Heekyoung Hahn
Associate Research Professor of Mathematics
Number Theory in the large: Automorphic represenations, Trace formula, Laplacian eigenfunctions and Littlewood-Richardson coefficients
Current Research Interests
Langlands' beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic groups. Historically, there are important antecedents of this in the relationship between Artin L-functions and Brauer theory, a beautiful subject combining Galois theory and finite group theory. At this point very little is known about the general picture and thus the community is in dire need of concrete examples. My current work is devoted to producing such examples using techniques from the representation theory of finite groups and algebraic groups.
Current Appointments & Affiliations
- Associate Research Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2020
Contact Information
- 220 Physics, Durham, NC 27708
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hahn@math.duke.edu
(919) 660-2850
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Personal Website
- Background
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Education, Training, & Certifications
- Ph.D., University of Illinois, Urbana-Champaign 2004
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Duke Appointment History
- Assistant Research Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 2014 - 2020
- Visiting Assistant Professor in the Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 2012 - 2014
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Leadership & Clinical Positions at Duke
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Director of Outreach and Public Lectures, August 2019
Associate Director of Undergraduate Research and Prizes, August 2019
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Director of Outreach and Public Lectures, August 2019
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Academic Positions Outside Duke
- Member, Institute for Advanced Study. 2018
- Visiting Scholar, Korea Institute for Advanced Study. 2016
- Visiting Assistant Professor, McGill University. 2010 - 2012
- Tenure Track Assistant Professor, Univeristy at Albany (SUNY). 2007 - 2011
- Visiting Assistant Professor, University of Rochester. 2004 - 2007
- Recognition
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In the News
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JUN 1, 2018
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Awards & Honors
- Bass Connections: Education and Human Development. Duke University. 2013
- University-wide Excellence in Undergraduate Teaching. University of Illinois at Urbana--Champaign. 2002
- University-wide Excellence in Undergraduate Teaching. University of Illinois at Urbana-Champaign. 2001
- University-wide Excellence in Undergraduate Teaching. University of Illinois at Urbana-Champaign. 2000
- University-wide Excellence in Undergraduate Teaching. University of Illinois at Urbana-Champaign. 1999
- Expertise
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Subject Headings
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Global Scholarship
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Research
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- Research
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Selected Grants
- Re:boot Number Theory awarded by National Security Agency 2016 - 2018
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Fellowships, Supported Research, & Other Grants
- Faculty Travel Support awarded by College of Art & Science, Duke University 2018
- Member of the IAS awarded by Institute for Advanced Study 2018
- Faculty Travel Support awarded by College of Art & Science, Duke University 2017
- Visiting Scholar awarded by Korea Institute for Advanced Study (KIAS) 2016
- Discovery Grant awarded by NSERC (386551-2010-RGPIN) 2010 - 2012
- Postdoctoral Support awarded by NSF FRG (DMS 0244660), University of Rochester 2005 - 2007
- University Fellowship awarded by University of Illinois at Urbana-Champaign 2004
- Predoctoral Fellowship awarded by University of Illinois at Urbana-Champaign 2003
- Publications & Artistic Works
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Selected Publications
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Books
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Berndt, Bruce C. Ramanujan's Forty Identities for the Rogers-Ramanujan Functions. American Mathematical Soc., 2007.
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Getz, J. R., and H. Hahn. An introduction to automorphic representations with a view towards trace formulae, n.d.Link to Item
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Academic Articles
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Hahn, H. “On Classical groups detected by the triple tensor product and the Littlewood–Richardson semigroup.” Research in Number Theory 2, no. 1 (December 1, 2016). https://doi.org/10.1007/s40993-016-0049-3.Full Text
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Hahn, H. “On tensor third L-functions of automorphic representations of GLn(AF).” Proceedings of the American Mathematical Society 144, no. 12 (January 1, 2016): 5061–69. https://doi.org/10.1090/proc/13134.Full Text
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Getz, J. R., and H. Hahn. “A general simple relative trace formula.” Pacific Journal of Mathematics 277, no. 1 (January 1, 2015): 99–118. https://doi.org/10.2140/pjm.2015.277.99.Full Text
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Hahn, H., S. Akhtari, C. David, and L. Thompson. “Distribution of square-free values of sequences associated with elliptic curves.” Contemporary Mathematics 606 (October 16, 2013): 171–88.
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Getz, J. R., and H. Hahn. “ALGEBRAIC CYCLES AND TATE CLASSES ON HILBERT MODULAR VARIETIES.” International Journal of Number Theory, no. 2 (2013): 1–16.
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Hahn, H. “A simple twisted relative trace formula.” International Mathematics Research Notices 2009, no. 21 (December 1, 2009): 3957–78. https://doi.org/10.1093/imrn/rnp075.Full Text
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Hahn, H. “Eisenstein series associated with Γ0(2).” Ramanujan Journal 15, no. 2 (February 1, 2008): 235–57. https://doi.org/10.1007/s11139-007-9075-z.Full Text
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Hahn, H. “Convolution sums of some functions on divisors.” Rocky Mountain Journal of Mathematics 37, no. 5 (December 1, 2007): 1593–1622. https://doi.org/10.1216/rmjm/1194275937.Full Text
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Hahn, H. “On zeros of Eisenstein series for genus zero Fuchsian groups.” Proceedings of the American Mathematical Society 135, no. 8 (August 1, 2007): 2391–2401. https://doi.org/10.1090/S0002-9939-07-08763-1.Full Text
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Ablowitz, M. J., S. Chakravarty, and H. Hahn. “Integrable systems and modular forms of level 2.” Journal of Physics A: Mathematical and General 39, no. 50 (December 15, 2006): 15341–53. https://doi.org/10.1088/0305-4470/39/50/003.Full Text
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Hahn, H. “Septic analogues of the Rogers-Ramanujan functions.” Acta Arithmetica 110, no. 4 (January 1, 2003): 381–99. https://doi.org/10.4064/aa110-4-5.Full Text
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Chan, H. H., H. Hahn, R. P. Lewis, and S. L. Tan. “New Ramanujan-Kolberg type partition identities.” Mathematical Research Letters 9, no. 5–6 (January 1, 2002): 801–11. https://doi.org/10.4310/mrl.2002.v9.n6.a8.Full Text
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Hahn, Heekyoung. “Poles of triple product $L$-functions involving monomial represenations.” International Journal of Number Theory, n.d.Open Access Copy Link to Item
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- Teaching & Mentoring
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Recent Courses
- MATH 218: Matrices and Vector Spaces 2020
- MATH 718: Matrices and Vector Spaces 2020
- MATH 221: Linear Algebra and Applications 2019
- MATH 371: Combinatorics 2019
- MATH 721: Linear Algebra and Applications 2019
- MATH 221: Linear Algebra and Applications 2018
- MATH 721: Linear Algebra and Applications 2018
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Advising & Mentoring
- In terms of undergraduate research mentoring, I have a proven track record of mentoring undergraduate students, especially women, who later go on to study mathematics or other STEM disciplines in graduates school. I have already supervised 7 female undergraduate students: Brigid Larkin (Duke, Summer 2014), Mathilde Gerbelli-Gauthier (McGill, Summer 2012), Catherine Hilgers (McGill, Summer 2011), Crystel Bujold (McGill, Spring 2011, co-supervised with A. Granville), Kelly C. Stange (SUNY at Albany, Spring 2010), N. Miya Sylvester (University of Rochester, Spring 2006) and Fabiana Ferrancina (University of Rochester, Spring 2006).
- Scholarly, Clinical, & Service Activities
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Presentations & Appearances
- Poles of triple product L-functions involving monomial representations. Partition Theory and Related Topics. AMS Session. November 2019 2019
- Poles of triple product L-functions involving monomial representations. Analytic and Combinatorial Number Theory: The Legacy of Ramanujan. University of Illinois at Urbana-Champaign. June 2019 2019
- Poles of triple product L-functions of monomial representations. AMS Session on Recent Developments in Automorphic Forms. AMS. March 2019 2019
- The Ramanujan congruences for partitions. Society for Undergraduate Mathematics (SUM series). NCSU. March 2019 2019
- Langlands' beyond endoscopy proposal and related questions on algebriac groups and combinatroics. University of Rochester. October 2018 2018
- Langlands' beyond endoscopy proposal and related questions on algebriac groups and combinatroics. Bryn Mawr College. April 2018 2018
- Langlands' beyond endoscopy proposal and related questions on algebriac groups and combinatroics. Algebraic and Combinatorics Seminar. NCSU. September 2017 2017
- Langlands' beyond endoscopy proposal and detection of classical groups. Automorphic Forms and Related Topics. Vietnam Institute Advanced Study in Math (VIASM). August 2017 2017
- Langlands' beyond endoscopy proposal and the Littlewood-Richardson semigroup. AMS Special Session on Automorphic Forms and Related Topics. AMS. October 2016 2016
- Langlands' beyond endoscopy proposal and the Littlewood-Richardson semigroup. Colloquium. Sookmyung Women's University. August 2016 2016
- Langlands' beyond endoscopy proposal and the Littlewood-Richardson semigroup. Number Theory Seminar. Korea Institute for Advanced Study (KIAS). August 2016 2016
- Langlands' beyond endoscopy proposal and the Littlewood-Richardson semigroup. Number Theory Seminar. Yonsei University. August 2016 2016
- Langlands' beyond endoscopy proposal and the Littlewood-Richardson semigroup. Langlands Program Seminar. CUNY. April 2016 2016
- Langlands' beyond endoscopy proposal and the Littlewood-Richardson semigroup. Automorphic Forms Workshop. Wake Forest University. March 2016 2016
- On tensor third L-functions of automorphic representations of GL_n(A). Grad/Fac seminar. Duke University. November 2015 2015
- On Symmetric third L-functions of automorphic representations of GL_9(A_F). Illinois Number Theory Conference. August 2015 2015
- A general simple relative trace fromula. Number Theory Seminar. University of Illinois at Urbana-Champaign. April 2015 2015
- Relative trace formulae and their applications. Colloquium. Emory University. January 2015 2015
- A general simple relative trace fromula. AMS Special Session. University of North Carolina at Greensboro. November 2014 2014
- Relative Weyl laws. Emerging Leaders and Evolving Frontiers in Anayltic Number Theory. Hausdorff Cenetr for Mathematics. July 2014 2014
- Algebraic cycles and Tate classes on Hilbert modular varieties. South Eastern Regional Meetings on Numbers. High Point University. April 13, 2013 2013
- Distribution of square-free values of sequences associated with elliptic curves. Grad/Fac seminar. Duke University. February 2013 2013
- Algebraic cycles and Tate classes on Hilbert modular varieties. Algebra and Combinatorics Seminar. North Carolina State University. November 2012 2012
- Algebraic cycles and Tate classes on Hilbert modular varieties. Number Theory Seminar. University of North Carolina at Chapel Hill. November 2012 2012
- Algebraic cycles and Tate classes on Hilbert modular varieties. Quebec-Vermont Number Theory Seminar. Concordia University, Canada. March 2012 2012
- Algebraic cycles and Tate classes on Hilbert modular varieties. Number Theory and Representation Theory Seminar. University of Maryland at College Park. January 2012 2012
- A simple twisted relative trace formula. Canada Number Theory Association Meeting XI. Acadia University, Canada. July 2010 2010
- A simple relative trace fomulae. Graduate Student seminar. University at Albany. April 2008 2008
- On zeros of Eisenstein series for genus zero Fuchsian groups. Partitiions, q-series and Modula forms. University of Florida at Gainesville. March 2008 2008
- The Selberg trace formula. Center for Women in Mathematics. Smith College. March 2008 2008
- On zeros of Eisenstein series for genus zero Fuchsian groups. Algebra and Number Theory Seminar. University at Albany. October 2007 2007
- On zeros of Eisenstein series for genus zero Fuchsian groups. Colloquium. University at Albany. February 2007 2007
- On zeros of Eisenstein series for genus zero Fuchsian groups. Number Theory Seminar. Johns Hopkins University. November 2006 2006
- On zeros of Eisenstein series for genus zero Fuchsian groups. Number Theory and Random Matrix Theory. University of Rochester. June 2006 2006
- On zeros of Eisenstein series for genus zero Fuchsian groups. AMS special session on Arithmetic Geometry and Modular Forms. AMS. April 2006 2006
- On zeros of Eisenstein series for genus zero Fuchsian groups. Algebra and Number Theory Seminar. University of Rochester. April 2006 2006
- On zeros of Eisenstein series for genus zero Fuchsian groups. Five College Number Theory Seminar. Amherst College. April 2006 2006
- Integrable systems and modular forms of level 2. Algebra and Number Theory Seminar. University of Rochester. December 2005 2005
- Convlotion sums for certain dividor functions. Additive Number Theory Conference. University of Florida. November 2004 2004
- Convlotion sums for certain dividor functions. AMS Session on Special Functions and Orthogonal Polynomials. AMS. October 2004 2004
- Eisenstein series associated with Gamma_0(2). Algebra and Number Theory Seminar. University of Rochester. September 2004 2004
- Eisenstein series associated with Gamma_0(2). Number theory seminar. UIUC. April 2004 2004
- Eisenstein series associated with Gamma_0(2). Graduate Student seminar. UIUC. February 2004 2004
- Eisenstein series associated with Gamma_0(2). AMS Joint Math Meeting. AMS. January 2004 2004
- Eisenstein series associated with Gamma_0(2). Midwest Number Theory Conference. University of Wisconsin. October 2003 2003
- Septic analogues of the Rogers--Ramanujan functions. Number theory seminar. UIUC. March 2003 2003
- New Ramanujan-Kolberg type partition identities. AMS Special Session on Combinatorics and Special Functions. AMS. October 2002 2002
- New Ramanujan--Kolberg type partition identities. Illinois Number Theory Conference. UIUC. May 2002 2002
- New Ramanujan--Kolberg type partition identities. Number theory seminar. UIUC. April 2002 2002
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Outreach & Engaged Scholarship
- Co-Director. Summer Workshop in Math (SWiM2019). Duke University. June 18, 2019 - June 28, 2019 2019
- Invited Speaker. Girls Exploring Math (GEM). Duke University. June 2019 2019
- Co-Director. Duke Opportunitites in Math (DOmath2019). Duke University. May 20, 2019 - July 12, 2019 2019
- Co-Organizer. Renaissance Math Event. Duke Math and Medieval/Renaissance Studies. January 2019 2019
- Organizer. Public Lectures Unveling Math (PLUM). 2019 2019
- Co-Director. Summer Workshop in Math (SWiM2018). Duke University. June 19, 2018 - June 29, 2018 2018
- Co-Director. Duke Opportunities in Math (DOmath2018). Duke University. May 2018 - July 2018 2018
- Organizer. Public Lectures Unveling Math (PLUM). Duke University. 2018 2018
- Co-Director. Summer Workshop in Math (SWiM2017). Duke University. June 20, 2017 - June 30, 2017 2017
- Co-Director. Duke Opportunities in Math (DOmath2017). Duke University. May 2017 - July 2017 2017
- Organizer. Public Lectures Unveling Math (PLUM). Duke University. 2017 2017
- Co-Director. Summer Workshop in Math (SWiM2016). Duke University. June 13, 2016 - June 23, 2016 2016
- Organizer. Public Lectures Unveiling Math (PLUM). Duke University. 2016 2016
- Founder and Organizer. Public Lectures Unveiling Math (PLUM). Duke University. 2015 2015
- No Apologies Campaign. Alice M. Baldwin Scholars. Duke University. September 2014 2014
- Speaker. Math Slam. Duke University. September 2013 2013
- Bass Connections Faculty Team Leader. Math Before Symbols. Duke University. August 2013 - May 2014 2013 - 2014
- Mentor. The Noetherian ring. Duke University. September 2012 2012
- Judge. Greater Matropolitan NY Math Fair. March 2009 2009
- Speaker. Societies of Undergrdaute Math Students (SUMS). McGill University. 2009 2009
- Faculty Advisor. Graduate Students Seminar. University at Albany (SUNY). September 2007 2007
- Faculty Co-Advisor. Metting for Workshop Leaders. University of Rochester. January 2005 2005
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Service to the Profession
- Participant. Geometric realizations of Jacquet-Langlands correspondences. AIM Workshop. November 2019 2019
- Participant. Hawaii Number Theory Conference (HINT 2019). March 2019 2019
- Participant. Porquerolles Conference. CIRM. September 2018 2018
- Participant. Representation theory and analysis on locally symmetric spcases. Institute for Advanced Study. April 2018 2018
- Algebra and Number Theory Seclection Committee Memeber. International Conference. Korean Women in Mathematical Sciences (KWMS). June 2017 2017
- Participant. Workshop on Mod p/p-adic Langlands programs. Korean Institute for Advanced Study (KIAS). August 2016 2016
- Co-Organizer. Reboot Workshop in Analytic Number Theory. Duke University. March 2016 2016
- Participant. Workshop on Automorphic Kernel Functions. AIM. December 2015 2015
- Participant. Analysis, Spectra, and Number Theory. Princeton University and IAS. December 2014 2014
- Workshop Team Leader. Women In Numbers. Banff International Research Station. November 2011 2011
- Participant. The Bellairs Workshop in Number Theory. McGill University. May 2011 2011
- Participant. Joint Montreal-Toronto Meeting II. Fields Institute. April 2011 2011
- Member. Committee of Undergraduate Affairs. McGill University. September 2010 2010
- Grant referee. 2010 2010
- Participant. Illinois Number Theory Conference. UIUC. March 2009 2009
- Member. College Faculty Council. University at Albany. September 2008 2008
- Member. Mathematics Undergraduate Committee. University at Albany. September 2007 2007
- Journal referee. 2007 2007
- Participant. Number Theory and Random Matrix Theory. University of Rochester. June 2006 2006
- Co-Organizer. Algebra and Number Theory Seminar. University of Rochester. September 2005 2005
- Student Representative. Graduate Affairs Committee. UIUC. September 2003 2003
- Participant. CBMS--The web of modularity. UIUC. June 2003 2003
- Co-Organizer. Numner Theory Seminar. UIUC. 2002 2002
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Service to Duke
- Associate Director of Undergraduate Research and Prizes. Duke Mathematics Department. August 2019 2019
- Director of Outreach and Public Lectures. Duke Mathematics Department. August 2019 2019
- Co-Director. Summer Workshop in Math (SWiM2019). Duke University. June 18, 2019 - June 28, 2019 2019
- Co-Director. Duke Opportunities in Math (DOmath2019). Duke University. May 20, 2019 - July 12, 2019 2019
- Co-Organizer. Renaissance Math Event. Duke Math and Medieval/Renaissance Studies. January 2019 2019
- Organizer. Public Lectures Unveling Math (PLUM). Duke University. 2019 2019
- Faculty Participant. Major Fair. Duke University. October 2018 2018
- Co-Director. Summer Workshop in Math (SWiM2018). Duke University. June 19, 2018 - June 29, 2018 2018
- Co-Director. Duke Opportunities in Math (DOmath2018). Duke University. May 2018 - July 2018 2018
- Organizer. Public Lectures Unveling Math (PLUM). Duke University. 2018 2018
- Faculty participant. Major Fair. Mathematics, Duke University. October 2017 2017
- Co-Director. Summer Workshop in Math (SWiM2017). Duke University. June 20, 2017 - June 30, 2017 2017
- Co-Director. Duke Opportunities in Math (DOmath2017). Duke University. May 2017 2017
- Organizer. Public Lectures Unveling Math (PLUM). Duke University. 2017 2017
- Faculty participant. Major Fair. Mathematics, Duke University. October 2016 2016
- Co-Director. Summer Workshop in Math (SWiM2016). Duke University. June 13, 2016 - June 23, 2016 2016
- Course Coordinator. Math202. Duke University. 2016 2016
- Organizer. Public Lectures Unveling Math (PLUM). Duke University. 2016 2016
- Co-Organizer. 100 Years of General Relativity. Duke University. October 2015 2015
- Founder and Organizer. Public Lectures Unveiling Math (PLUM). Duke University. August 2015 2015
- Faculty Advisor. Kenan-Biddle Partnership. January 2015 2015
- A&S Academic Advisor. September 2014 2014
- Faculty Co-Advisor. Duke University Math Union (DUMU). September 2014 2014
- Course Coordinator. Math202. 2014 2014
- Co-Founder and Co-Organizer. Number Theory Seminar. Duke University. 2012 2012
- Course Coordinator. Math202. 2012 2012
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