## Solomon Friedberg

Department of Mathematics Boston CollegeChestnut Hill, MA 02467-3806 Email: solomon.friedberg@bc.eduPhone: (617) 552-3002 Office: Maloney Hall, Room 523

### Biographical Information

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. Ph.D. Advisor: Harold M. Stark

Curriculum Vitae (in pdf format) (updated December 24, 2023)

### Teaching

In Spring 2024 I am teaching Math 8845, Topics in Algebra and Number Theory. This course will be about quaternion algebras, and will use the book by Prof. John Voight in the GTM series. Information about the course is available on BC's Canvas learning management system. I will also work with graduate students and postdocs and with area high school math teachers.

In Fall 2023 I taught Math 8806, Algebra I. This was the first semester graduate course in abstract algebra (and was also taken by several undergraduates). I also worked with area high school math teachers and supervised the studies and research of several BC graduate students.

### Research

Publications from 2010 on (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 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, introduced generalized doubling integrals and studied their applications with Yuanqing Cai, David Ginzburg and Eyal Kaplan. Presently, I am developing a new instance of the relative trace formula with Omer Offen, working on several projects related to number theory and representation theory with NSF postdoc Claire Frechette, working on periods with David Ginzburg and Omer Offen, and working on some new projects involving number theory and string theory with several physicists.

My research is supported by NSF grant DMS-2100206. The NSF grant also supports graduate students at BC. I am thankful for this support of my research. During my career, I have benefited greatly from external support for my research from the NSF, the Simons Foundation, the NSA's Mathematical Sciences program, the US-Israel Binational Science Foundation, the Sloan Foundation, and Boston College, and I am pleased to express my appreciation of this support.

I am an organizer for BC's Number Theory & Representation Theory Seminar.

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

### 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.

Ting-Fang Lee, 2013, National Tsing Hua University, Taiwan, On arithmetic over function fields (co-advisor with Prof. Jing Yu).

Yuanqing Cai, 2017, Boston College, Theta representations on covering groups.

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

Yusheng Lei, 2021, Boston College, Theta liftings on double covers of orthogonal groups.

Eric Moss, Boston College, in progress.

Siddharth Mahendraker, Boston College, in progress (co-advisor with Prof. Spencer Leslie).

Tianxiang (Jimmy) Liu, Boston College, in progress.

Alan Hou, Brandeis University, in progress (co-advisor with Prof. Omer Offen).

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.

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

### K-12 Mathematics Education 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 am an ex officio member of the National Academy of Science's U.S National Commission on Mathematics Instruction, serving as Vice Chair, 2019-2020, and Chair, 2021-2022. I was an organizer for the USNC/MI webinar series "Moving Forward in the Midst of a Pandemic: International Lessons for Math Teachers," which we initiated in summer 2020. I was the lead math reviewer on a project to evaluate the nation's K-12 curriculum standards organized by the non-profit Fordham Institute, resulting in two reports: The State of State Standards Post-Common Core, released August 2018, and The State of the Sunshine State's Standards: The Florida B.E.S.T. Edition, released June 2020. Additional service includes: Board of Directors, Math for America Boston (2012-2021), editor of the CBMS book series Issues in Mathematics Education (2006-2020), Massachusetts Board of Elementary and Secondary Education's Math-Science Advisory Council (2007-2013), 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: The "Rule of Signs" in Arithmetic (joint with Roger Howe) and The Equal Sign, Equations, and Functions. 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 am co-PI on a 6-year (2020-2026), $1.78M, NSF grant "Developing Exemplary Mathematics Teacher Leaders for High-Need Schools: Content, Equity and Leadership" which seeks to connect mathematicians, mathematics educators, teachers, and mentor experts to create a professional community focused on mathematics content, equitable teaching and learning approaches, and teacher leadership development. This project is joint with my BC colleagues Professors Lillie Albert of the Lynch School of Education and Human Development and Juliana Belding and C.K. Cheung of the Math Department, and with Matthew McLeod at the EDC. This work builds on my joint 7-year (2013-2020), $1.6M, NSF-funded project "Exemplary Mathematics Educators for High-need Schools." A video about that project may be found here, and a report on it, which was presented at ICME-14 in 2021, may be found here.

### Public Advocacy of Math Education

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. And I discuss international aspects of mathematics education in an editorial written jointly with Profs. T. Lott Adams and P. Seshaiyer in the December 2023 issue of Mathematics Teacher: Learning & Teaching PK–12.

### Work with Graduate Students and Case Studies

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. My involvement with this area has continued through my service on AMS-MAA Joint Committee on TAs and Part-Time Instructors, 2014-2020, including serving as Chair of the committee 2016-2020.

### 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. AMS service includes: ICM2002 Grants Selection Panel, the Working Group on Preparation for Technical Careers (2007–2008), AMS representative to the JPBM committee on The Partnership for Mathematical Sciences in America (2009), Joint Math Meetings Travel Grants Selection Committee (Chair, 2009 and 2010), New England Regional Committee of the AMS's Next Generation Campaign (2018-2019), Committee on the Profession (2019-2022). MAA service includes: AMS-MAA Joint Committee on TAs and Part-Time Instructors (member 2014-2020; Chair, 2016-2020), MAA Council on the Profession (2016-2020), mentor for the MAA's Project NExT, 2002-2004 and 2017-2019. I am also a mentor for the Math Alliance.

### 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

Simons Fellowship in Mathematics, 2021

AMS Award for Impact on the Teaching and Learning of Mathematics, 2021

### Photos

Here are a few photos from various trips and conferences.

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

Purdue University, Department of Mathematics External Review Committee, September 2024.

VII Latin American and Caribbean Congress on Mathematics, João Pessoa, Brazil, August 2024.

Solvable Lattice Models, Number Theory and Combinatorics, Trinity College Dublin, Ireland, June 2024. Conference co-organizer.

International Scientific Advisory Committee meeting, Centro de Modelamiento Matemático, Universidad de Chile, June 2024.

What, Where, and for What Purpose Is the Mathematics in Mathematics Teacher Education?, A conference in honor of Jim Lewis, University of Nebraska-Lincoln, May-June 2024.

Automorphic Forms and L-Functions, Vanderbilt University, May 2024.

Bhaskaracharya celebrating Harish-Chandra, Bhaskaracharya Pratishthana, Pune, India, hybrid/on-line, May 2024.

Question & Answer Seminar, CMSA, Harvard, February 2024.

Arithmetic Quantum Field Theory, Center of Mathematical Sciences and Applications, Harvard, Spring 2024. Program co-organizer.

École Polytechnique, Paris, working visit to carry out joint research with theoretical physicists Guillaume Bossard and Axel Kleinschmidt, January 2024.

BC-TCD Maths Colloquium Series, Trinity College Dublin, Ireland, December 2023.

Colloquium, Brown University, December 2023.

Number Theory Seminar, Boston University, November 2023.

24th Autumn Workshop on Number Theory, Hokkaido University, Sapporo, Japan, Fall 2023.

PAC-Math Conference/working group on Math TA Development Program Self-Assessment, University of Tennessee, Knoxville, October 2023.

New Connections Between Physics and Number Theory, Pollica Physics Centre, Italy, June 2023. Conference co-organizer.

Center For Advanced Mathematical Sciences, American University of Beirut, Lebanon, March 21, 2023 (On-line).

AMS Special Session on Automorphic Forms and Representation Theory, Joint Math Meetings, Boston, January 2023. Special session co-organizer.

AMS Special Session on Mathematics Standards, Equity, Policy, and Politics, Joint Math Meetings, Boston, January 2023.

Langlands Program: Number Theory and Representation Theory, BIRS/CMO, Oaxaca, México, Fall 2022. (Hybrid format conference.)

Number Theory Seminar, University of Nottingham, September 2022.

Number Theory Seminar, University of Sheffield, September 2022.

New Connections in Number Theory and Physics, Newton Institute for Mathematical Sciences, Cambridge, England. August 1, 2022 to September 23, 2022. Programme co-organizer. Also co-organizer for the two workshops attached the program.

Making the bridge: Exploring new connections between number theory and physics, Newton Institute for Mathematical Sciences, Cambridge, England. August 1 to 5, 2022. Series of 3 lectures; videos are available on the workshop web page. [This is the first workshop attached to the 8-week programme listed directly above.]

APAW 2022 (A Pair of Automorphic Workshops in 2022), University of Oregon, July 2022. Graduate Instructional Workshop, Mini-course of 4 lectures. Notes by Pan Yan are available on the workshop website.

US-ICME, Topic Study Group presentation, April 2022. (On-line.)

Tel-Aviv University, working visit to carry out joint research with Prof. David Ginzburg, March-April 2022.

Recent Developments in Automorphic Forms and Representations of p-adic Groups, AMS Special Session, Spring Central Sectional Meeting (formerly at Purdue University), March 2022. (On-line.)

Periods, functoriality and L-functions, Centre International de Rencontres Mathématiques, France, January 2022. (Hybrid format conference.)

A Roundtable Discussion on Math Education in the U.S., National Museum of Mathematics, July 2021. (On-line.)

The 14th International Congress on Mathematics Education, Shanghai, China, July 2021 (hybrid). Topic Study Group presentation and Co-organizer of a Discussion Group on Roles for Mathematicians in Math Education.

New Connections in Number Theory and Physics, Newton Institute for Mathematical Sciences, Cambridge, England. On-line Workshop May 24-28, 2021, Co-organizer.

Berkeley-Caltech-Stanford Number Theory Seminar, April 2021. (On-line.)

External Review Committee, Department of Mathematics, Texas Christian University. March 2021.

Recent Developments in Automorphic Representations, AMS Special Session, Spring Eastern Section Meeting, March 2021. (On-line.)

Number Theory Seminar, Rutgers University, November 2020. (On-line.)

Colloquium, Rutgers University, October 2020. (On-line.)

Lunch in the Time of Covid, panelist, September 2020. (On-line.)

Thesis defense of Navya Teja Mandava, University of Buffalo, SUNY, August 2020.

Fields Institute Number Theory Seminar, University of Toronto, August 2020. On-line; video of my talk, slides and a video lecture and slides on background material are all available here.

Algebraic Geometry and Representation Theory Seminar, Weizmann Institute of Science, July 2020. On-line; video here.

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