Department of Mathematics

Boston College

Chestnut Hill, MA 02467-3806

Phone: (617) 552-3002

Department Fax: (617) 552-3789

Email:friedber@bc.eduLocation: Maloney Hall, Room 523

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

Education:

Ph.D. University of Chicago, 1982

M.S. University of Chicago, 1979

B.A. Summa cum Laude, University of California, San Diego, 1978

Roots: My grandfather's education certificate (1914)

Position:James P. McIntyre Professor of Mathematics

Teaching:

For the academic year 2016-2017, I taught two lectures of Multivariable Calculus, Math 2202, in the fall and am teaching a second-year graduate class, Number Theory II, Math 8822, in the spring. In addition, I meet weekly with my two doctoral students Yuanqing Cai and (Winston) Spencer Leslie. I am happy to meet other students by appointment. 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 unique functionals and Iwahori Hecke algebras, joint with Ben Brubaker and Dan Bump. Besides on-going work with prior research collaborators, I am also working on projects with Yuanqing Cai and Eyal Kaplan (also joint with David Ginzburg), with Valentin Buciumas (also joint with Ben Brubaker and Dan Bump), 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 thatallchildrenshould 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 was 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:

- an Op-Ed concerning the Common Core which appeared in USA Today on September 16, 2014 (and was posted on-line on www.usatoday.com on September 15). In this op-ed I talk about "memorized rules." Here is a good example of what I have in mind. (This op-ed has been republished through Gannett subsidiaries, including among others: Springfield News-Leader, Florida Today, Gaumpdn.com, Baxter Bulletin, Indianapolis Star, and Inside Sources. As of May 13, 2015, it also has had 38,322 postings on Facebook and been shared 1,235 times on Twitter.)
- an Op-Ed concerning the implementation of the Common Core which appeared in the Los Angeles Times on December 11, 2013. (This op-ed was reprinted in The Anniston Star, Chattanooga Times Free Press, The Columbian, Glen Falls Post-Star, The Gulf Today (United Arab Emirates), Honolulu Star-Advertiser, Long Island Newsday, The State, The Times-Tribune, The Virgin Islands Daily News, and several on-line sites.)

- an Op-Ed concerning the need to invest in math and science education which appeared in the Boston Globe on May 21, 2009. (This op-ed was reprinted under the title "Addressing the Crisis in Math and Science" by Business West, June 8, 2009.)
- an Op-Ed concerning the math education of future elementary school teachers which appeared in the Boston Herald on April 23, 2007.

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. (Full paper is roughly 70 pages.)

7. (Winston) Spencer Leslie, Boston College, in progress.

Paper: "A generalized theta lifting, CAP representations, and Arthur parameters" here.

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.

Photos:

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

- The Langlands program: endoscopy and beyond, Institute for Mathematical Sciences, National University of Singapore, December 2018 to January 2019.
- Brigham Young University, Mathematics Department External Review Committee, November 30-December 1, 2017.

- Automorphic Forms, Mock Modular Forms and String Theory, Banff International Research Station, Canada, October 29 to November 2, 2017.
- Thesis Defense of Henrik Gustafsson, Department of Physics, Chalmers University of Technology, Gothenberg, Sweden, August 25, 2017.

- Chalmers University of Technology, Gothenburg, Sweden, July 22-28, 2017. Working visit to carry out joint research.

- Noyce Summit, Washington DC, July 19-21, 2017.

- International Seminar on Mathematics Education, Park City Math Institute, July 2-9, 2017.

- Arithmetics on Automorphic Forms (3 lectures), Harbin Institute of Technology, Harbin, China, June 27-30, 2017.
- Tel-Aviv University, working visit to carry out joint research with Prof. David Ginzburg, June 4 to 15, 2017.
- University of San Francisco, Mathematics and Statistics Department Academic Program External Review Committee, May 8-10, 2017.
- Special Session on Recent Developments in Automorphic Forms and Representation Theory, AMS Special Session, Hunter College, CUNY, May 6-7, 2017.
- Saint Louis University, Mathematics and Statistics Department External Review Committee, April 27-28, 2017.
- Thesis Defense of Vladislav Petkov, Columbia University, April 20, 2017.

- Number Theory Seminar, Institute for Mathematical Research, ETH, Zürich, Switzerland, March 5-11, 2017.
- Joint Math Meetings, special session on "Teaching Assistant Development Programs: Why and How?" Special session co-organizer. Atlanta, January 4-7, 2017.
- Québec-Maine Number Theory Conference, Université Laval, Québec, Canada, October 8-9, 2016.
- Automorphic forms, mock modular forms and string theory, Simons Center for Geometry and Physics, September 23-27, 2016.

- Whittaker Functions: Number Theory, Geometry and Physics, Banff International Research Station, Canada, July 24-29, 2016. Workshop co-organizer.
- Conference on Automorphic Forms on Metaplectic Groups and Related Topics, Indian Institute of Science Education and Research (IISER), Pune, India, July 4-9, 2016. Conference co-organizer.
- Tel-Aviv University, May 29-June 8, 2016. Working visit to carry out joint research with Prof. David Ginzburg.

- Duke University, May 8-11, 2016. Working visit to carry out joint research with Prof. Jayce Getz.

- Automorphic Forms, Combinatorics and Representation Theory, AMS Special Session, University of Utah, April 9-10, 2016. Special session co-organizer.
- University of Buffalo, Algebra Seminar, March 28, 2016.

- University of Maine, Number Theory Seminar, March 24, 2016.

- L-Functions and Automorphic Forms, University of Heidelberg, February 22-26, 2016.
- Automorphic Forms, Automorphic L-Functions and Related Topics, RIMS, Kyoto, Japan, February 1-5, 2016.

- Eisenstein Series on Kac-Moody Groups and Applications to Physics, Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul, South Korea, November 12-20, 2015.
- National University of Singapore, August 2015. Colloquium and working visit to carry out joint research with Prof. Lei Zhang.

- Tel-Aviv University, July 2015. Working visit to carry out joint research with Prof. David Ginzburg.

- International Conference on Number Theory and Physics, IMPA, Rio de Janeiro, Brazil, June 2015.

- Automorphic Forms: Advances and Applications, CIRM, Luminy, France, May 2015.
- Ohio State University, Representations and Lie Theory Seminar, April 22, 2015.
- NCTM Annual Meeting, Mathematicians on the Common Core State Standards for Mathematics: A Panel Discussion (organizer and panelist), Boston, April 17, 2015.
- Mathematics Matters in Education: A Workshop in Honor of Roger Howe, Texas A&M University, March 26-28, 2015.
- Stanford University, Number Theory Seminar, March 2, 2015.

- UNC-Duke Number Theory Seminar, February 25, 2015.
- Joint Math Meetings, special session on Algebraic Combinatorics and Representation Theory, San Antonio, January 10-13, 2015.
- Duquesne University, Department of Mathematics and Computer Science External Review Committee, November 2-4, 2014.

- Analytic Number Theory and its Applications: A Conference in Honor of Jeff Hoffstein, Perrotis College, Thessaloniki, Greece, July 14-18, 2014.
- Second US-EU Building Bridges Automorphic Forms Summer School and Workshop, Bristol, U.K., June 30-July 11, 2014. Workshop lecture and mini-course instructor, "The Langlands Program" (co-instructor with Prof. Jim Cogdell, Ohio State University). Notes for my mini-course here.

- SUMO Colloquium/Speaker Series, Stanford University, April 2014.

- Workshop on The roles of mathematics departments and mathematicians in the mathematical preparation of teachers, MSRI, March 26-28, 2014. (Workshop co-organizer.)
- Northeastern University, Representation Theory Seminar, March 21, 2014.

- Distinguished Ordway Visitor, University of Minnesota, February 24 to March 7, 2014. (Includes Colloquium lecture on February 27, 2014 and Lie Theory seminar lecture on February 28, 2014.)

- Mathematicians and School Mathematics Education: A Pan-American Workshop, Banff International Research Station, January 26-31, 2014. (Workshop co-organizer.)
- Workshop on Whittaker Functions: Number Theory, Geometry and Physics, Banff International Research Station, October 13-18, 2013. (Workshop co-organizer.)
- Brown University, Algebra and Number Theory Seminar, September 30, 2013.

- Stark's Conjecture and Related Topics (honoring Harold Stark on his retirement), UCSD, September 2013.

- POSTECH Summer School in Number Theory, Pohang Math Institute, Republic of Korea, July 5-11, 2013, 5 lectures.

- 2013 NCTS Special Day on Automorphic Forms, National Center for Theoretical Sciences, Hsinchu, Taiwan, July 1, 2013.
- The Many Ways of IBL, University of Chicago, June 17-21, 2013 (attending but not presenting).

- Preparing Graduate Students to Teach Undergraduate Mathematics: A Working Conference, Harvard University, June 12-13, 2013.
- Initiative on a Common Core Mathematics Licensure Examination for Entry into Teaching, University of Michigan, May 31-June 1, 2013 (attending but not presenting).
- Commencement Address to Boston College Arts & Sciences Masters and PhD Recipients, May 20, 2013.

- Rutgers University, Number Theory Seminar and Teaching Math Seminar (2 separate talks), April 3, 2013.
- ICERM, January 28, 29; February 4, 5, 6, 19, 26, March 12, April 9, 23: Lectures, tutorials, panels related to the special semester there.

- AMS-MAA Joint Math Meetings, The Training and Professional Development of Teaching Assistants (sponsored by the AMS-MAA Joint Committee on TAs and Part-Time Instructors), Panel Member, San Diego, CA, January 9-12, 2013. Slides available here.

- Number Theory Seminar, Texas A&M University, December 12, 2012.
- Georgetown University, Department of Mathematics and Statistics External Review Committee, December 5-7, 2012.

- Palmetto Number Theory Series XVIII, Plenary Speaker, Wake Forest University, Winston-Salem, NC, September 2012.

- Automorphic Forms, Representations and Combinatorics: A Conference in Honor of Daniel Bump, Stanford University, August 13-16, 2012, speaker and conference co-organizer.
- Tsinghua University Mathematical Sciences Center, Colloquium, Beijing, China, July 27, 2012.

- Workshop on Lie Group Representations and Automorphic Forms (3 lectures), Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing, China, July 23-27, 2012.
- Emory University, REU Program in Number Theory, June 25, 2012.

- 2012 KIAS-POSTECH Number Theory Workshop (2 lectures), Pohang University of Science and Technology (POSTECH), Pohang, Republic of Korea, June 10-14, 2012.
- Caltech Number Theory Seminar, March 8, 2012.

- Modular Forms, Mock Theta Functions, and Applications, University of Cologne, Cologne, Germany, 27 February -1 March 2012.
- Matemáticos en la Educación Matemática Escolar: En la búsqueda de impacto en nuestra realidad educacional (Mathematicians and School Mathematics Education: Looking for impact in transforming our educational reality), Santiago, Chile, January 11-13, 2012.
- Universidad de Chile, Public Lecture, January 10, 2012.

- TORA I (TORA=Texas-Oklahoma Representations and Automorphic forms), plenary lecture, Denton, TX, September 17-18, 2011.
- Undergraduate Math Research Colloquium, University of North Texas, Denton, TX, September 16, 2011.

- Number Theory Xi'an 2011 - Workshop on Number Theory (4 lectures), Northwest University, Xi'an, China, June 2011.
- ETH, Zürich, May 2011 (2 lectures).

- Ohio State University, Number Theory Seminar, May 9, 2011.

- Yale University, Number Theory/Algebraic Geometry Seminar, March 29, 2011.
- Workshop on Knowledge of Mathematics for Teaching at the Secondary Level (workshop participant and advisory board member for the related research project), Institute for Mathematics and Education, University of Arizona, March 23-26, 2011.
- University of Rochester, Colloquium & Number Theory Seminar, March 16-17, 2011.

- Brigham Young University, "Focus on Math" Colloquium Lecture & Number Theory Seminar, January 11, 2011.

- 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 7-9, 2010; lecture for graduate students July 12, 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. (Did not lecture; university-associated 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.

## Selected Publications

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