976). They involved what was affectionally known as the sack-of-potatoes construction, pictured above. Such simplifications turned out to lead to applications in other mathematical fields. Bill used his methods to develop what have become known as the Zipper Lemma and the Term Condition.

As well as these positive results, he had several striking negative results. For example,
a longstanding conjecture was that every algebraic lattice could be represented as the congruence lattice of an algebra having only one operation. Bill showed that there are lattices such that the algebra must have at least $\kappa$ many operations, for any cardinal $\kappa$.

In Bill’s last paper, The strength of the Grätzer-Schmidt theorem (with Brodhead, Khan, Kjos-Hanssen, Nguyen and Shore, 2016) the GS theorem is studied in the context of reverse mathematics. As a follow-up, Jack Yoon showed in his 2020 dissertation that surprisingly the Grätzer-Schmidt theorem is provable in the system Arithmetic Transfinite Recursion of reverse mathematics.

After working on many other problems in universal algebra and lattice theory through his career, Bill returned to this topic for his talk at the conference Algebra and Lattices in Hawaii in 2018, held in honor of him and his colleagues in lattice theory and universal algebra in Hawaii.

Primer 4 coauthors photo

New book on Subquasivariety Lattices

Professor Emeritus J.B. Nation, frequent visitors Kira Adaricheva and Jennifer Hyndman, and UH’s Joy Nishida have published a new book:

A Primer of Subquasivariety Lattices uniquely develops universal algebra in languages that may not contain equality.

It presents new results in representations of various types of lattices by subquasivarieties, and illustrates theory through concrete examples.

Part of the book series: Canadian Mathematical Society/CAIMS Books in Mathematics (CMS/CAIMS BM, volume 3)