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 9, 2009)  
                                                        
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.  As Chair, besides responsibility for the overall administration of the department, this year my tasks include helping to initiate our new Ph.D. program and working to insure our continued excellence in undergraduate education as we make the transition to a doctoral-granting department. 

Present Teaching:
During the Fall 2010 semester, I will be co-teaching two seminars for graduate students, MT890, Graduate Teaching Seminar 1, and MT891, Graduate Teaching Seminar II. I am also available to supervise independent reading courses for undergraduates and for graduate students.

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.  In the last few years, I and my collaborators Profs. Ben Brubaker (MIT) and Daniel Bump (Stanford) have established surprising links to combinatorial representation theory, quantum groups and statistical mechanics.  Multiple Dirichlet series may also be attached to other classes of mathematical objects, such as affine Weyl groups.  If their continuation to a suitable region can be proven, 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.

I am also one of the organizers for the BC-MIT Number Theory Seminar.  The year 2010-2011 will be the third year of this joint seminar series.

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 returned to Chile in June 2008 for additional work with their project, and I also gave two lectures in a conference in Santiago about the mathematical preparation of future K-8 teachers.  An interview with me during this trip concerning mathematics education is posted on the website of the Centro de Modelmiento Matemático, here.

I am also involved in pre-collegiate mathematics education in other ways.  I am a member of the Focus on Mathematics Phase II Advisory Board, and am serving as an advisor to the Massachusetts Department of Elementary and Secondary Education concerning the Massachusetts mathematics framework and concerning its response to the Common Core.  I have been part of a team of mathematicians and math educators who have been working to develop essays concerning middle school and high school mathematics; my initial writing partner for this project was Prof. Roger Howe of Yale.  Here are some essays from the project. I have served a 3-year term (Fall 2007-Spring 2010) on the Massachusetts Department of Education's Math-Science Advisory Council.  Additional service includes: AMS representative on a JPBM committee to explore a Partnership for Mathematical Sciences in America; member of the Advisory Board for the American Mathematical Society's Working Group on Preparation for Technical Careers; member of 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); member of the Arithmetic Test Online Math Content Board.  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 wrote an Op-Ed concerning the need to invest in math and science education which appeared in the Boston Globe on May 21, 2009 and an Op-Ed concerning the math education of future elementary school teachers which appeared in the Boston Herald on April 23, 2007.   (My Globe op-ed was also reprinted under the title "Addressing the Crisis in Math and Science" by Business West, June 8, 2009.)  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.  During the 2009-2010 academic year I co-organized a monthly Seminar in Mathematics Education jointly with Prof. Lillie Albert of the Department of Teacher Education.  This seminar series was sponsored by TNE.  We are hoping to continue this series in some form for the coming year.

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

Photos:
Here are a few photos from various trips and conferences.

Recent and Planned External Lectures:

• University of Rochester, Spring 2011, date to be determined.
  
• First joint meeting of the AMS and the Sociedad de Matemática de Chile (SOMACHI), Session on Automorphic Forms and Dirichlet Series, Pucón, Chile, December 15-18, 2010.  (Session co-organizer.)
• AMS Meeting, Session on Automorphic Forms and Number Theory, Los Angeles, October 9-10, 2010.
  
• University of Maine, Colloquium in the Math Department & Lecture at the Center for Science and Mathematics Education Research, October 4, 2010.
• NCTS International Conference on Automorphic Forms and Related Topics, National Center for Theoretical Sciences, Hsinchu, Taiwan, July 2-13, 2010.
  
• Workshop on Whittaker Functions, Crystal Bases, and Quantum Groups, Banff International Research Station, June 6-11, 2010.  
• BC Faculty/Staff Nicaragua Immersion Trip, May 28-June 4, 2010.  (I am hoping to meet mathematics educators in Nicaragua during this trip.)
• University of Wisconsin, Number Theory Seminar, April 29, 2010.  
• College of the Holy Cross, Colloquium on the occasion of the Pi Mu Epsilon Induction Ceremony, April 14, 2010.
  
• 24th Automorphic Forms Workshop, University of Hawaii at Manoa, March 22-26, 2010.
• Columbia-CUNY-NYU Number Theory Seminar, February 18, 2010.
  
• University of Maryland, Lie Groups and Representation Theory Seminar, November 30, 2009.
  
• MAA New England Section Fall Meeting, Distinguished Teaching Lecture & Case Studies Workshop, Western New England College, November 20-22, 2009.
• Purdue University, Automorphic Forms Seminar & Colloquium, November 9-10, 2009.
  
• University of Connecticut, Colloquium, November 5, 2009.
  
• Midwest Conference on Automorphic Forms, Representation Theory, and Number Theory,  Iowa City, October 24-25, 2009.
  
• Fourth Workshop on Multiple Dirichlet Series, Stanford, June 2009.
  
• UCLA Number Theory Seminar, June 2009.
  
• Conference on Mock Theta Functions and Applications in Combinatorics, Algebraic Geometry, and Mathematical Physics, Max-Planck-Institut für Mathematik, Bonn, May 2009.
• Workshop on Mapping the High School Algebra Curriculum (workshop participant/essayist), Institute for Mathematics and Education, University of Arizona, February 19-21, 2009.
  
• Arizona State University, Number Theory Seminar, November 2008.
  
• 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.  Notes of my lecture (pdf file).
  
• 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). 
• 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.  I'm looking forward to having doctoral students at Boston College now that our Ph.D. program has been approved, so if you are interested in number theory please apply to our program.

Selected Publications

Math Department Home Page