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
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 National Science Foundation (NSF) has selected UH Math Professor Michelle Manes as a Program Director in the Division of Mathematical Sciences (DMS). She will work with a team to make funding recommendations in the areas of Algebra and Number Theory, and she will serve on several other special programs at NSF.
From the NSF website: “DMS supports research in mathematics and statistics, training through research involvement of the next generation of mathematical scientists, conferences and workshops, and a portfolio of national mathematical sciences research institutes.”
Manes’s appointment began in September, 2018 and may be renewed for a second year. During her appointment, she will be living in Washington, DC.
Professor Ruth Haas is the President-Elect of, and in the inaugural class of Fellows of, the Association for Women in Mathematics.
For more, please see her recent interview by the Notices of the AMS.
Dr. Piper Harron is now blogging for the American Mathematical Society. The AMS has several blogs of interest to mathematicians, including graduate students (AMS Grad Student blog) and early career faculty (PhD + epsilon blog). A full roundup of AMS blogs can be found here: http://blogs.ams.org/
The newest AMS blog is called inclusion / exclusion; it’s a blog about underrepresented groups in mathematics. The first blog post by Adriana Salerno introduces the blog and the editing team: http://blogs.ams.org/inclusionexclusion/2017/02/06/inclusionexclusion-principle/. Dr. Harron’s first post just went up: http://blogs.ams.org/inclusionexclusion/2017/02/22/hands-off-my-confidence/.
University of Hawaiʻi at Mānoa
Visiting mathematicians from UC San Diego, Alina Bucur and Kiran Kedlaya, will give two number theory talks on Thursday, February 24 in Keller 301.