Solomon Friedberg

Department of Mathematics                                        
Boston College
Chestnut Hill, MA 02467-3806
(617) 552-3002 
Department Fax:  (617) 552-3789 
Email:  friedber@bc.edu

Curriculum Vitae (in pdf format) (updated December 4, 2007)  
                                                        
Education:
Ph.D. University of Chicago, 1982
M.S. University of Chicago, 1979
B.A. Summa cum Laude, University of California, San Diego, 1978

Position:
Professor of Mathematics and Chairman of the Department of Mathematics.

Present Teaching:
During the Fall 2008 semester, I will not be teaching a lecture course as I focus on work related to chairing the Mathematics Department.  However, I will be supervising an undergraduate reading course on Elliptic Curves and related topics.  During the Spring 2009 semester  I will be teaching MT695, Honors Seminar.  This is a seminar course that is required for undergraduate students in the Departmental Honors program.  Other interested undergraduates may also enroll with my permission; please see me if you are interested.

The websites for some of my previous courses may be found here.  For 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 Bump and 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 unexpectedly 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.  In many cases they have meromorphic continuation and a finite group of functional equations that is generated by reflections.  I and my collaborators have recently found some surprising links to combinatorial representation theory.  It is possible that multiple Dirichlet series may be attached to other classes of mathematical objects, such as affine Weyl groups.  If this can be done, it would lead to striking advances. 

For a .pdf file which gives an annotated bibliography of introductory material on automorphic forms, which should be of use to graduate students considering working in the area, click here.

Other Activities:
I am the founder and director of the Boston College Mathematics Case Studies Project, a project to develop new training materials--Case Studies--for use in TA-development programs for mathematics graduate students.  Over the past few years I have given numerous workshops and talks on these materials.  In May 2007 I presented a series of talks on case studies in Chile, where a project of nationwide scope is underway to use these methods to improve the pedagogical skills of future high school teachers.  The project was directly motivated by the BCCase materials.  I also organized a workshop at the Institute for Mathematics and Education at the University of Arizona in February 2008 on Case Studies in the context of secondary-school teacher education.  I am scheduled to return to Chile in June 2008.

I am also involved in pre-collegiate mathematics education in other ways.  I am part of a team of 10 mathematicians and math educators who will meet several times in Berkeley in 2008 to develop essays concerning middle school and high school mathematics; my initial writing partner for this project will be Prof. Roger Howe of Yale.  I have been appointed to a 3-year term (Fall 2007-Spring 2010) on the Massachusetts Department of Education's Math-Science Advisory Council.  I am also a member of the Advisory Board for the American Mathematical Society's Working Group on Preparation for Technical Careers. I served on the Steering Committee for the Commonwealth of Massachusetts's Mathematics and Science Partnerships Program during the 3 1/2 years it was constituted (Jan. 2004 to June 2007).  I was also part of a group of mathematicians who carried out a series of meetings about the teaching of mathematics, organized by Prof. Howe; an article about this work appeared in the December 2004 Notices of the American Mathematical Society.  I have also served on a committee organized by Profs. Doug Carnine and James Milgram concerned with the mathematical preparation of teachers, funded by the U.S. Department of Education. I have been a member of the Arithmetic Test Online Math Content Board, which is preparing on-line tests that parents can use to evaluate their children's mathematical progress.   I wrote an Op-Ed concerning the math education of future elementary school teachers which appeared in the Boston Herald on April 23, 2007.   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 also an editor of the book series Issues in Mathematics Education.  

Locally, I have served as a mentor and as a content-advisor for preservice teachers at BC. I am also the BC Teachers for a New Era point person for the mathematics department.  As such, I hope to involve more math students in K-12 education, and more math faculty in interacting with pre- and in- service K-12 teachers. Please contact me about this if you are interested.

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

Recent and Planned External Lectures:

• Wellesley College, Colloquium, November 2008.
• Conference on Multiple Dirichlet Series and Applications to Automorphic Forms, International Centre for Mathematical Sciences, Edinburgh, United Kingdom, August 4-8, 2008.
• Workshop on the development of Spanish-language case studies for future high school mathematics teachers and Conference on La capacidad para enseñar matemática de los futuros profesores de Enseñanza Pre-básica y Básica (K-8), Universidad de Chile, June 2008.  Conference poster (pdf) here.
  
• AMS Meeting, Session on L-Functions and Automorphic Forms, New York City, NY, March 15-16, 2008.
• Stanford/AIM Number Theory Seminar, March 7, 2008.
  
• Workshop on Using Cases to Develop Knowledge for Teaching Mathematics, Institute for Mathematics and Education, University of Arizona.  (Chair, organizing committee), February 14-16, 2008.
• San Diego Joint Math Meetings, AMS Session on Automorphic Forms and Related Topics, January 6, 2008 and Panel Member, Making Teacher Preparation Our Business (sponsored by the AMS Committee on Education), January 8, 2008.
  
• The Langlands and Geometric Langlands Program, Guangzhou, China, June 2007.
• Conference on  Análisis de la Práctica Pedagógica para la Formación de Profesores de Matemáticas, Case Studies Workshops, and Mathematics Colloquium, Universidad de Chile, Santiago, May-June 2007.
• Conference on L-functions and Automorphic Forms (on the occasion of Dorian Goldfeld's 60th Birthday), Columbia University, May 2007.
• Boston University Algebra Seminar, April 2007.
• AMS Meeting, Session on Automorphic Forms and Arithmetic Geometry, Hoboken, NJ, April 2007.
• KIAS-POSTECH-SNU International Number Theory Workshop, Seoul, Korea, December 2006.
• California Institute of Technology, November 2006.
• Princeton University, November 2006.
• Québec-Vermont Number Theory Seminar, October 2006.
• University of Massachusetts, Amherst, Colloquium, October 2006.
• Conference on Zeta Functions, Independent University of Moscow, September 2006.
• ETH, Zurich, Switzerland, September 2006.
• Stanford Workshop on Multiple Dirichlet Series, July 2006.  (Workshop organizer; I also provided a list of open problems for workshop participants to work on but did not formally speak.  We were trying to keep formal lectures to a minimum in order to encourage maximum research interactions during the workshop.)
• Georgia Tech, April 2006.
• Boston University, February 2006.
• University of New Mexico, January 2006.
• San Antonio Joint Math Meetings:  AMS Session on Arithmetic Geometry and Modular Forms; AMS Workshop on TA Development for Faculty; MAA Workshop on Training TAs, January 2006.  
• Conference on Modular Forms and Related Topics in Honor of Marvin Knopp's 73rd Birthday,  Temple University, January 2006.
• Penn State University (two talks:  one on number theory and on one TA development via case studies), November 2005.
• Maine-Québec Conference on Number Theory & Related Topics, October 2005.
• Bretton Woods Workshop on Multiple Dirichlet Series, July 2005 (conference co-organizer).  Conference photo (photo by C. J. Mozzochi).
• Seoul National University, Colloquium and two Number Theory Seminar lectures, May 2005.
• Korean Institute for Advanced Study, two Number Theory Seminar lectures, May 2005.
• 1st KAIST International Symposium on Enhancing University Mathematics Teaching, Korean Advanced Institute  of Science and Technology, Daejeon, May 2005 (plenary speaker).
• University of Colorado, Boulder, Kempner Colloquium, April 2005.
• Atlanta Joint Math Meetings, Session on Mathematicians' Work on Mathematics Education, January 2005.
• Brown University, Algebra and Number Theory Seminar, December 2004.
• Brandeis University, Fellowship of the Ring seminar, October 2004.
• Number Theory Conference in Honor of Harold Stark, University of Minnesota, August 2004 (conference co-organizer).
• California Institute of Technology, May 2004.
• AMS Meeting, Session on Automorphic Forms and Analytic Number Theory, Lawrenceville, April 2004.
• Sixth Autumn Workshop of Number Theory, Hakuba, Japan, September 2003.  (Three hours of lectures as plenary lecturer.)
• Columbia University Number Theory Seminar, March 2003.
• Boston University Algebra Seminar, December 2002.
• AMS Meeting, Session on Number Theory and Arithmetic Geometry, Boston, October 2002.
• IAS/Park City Mathematics Institute, July 2002.
• Conference on Recent Progress in Langlands Functoriality, Luminy, France, June 2002.
• Conference on L-Functions and Automorphic Forms, Johns Hopkins Univesity, May 2002.
• Harvard University Number Theory Seminar, April 2002.
• Brown University Analysis Seminar, April 2002.
• 16th Annual Workshop on Automorphic Forms and Related Topics, UCLA, March 2002.
• Brown University Algebra Seminar, February 2002.
• AMS-MER Workshop on Excellence in Undergraduate Mathematics, Arizona State University, December 2001    (Plenary Speaker).
• Boston University Algebra Seminar, April 2001.
• Harvard University Seminar on Teaching in the Mathematical Sciences, April 2001.
• Conference on Analytic and Geometric Aspects of the Langlands Program, Tel-Aviv University, March 2001.

Ph.D. Students:
Ozlem Imamoglu, 1992, UCSC, Theta functions and Kubota homomorphisms for the symplectic group over the Gaussian integers.
Thomas Goetze, 1995, UCSC, On a cubic Shimura integral for a rank two symplectic group.
Nancy Allen, 1996, UCSC, On the spectra of certain graphs arising from finite fields.
Ji Li, 2005,  Boston University, Determination of a GL(2) cuspform by twists of critical L-values.

I welcome inquiries from mathematics graduate students in the greater Boston area interested in writing a Ph.D. dissertation in automorphic forms or related areas of number theory.  My most recent student, Ji Li, found me in this way.

Selected Publications

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