Category Archives: Research

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Research

Logic Seminar

The logic seminar this semester will be held Wednesdays at 2:30–3:20pm in Keller 301, starting next week. If you are interested in the seminar, please let Kameryn Williams know to be added to the mailing list.

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.

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

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
Fall 2017 course break - -
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

Future offerings:

Semester Course number Course title Instructor
Fall 2019 course break - -
Spring 2020 MATH 657 Computability and Complexity Kjos-Hanssen
Fall 2020 MATH 654 Graduate Introduction to Logic TBA
Spring 2021 MATH 649 Applied model theory Ross

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

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

Future offerings:

Semester Course number Course title Instructor
Fall 2019 MATH 454 Axiomatic Set Theory Williams

Faculty teaching in the program

David A. Ross, Professor
Bjørn Kjos-Hanssen, Professor
Kameryn Williams, Temporary Assistant Professor 2018–2021

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Research

Approximation and K-theory

Professor Rufus Willett has been awarded a grant by NSF with the title “Approximation and K-theory”. From the abstract:
Traditionally, mathematics studies precise solutions: one has for example an equation with an unknown quantity ‘x’, and wants to know precisely which value(s) of x make it true. Often in the real world, good approximate solutions will always be very close to precise solutions, and are therefore just as good for practical purposes. However, sometimes very good approximate solutions to a problem can exist without there being any actual solution at all: for example, this is a fundamental phenomenon in parts of semi-conductor physics that are closely related to the ‘K-theoretic’ methods used in this project.
OLYMPUS DIGITAL CAMERA
Conferences

HINT 2019

The Hawai’i Number Theory Conference 2019 (HINT 2019) was held in Keller (with plenary talks in Bilger Hall) during Spring break (March 18–21, 2019) and boasted 54 speakers and more than 150 participants from around the world. The five plenary speakers,
  • Jennifer Balakrishnan (Boston U.),
  • Wen-Ching Winnie Li (Penn State),
  • Joseph Silverman (Brown),
  • Kristin Lauter (Microsoft Research), and
  • Barry Mazur (Harvard))
were joined by speakers in four concurrently running special sessions:
  • Algebraic numbers and Diophantine equations,
  • Arithmetic geometry,
  • Arithmetic statistics and its environs, and
  • Modular forms and related topics.
The organizers were UH faculty members Annie Carter, Pavel Guerzhoy, and Robert Harron, as well as regular visitor Claude Levesque (U. Laval). They were joined by special session organizers Piper H (UH), Michelle Manes (UH/NSF), and Ken Ono (Emory). The NSF grant DMS-1903815 provided funding to support participants’ travel and lodging and the UH Mānoa Department of Mathematics provided some additional funds for refreshments.