Solomon Friedberg

Department of Mathematics                                        Solomon Friedberg's picture
Boston College
Chestnut Hill, MA 02467-3806
Phone:  (617) 552-3002 
Department Fax:  (617) 552-3789 
Location: Maloney Hall, Room 523

Curriculum Vitae (in pdf format) (updated December 14, 2016)  

Ph.D. University of Chicago, 1982
M.S. University of Chicago, 1979
B.A. Summa cum Laude, University of California, San Diego, 1978

RootsMy grandfather's education certificate (1914)

Position: James P. McIntyre Professor of Mathematics

This summer, I am meeting regularly with my doctoral students Yuanqing Cai, who has defended his thesis and will graduate in August 2017, and (Winston) Spencer Leslie.  I am happy to meet other students by appointment.  In the Fall semester of academic year 2017-2018, I will be teaching Math 4460, Complex Variables. The websites for many of my previous courses may be found here

For students who are seeking more information about which mathematics course to take, please see the Mathematics Department's Advisement Website

Research Areas:
Automorphic forms, number theory, and representation theory.  Selected publications (including preprints).  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 recently studied other aspects of automorphic forms on covering groups, joint with David Ginzburg, and worked on functionals, Iwahori Hecke algebras, and quantum groups, joint with Ben Brubaker, Valentin Buciumas and Dan Bump.  Besides on-going work with prior research collaborators, I am also working on projects with Yuanqing Cai and Eyal Kaplan (parts also joint with David Ginzburg and David Soudry),  and with Nikos Diamantis and Martin Westerholt-Raum.

My research is supported by NSF grant DMS-1500977.  I have benefited greatly from prior external support for my research from both the NSF and from the NSA's Mathematical Sciences program, as well as from support by Boston College.

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

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 complimentary commitment to excellence in undergraduate instruction can coexist and even reinforce each other. 

Other 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 have been an editor of the CBMS book series Issues in Mathematics Education from 2006 on.  I serve on the National Academy of Science's U.S National Commission on Mathematics Instruction, am a member of the Board of Directors of Math for America Boston, and am the lead organizer for a project to evaluate the nation's math standards organized by the Fordham Institute.  I was also an 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).  Additional service includes: Massachusetts Board of Elementary and Secondary Education's Math-Science Advisory Council (2007-2013), Focus on Mathematics Phase II Advisory Board (2009-2011), Community for Advancing Discovery Research in Education Advisory Board (2011-2012), AMS representative on a JPBM committee to explore a Partnership for Mathematical Sciences in America (2009); member of the Advisory Board for the American Mathematical Society's Working Group on Preparation for Technical Careers (2007-2009); 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 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 have written 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. 

Locally, I am co-PI on a 6-year (2013-2019) NSF-funded project "Exemplary Mathematics Educators for High-need Schools," joint with Profs. Prof. Lillie Albert of the Department of Teacher Education and C.K. Cheung of the Mathematics department. Together with colleagues at BU, the EDC and Math for America-Boston, we are working with both beginning and master math teachers for high-needs schools and developing infrastructure to support excellence in math instruction in Boston-area schools.  From 2009-2010 on I have also co-organized a monthly Seminar/Colloquium in Mathematics Education jointly with Prof. Albert, and from 2012 on, also jointly with Prof. Cheung.  Prior local service includes: mentor and content-advisor for preservice teachers,  BC Teachers for a New Era (TNE) point person for the mathematics department, and Chair of the TNE Coordinating Council (2011-2013). I hope to involve more BC math students in K-12 education, and more BC math faculty in interacting with pre-service and in-service K-12 teachers. Please contact me about this if you are interested. 

In another direction, 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. Continuing this interest, I have been a member of the AMS-MAA Joint Committee on TAs and Part-Time Instructors since February 2015, serving as Chair of the committee from February 2016 to January 2020.

Honors and Awards:
Phi Beta Kappa, University of California, San Diego, 1978
McCormick Graduate Fellowship, University of Chicago, 1978-81
NSF Postdoctoral Research Fellowship, 1982-84
NATO Postdoctoral Fellowship in Science, 1985-86
Indo-American (Fullbright) Fellowship, 1987-88
Sloan Fellowship, 1989-92
Distinguished Visiting Professor of Mathematics, Brown University, Spring 2002
MAA Northeastern Section Award for Distinguished College or University Teaching, 2009
McIntyre Chair, Boston College, appointed 2013
Fellow of the American Mathematical Society, Class of 2014
Distinguished Ordway Visitor, University of Minnesota, 2014

Ph.D. Students:
1.  Ozlem Imamoglu, 1992, UCSC, Theta functions and Kubota homomorphisms for the symplectic group over the Gaussian integers. 
2.  Thomas Goetze, 1995, UCSC, On a cubic Shimura integral for a rank two symplectic group. 
3.  Nancy Allen, 1996, UCSC, On the spectra of certain graphs arising from finite fields. 
4.  Ji Li, 2005,  Boston University, Determination of a GL(2) cuspform by twists of critical L-values. 
5.  Ting-Fang Lee, 2013, National Tsing Hua University, Taiwan, On arithmetic over function fields (co-advisor with Prof. Jing Yu). 
6.  Yuanqing Cai, 2017, Boston College (degree will be awarded at the end of the summer).
Papers: "Fourier coefficients for theta representations on covers of general linear groups" here. "Fourier coefficients for degenerate Eisenstein series and the descending decomposition" here.  "Doubling constructions for covering groups and tensor product L-functions," joint with Friedberg, Ginzburg and Kaplan, announcement here.  The full paper is roughly 70 pages. Another paper, concerning the applications of doubling constructions to functoriality, joint with Friedberg and Kaplan, is in preparation.
7.  (Winston) Spencer Leslie, Boston College, in progress.
Paper:  "A generalized theta lifting, CAP representations, and Arthur parameters" here. Another paper, concerning parity sheaves and joint with Gus Lonergan, is in preparation.

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.  

Here are a few photos from various trips and conferences.

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

External lectures, 2001-2009

Selected Publications

Math Department Home Page
Last update: June 23, 2017