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 21, 2018)

James P. McIntyre Professor of MathematicsPosition:

Roots: My grandfather's education certificate (1914)

Education:

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

M.S. University of Chicago, 1979

Ph.D. University of Chicago, 1982

Teaching:During Fall 2019-2020, I will be teaching Sections 01 and 02 of MATH 1105, Calculus II-AP. Information about my course is here. In Spring 2020, I am scheduled to teach MATH 4460, Complex Variables.

During the academic year, I also will be meeting regularly with my doctoral student Yusheng Lei, and I am happy to meet other students by appointment.

The websites for many of my previous courses may be found here.

Research:Recent publications (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 recently 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, and introduced generalized doubling integrals and studied their applications with Yuanqing Cai and Eyal Kaplan; parts also joint with David Ginzburg. I have some new projects underway, too!

My research is supported by NSF grant DMS-1801497. I have also 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, and I am pleased to express my appreciation of this support.

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.

K-12 Mathematics Education Activities:

I have been involved in precollegiate 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 serve as Vice Chair of the National Academy of Science's U.S National Commission on Mathematics Instruction, and am a member of the Board of Directors of Math for America Boston. In 2017-2018 I served as the lead math reviewer for a project to evaluate the nation's standards organized by the non-profit Fordham Institute. Our report, The State of State Standards Post-Common Core, was released August 22, 2018. Additional service includes: editor of the CBMS book series Issues in Mathematics Education (2006-2018), 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), 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 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 one blog opinion piece and four op-eds concerned with math education:

- "Solid math standards: Necessary...but not sufficient" which appeared in The Education Gadfly Weekly on August 22, 2018 (Vol. 18, No. 33) and which was also posted on the Fordham Institute's website in their Commentary/Blogs/Flypaper section.

- "Common Core math is not fuzzy" 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.)
- "Can American students get smart?" 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.)

- "The crisis in math, science" 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.)
- "Teachers must be up for [the] count" 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.

I am co-PI on a 7-year (2013-2020) NSF-funded project "Exemplary Mathematics Educators for High-need Schools," joint with my BC colleagues Professors Lillie Albert of the Department of Teacher Education, Special Education, Curriculum & Instruction and C.K. Cheung of Math. Together with colleagues at 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. A video about our project may be found here. 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 BC service related to K-12 education includes: mentor and content-advisor for pre-service teachers, BC Teachers for a New Era (TNE) point person for the mathematics department, and Chair of the TNE Coordinating Council (2011-2013).

I encourage BC and other college math students to consider becoming math teachers, and higher education math faculty who are interested in K-12 math education to interact with pre-service and in-service teachers. Please contact me about this if you are interested.

Work with Graduate Students and Case Studies:

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.

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. For the AMS, I have served on the ICM2002 Grants Selection Panel, on the Working Group on Preparation for Technical Careers (2007–2008), as the AMS representative to the JPBM committee on The Partnership for Mathematical Sciences in America (2009), as Chair of the 2009 and 2010 Joint Math Meetings Travel Grants Selection Committee, as a member of the New England Regional Committee of the AMS's Next Generation Campaign (2018-2019), and on the AMS's Committee on the Profession, 2019-2022. I have also been a member of the AMS-MAA Joint Committee on TAs and Part-Time Instructors since February 2014, serving as Chair of the committee from February 2016 to January 2020, and serve on the MAA's Council on the Profession (2016-2020) (ex officio). I have also served as a mentor for the MAA's Project NExT, 2002-2004 and 2017-2019.

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 (Fulbright) 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

Conference Honoree, Forschungsinstitut für Mathematik, ETH Zürich, 2018

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, Theta representations on covering groups.

7. (Winston) Spencer Leslie, 2018, Boston College, Theta liftings on higher covers of symplectic groups.

8. Yusheng Lei, Boston College, in progress.

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):

- Graduate summer school on the algebraic theory of automorphic forms, University of Oregon, July 2021. (Series of 4 lectures.)

- New Connections in Number Theory and Physics, Newton Institute for Mathematical Sciences, Cambridge, England, May-June 2021. Program co-organizer.
- Langlands Program: Number Theory and Representation Theory, Casa Matemática Oaxaca, Oaxaca, Mexico, November-December 2020.

- The 14th International Congress on Mathematics Education, Shanghai, China, July 2020.
- Recent Developments on Automorphic Forms and Representations of p-adic Groups, AMS Special Session, Purdue University, April 2020.

- University of Minnesota, Colloquium, September 2019.
- Purdue University, Department of Mathematics External Review Committee, September 2019.

- Purdue University, Colloquium lecture and Automorphic Forms and Representation Theory Seminar lecture, August 2019.
- The Role of Teacher Preparation in STEM Teacher Retention in High-Need School Districts, Noyce Summit, Washington DC, July 2019. Poster presentation.

- Tel-Aviv University, working visit to carry out joint research with Prof. David Ginzburg, May-June 2019.

- University of Rhode Island, Knowledge Across Borders: Conversations Among Disciplines, keynote speaker, April 2019.
- NCTM annual meeting, San Diego, April 2019.

- Recent Developments in Automorphic Forms, AMS Special Session, University of Hawaiʻi at Mānoa, March 22-24, 2019. Special session co-organizer.
- HINT 2019 (Hawaii Number Theory 2019), University of Hawaiʻi at Mānoa, March 2019.
- Automorphic Structures in String Theory, Simons Center for Geometry and Physics, Stony Brook, March 4-April 5, 2019.

- University of Chicago, Number Theory Seminar, February 26, 2019.

- Northwestern University, Number Theory Seminar, February 25, 2019.

- POSTECH, Republic of Korea, February 2019. Series of ten lectures on The Langlands Conjectures and L-Functions presented together with Prof. Lei Zhang (NUS), February 11-14, 2019.
- Boston University Number Theory Seminar, February 4, 2019.

- The Langlands Program: Endoscopy and Beyond, Institute for Mathematical Sciences, National University of Singapore, January 2019.
- Harvard Number Theory Seminar, December 5, 2018.
- 2018 HKU Number Theory Days, Hong Kong University, July 2018. Conference lecture, July 16, 2018; colloquium lecture, July 17, 2018.

- Automorphic Forms on Reductive Groups and Their Covers: A Conference in Honour of Solomon Friedberg, Forschungsinstitut für Mathematik (FIM), ETH Zürich, June 25-28, 2018. Conference poster.

- Tel-Aviv University, working visit to carry out joint research with Prof. David Ginzburg, May 23-June 3, 2018.
- Simons Symposium on Relative Trace Formulas, Germany, April 22-28, 2018.
- Berkeley Arithmetic Geometry and Number Theory Seminar, April 16, 2018.
- 32nd Automorphic Forms Workshop, Tufts University, March 19-22, 2018.
- Brown Algebra/Number Theory Seminar, March 19, 2018.

- Joint Math Meetings, Moderator for panel on The Experiences of Foreign Graduate Students as GTAs, San Diego, January 10-13, 2018.

- 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 23-28, 2017. Working visit to carry out joint research.

- Stimulating Research and Innovation for Preservice Education of STEM Teachers in High-Need Schools, Noyce Summit, Washington DC, July 19-21, 2017. Poster presentation.

- 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.

External lectures and other professional travel, 2001-2015

## Selected Publications

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