Solomon Friedberg

James P. McIntyre Professor of Mathematic
Department of Mathematics                                         Boston CollegeChestnut Hill, MA 02467-3806 Email:  solomon.friedberg@bc.eduPhone:  (617) 552-3002 Office: Maloney Hall, Room 523

Biographical Information

RootsMy grandfather's education certificate (1914)

Education:

Curriculum Vitae (in pdf format) (updated December 24, 2023)   

Teaching

In Spring 2024 I am teaching Math 8845, Topics in Algebra and Number Theory.  This course will be about quaternion algebras, and will use the book by Prof. John Voight in the GTM series.  Information about the course is available on BC's Canvas learning management system. I will also work with graduate students and postdocs and with area high school math teachers.

In Fall 2023 I taught Math 8806, Algebra I.  This was the first semester graduate course in abstract algebra (and was also taken by several undergraduates).  I also worked with area high school math teachers and supervised the studies and research of several BC graduate students.

Research

Publications from 2010 on (including preprints)

My scholarship concerns automorphic forms, number theory, and representation theory.  A good part of my work has concerned the study of families of L-functions by means of analytic methods involving Dirichlet series in several complex variables.  For example, my 1989 paper with Dan Bump  and Jeff Hoffstein used these to prove a first-order-vanishing theorem for GL(2) L-functions under quadratic twists, which has applications to arithmetic.  The study of such series has proved remarkably rich. I and my collaborators now refer to this area as the study of Multiple Dirichlet Series (though it might be more accurate to tack on "Automorphic" in front).   Multiple Dirichlet series, which are related to the theory of automorphic forms on metaplectic covers of reductive groups, are not Euler products (in contrast to Langlands L-functions), but rather twisted Euler products - the interplay between the contributions from different primes is governed by n-th order residue symbols for some fixed n>1.  In many cases they have meromorphic continuation and a finite group of functional equations that is generated by reflections.  I introduced Multiple Dirichlet Series together with Ben Brubaker, Dan Bump, Gautam Chinta, Dorian Goldfeld and Jeff Hoffstein (see here for the original 1996 paper of Bump, Friedberg and Hoffstein and this volume for the 2006 article of Brubaker, Bump, Chinta, Friedberg and Hoffstein introducing Weyl Group Multiple Dirichlet Series). More recently, together with my collaborators Ben Brubaker, Dan Bump, Gautam Chinta, Jeff Hoffstein, Paul Gunnells and Lei Zhang, I have established surprising links to combinatorial representation theory, quantum groups and statistical mechanics.  In addition, I have studied other aspects of automorphic forms on covering groups, joint with David Ginzburg, worked on functionals, Iwahori Hecke algebras, and quantum groups, joint with Ben Brubaker, Valentin Buciumas and Dan Bump, introduced generalized doubling integrals and studied their applications with Yuanqing Cai, David Ginzburg and Eyal Kaplan. Presently, I am developing a new instance of the relative trace formula with  Omer Offen, working on several projects related to number theory and representation theory with NSF postdoc Claire Frechette, working on periods with David Ginzburg and Omer Offen, and working on some new projects involving number theory and string theory with several physicists.

My research is supported by NSF grant DMS-2100206. The NSF grant also supports graduate students at BC. I am thankful for this support of my research. During my career, I have benefited greatly from external support for my research from the NSF, the Simons Foundation, the NSA's Mathematical Sciences program, the US-Israel Binational Science Foundation, the Sloan Foundation, and Boston College, and I am pleased to express my appreciation of this support.

I am an organizer for BC's Number Theory & Representation Theory Seminar.

I am an editor for the Springer journal Research in Number Theory.

Ph.D. Students

I greatly enjoy having doctoral students, and welcome graduate students interested in writing a Ph.D. dissertation in automorphic forms or related areas of number theory or representation theory.  Please apply to our doctoral program if you are interested in working with me.  

Departmental Leadership

I served as Chair of the Department of Mathematics for 9 years, from June 2007 through May 2016. During my period of service, the Math Department wrote a self-study and had an external program review, started a Ph.D. program, instituted a new B.S. degree, hired superb young scholars and teachers into tenure-track and postdoctoral positions (with 4 tenure track hires winning Sloan Fellowships and 6 winning NSF Career awards so far), dramatically increased its external funding (as of May 2016 we had 17 faculty members with NSF grants in support of their research), revised its undergraduate offerings significantly, started an annual Alumni Newsletter and the BC Math Alumni Network, organized a Distinguished Lecturer series and the BC-MIT Number Theory Seminar, built new ties to the Lynch School of Education, hosted an American Mathematical Society sectional meeting, signed a Memorandum of Understanding with the Mathematical Sciences Center and Department of Mathematical Sciences at Tsinghua University to encourage cooperation and the exchange of scholars, carried out a planning process to determine next steps as we seek to become one of the top departments in the country in both research and teaching, moved to a new location on the fifth floor of Maloney Hall (with many aspects of this space specifically designed for the department), and saw a dramatic rise in the number of Mathematics majors (in my last semester as Chair we passed the milestone of 350 majors; by contrast, in Fall 2000 there were 135).  Here is a November 2012 news report on the department's progress. 

Our progress during this period is clear evidence that a deep commitment to excellence in research and a complementary commitment to excellence in undergraduate instruction can coexist and even reinforce each other. 

K-12 Mathematics Education Activities

I have been involved in pre-collegiate mathematics education since the 1990s.  I am committed to the principle that all children should have access to an excellent school education in the mathematical sciences. I also believe it is important for mathematicians to contribute their expertise to discussions concerning the K-12 math curriculum, to be involved in the pre-service teaching of math content to future math teachers at all levels, and to support practicing classroom teachers.

I am an ex officio member of the National Academy of Science's U.S National Commission on Mathematics Instruction, serving as Vice Chair, 2019-2020, and Chair, 2021-2022. I was an organizer for the USNC/MI webinar series "Moving Forward in the Midst of a Pandemic: International Lessons for Math Teachers," which we initiated in summer 2020.  I was the lead math reviewer on a project to evaluate the nation's K-12 curriculum standards organized by the non-profit Fordham Institute, resulting in two reports: The State of State Standards Post-Common Core, released August 2018, and  The State of the Sunshine State's Standards: The Florida B.E.S.T. Edition, released June 2020. Additional service includes: Board of Directors, Math for America Boston (2012-2021), editor of the CBMS book series Issues in Mathematics Education (2006-2020), Massachusetts Board of Elementary and Secondary Education's Math-Science Advisory Council (2007-2013), advisor to the Massachusetts Department of Elementary and Secondary Education concerning the Massachusetts mathematics framework and concerning its response to the Common Core (2009-2010), member of the Steering Committee for the Commonwealth of Massachusetts's Mathematics and Science Partnerships Program (2004-2007).  I was also on a team of mathematicians and math educators who developed essays concerning middle school and high school mathematics (2008-2009).  Here are some essays:  The "Rule of Signs" in Arithmetic (joint with Roger Howe) and The Equal Sign, Equations, and Functions. from the project.  And I served as an (unpaid) consultant in the writing of the Massachusetts Board of Education's Guidelines for the Mathematical Preparation of Elementary Teachers (July 2007).

I am co-PI on a 6-year (2020-2026), $1.78M, NSF grant  "Developing Exemplary Mathematics Teacher Leaders for High-Need Schools: Content, Equity and Leadership" which seeks to connect mathematicians, mathematics educators, teachers, and mentor experts to create a professional community focused on mathematics content, equitable teaching and learning approaches, and teacher leadership development. This project is joint with my BC colleagues Professors Lillie Albert of the Lynch School of Education and Human Development and Juliana Belding and C.K. Cheung of the Math Department, and with Matthew McLeod at the EDC.  This work builds on my joint 7-year (2013-2020), $1.6M, NSF-funded project "Exemplary Mathematics Educators for High-need Schools." A video about that project may be found here, and a report on it, which was presented at ICME-14 in 2021, may be found here

Public Advocacy of Math Education

I have written one blog opinion piece and four op-eds concerned with math education:

Also, I am featured in a series of video conversations (released spring 2015) with Dr. Diane Briars, President of the National Council of Teachers of Mathematics, about the Common Core State Standards for Mathematics.   And I discuss international aspects of mathematics education in an editorial written jointly with Profs. T. Lott Adams and P. Seshaiyer in the December 2023 issue of Mathematics Teacher: Learning & Teaching PK–12.

Work with Graduate Students and Case Studies

In the late 1990s I founded the Boston College Mathematics Case Studies Project to develop new training materials–Case Studies–for use in TA-development programs for mathematics graduate students.  Though the project ended well over a decade ago, the materials are still in use. Following the publication of our cases, a group of Chilean mathematicians carried out a project to improve the pedagogical skills of future Chilean high school teachers using, in part, case studies, and I made 3 trips to Chile in support of their efforts. A volume by Cristián Reyes of the Universidad de Chile containing Spanish-language cases for secondary teachers appeared in 2011. My involvement with this area has continued through my service on AMS-MAA Joint Committee on TAs and Part-Time Instructors, 2014-2020, including serving as Chair of the committee 2016-2020.

Involvement with Professional Organizations

I am a lifetime member of the American Mathematical Society, and also a long-time member of the Mathematical Association of America and of the Association for Women in Mathematics.  AMS service includes: ICM2002 Grants Selection Panel, the Working Group on Preparation for Technical Careers (2007–2008),  AMS representative to the JPBM committee on The Partnership for Mathematical Sciences in America (2009), Joint Math Meetings Travel Grants Selection Committee (Chair, 2009 and 2010), New England Regional Committee of the AMS's Next Generation Campaign (2018-2019), Committee on the Profession (2019-2022).  MAA service includes:  AMS-MAA Joint Committee on TAs and Part-Time Instructors (member 2014-2020; Chair, 2016-2020), MAA Council on the Profession (2016-2020), mentor for the MAA's Project NExT, 2002-2004 and 2017-2019.  I am also a mentor for the Math Alliance.

Honors and Awards

Photos

Here are a few photos from various trips and conferences.

Recent and Planned External Lectures (and occasional other travel or events)


External lectures and other professional travel, 2001-2015


Page last updated: April 7, 2024