Category Archives: Research

Screenshot 2023-10-30 at 10.56.11 AM

Nasrin’s NIH grant

press-release 2023ver2Assistant Professor Farzana Nasrin has collaborated with the School of Life Sciences in a project to investigate genetic and metabolic components that may be related to repetitive behaviors that are common in people with autism. Their project received a five-year, $1.5M R01 National Institutes of Health/National Institute of General Medical Sciences grant.

This project will analyze complex sets of data (20,000 genes, 300 serum metabolites, and 1,000 gut microorganisms, as well as 3D-imaging of active neurons in fish brains). The team assumes that it is fair to use the fish project to predict the possible genetic and molecular pathways because humans and fish share more than 90% of gene and molecular pathways. These high dimensional data sets are challenging to visualize and analyze. However, by integrating topological mapping and statistical machine learning algorithms, the researchers are developing effective and flexible methods to analyze them with a limited amount of training samples.

More at UH News.

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Graduate & Undergraduate programs in mathematical logic

The Department of Mathematics at University of Hawaii at Manoa has long had an informal graduate program in logic, lattice theory, and universal algebra (People, Courses, Description) going back to Alfred Tarski’s 1963 student William Hanf.

During 2022-2023 the logic seminar had talks by outside speakers from Chiba, Yamaguchi, Wisconsin, and Belgrade.

We are offering the following course rotation (courses mostly repeating after two years):

Graduate courses

Past offerings
Semester Course number Course title Instructor
Spring 2016 MATH 649 Applied Model Theory Ross
Fall 2016 MATH 654 Graduate Introduction to Logic Beros
Spring 2017 MATH 657 Computability and Complexity Khan
Spring 2018 MATH 649 Applied Model Theory Ross
Fall 2018 MATH 654 Graduate Introduction to Logic Kjos-Hanssen
Spring 2019 MATH 655 Set theory Williams
Spring 2020 MATH 657 Computability and Complexity Kjos-Hanssen
Fall 2020 MATH 654 Graduate Introduction to Logic Kjos-Hanssen
Spring 2021 MATH 649 Applied model theory Ross
Spring 2022 MATH 657 Computability and Complexity Kjos-Hanssen
Fall 2022 MATH 654 Graduate Introduction to Logic Kjos-Hanssen
Spring 2023 MATH 649B Applied model theory Ross

Future offerings:

Semester Course number Course title Instructor
Spring 2024 MATH 657 Computability and Complexity Kjos-Hanssen
Fall 2024 MATH 654 Graduate Introduction to Logic TBA

It is also recommended that students familiarize themselves with undergraduate level logic, which is offered on the following schedule:

Undergraduate courses

Past offerings
Semester Course number Course title Instructor
Fall 2012 MATH 454 Axiomatic Set Theory Kjos-Hanssen
Spring 2013 MATH 455 Mathematical Logic Kjos-Hanssen
Fall 2014 MATH 454 Axiomatic Set Theory Ross
Spring 2015 MATH 455 Mathematical Logic Khan
Spring 2016 MATH 454 Axiomatic Set Theory Khan
Spring 2017 MATH 455 Mathematical Logic Ross
Spring 2018 MATH 455 Mathematical Logic Khan
Fall 2019 MATH 454 Axiomatic Set Theory Williams
Spring 2020 MATH 455 Mathematical Logic Williams
Fall 2021 MATH 454 Axiomatic Set Theory Kjos-Hanssen
Spring 2022 MATH 455 Mathematical Logic Ross

Future offerings:

Semester Course number Course title Instructor
Fall 2023 MATH 455 Mathematical Logic Kjos-Hanssen

Faculty teaching in the program

David A. Ross, Professor
Bjørn Kjos-Hanssen, Professor

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YashLodha_scilog

Group Actions on 1-Manifolds

We are proud to announce that Assistant Professor Yash Lodha has been awarded a prestigious CAREER grant from the National Science Foundation to work on Algebraic, Analytic, and Dynamical Properties of Group Actions on 1-Manifolds and Related Spaces.

From the Award abstract:

A group is a mathematical abstraction of symmetries of a physical object or a theoretical space. Groups are fundamental objects in mathematics that also emerge in various applications such as in computer science and physics. The algebraic notion of a group associates to a set a binary operation, like multiplication, which satisfies a list of axioms. Groups emerge naturally as symmetries of various types of concrete or abstract spaces in mathematics. There is an intricate relationship between the geometric properties of these spaces and the algebraic properties of their groups of symmetries. The PI will continue his investigation of the landscape of infinite groups that emerge as symmetries of the most natural spaces in mathematics, the circle and the real line. The PI will organize two research workshops aimed at graduate students, and two research experiences programs for undergraduates. These shall be aimed at training a diverse body of students to become future leaders in mathematics. These activities will incorporate computational methods into the students’ mathematical exploration of the landscape of infinite groups.

More at UH News.

Another active CAREER award in our department is that of Associate Professor Elizabeth Gross.