# Number Theory Seminars 2/24

Visiting mathematicians from UC San Diego, Alina Bucur and Kiran Kedlaya, will give two number theory talks on Thursday, February 24 in Keller 301.

Schedule:
3-3:45 PM Kiran Kedlaya
The relative class number one problem for function fieldsAbstract: Gauss conjectured that there are nine imaginary quadratic fields of class number 1; this was resolved in the 20th century by work of Baker, Heegner, and Stark. In between, Artin had introduced the analogy between number fields and function fields, the latter being finite extensions of the field of rational functions over a finite field. In this realm, the class number 1 problem admits multiple analogues; we recall some of these, one of which was “resolved” in 1975 and then falsified (and corrected) in 2014, and another one of which is a brand-new theorem in which computer calculations (in SageMath and Magma) play a pivotal role.

3:45-4:15 PM
Q&A, break, refreshments

4:15-5 PM Alina Bucur
Counting points on curves over finite fields

Abstract: A curve is a one dimensional space cut out by polynomial equations. In particular, one can consider curves over finite fields, which means the polynomial equations should have coefficients in some finite field and that points on the curve are given by values of the variables in the finite field that satisfy the given polynomials. A basic question is how many points such a curve has, and for a family of curves one can study the distribution of this statistic. We will give concrete examples of families in which this distribution is known or predicted, and give a sense of the different kinds of mathematics that are used to study different families. This is joint work with Chantal David, Brooke Feigon, Kiran S. Kedlaya, and Matilde Lalin.

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.

The local logic seminar is meeting weekly in-person in Fall 2021 after being on pandemic hiatus during the academic year Fall 2020 – Spring 2021.

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
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

Future offerings:

Semester Course number Course title Instructor
Spring 2022 MATH 657 Computability and Complexity Kjos-Hanssen
Fall 2022 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:

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

Future offerings:

Semester Course number Course title Instructor
Spring 2022 MATH 455 Mathematical Logic Ross

#### Faculty teaching in the program

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

# Jovovic Grant Addresses Shortage of Mathematics Teachers

Assistant Specialist, and Director of Undergraduate Studies, Mirjana Jovovic is the co-principal investigator on a new NSF grant,

Capacity Building to Address the Shortage of Mathematics Teachers in Hawaii

in the Robert Noyce Teacher Scholarship Program.