### Postal Address:

Mathematics Department

American University of Beirut (AUB)

Bliss Street

Beirut, LEBANON

**Email:** kmakdisi@aub.edu.lb

**Website:** https://sites.aub.edu.lb/kmakdisi/

**Office:** AUB extension 4234

**Office (Math Dept Secretary):** AUB extension 4210

**Fax:** (+961) 1 365087

**AUB switchboard numbers:** (+961) 1 340460, 350000, 374374, and 374444.

### Mathematical Research Interests:

- Number theory, including algorithmic number theory; automorphic forms and representation theory.

### Education:

- Ph.D. in Mathematics, Princeton University, November 1993. Advisor: Goro Shimura.
- Fulbright Scholar, University of Bonn, October 1988-July 1989. Attended graduate-level courses and seminars in the mathematics department.
- B.S. in Mathematics and Electrical Engineering (double major), summa cum laude, with distinction in both majors, Yale University, May 1988.

### Work Experience:

- February 2022-July 2022: Member, Institute for Advanced Study (IAS), Princeton, New Jersey.
- February 2021-January 2022: Visiting Scientist, Max Planck Institute for Mathematics, Bonn.
- October 1999-present: Full Professor (2009-), Associate Professor (2003-2009), Assistant Professor (1999-2003), Mathematics Department, American University of Beirut (AUB); also, Fellow, Center for Advanced Mathematical Sciences (CAMS), at AUB (1999-2012). On leave for three semesters, starting February 2021.
- Academic year 1998-1999: Postdoctoral Fellow, Mathematics Department, McGill University and CICMA (Centre interuniversitaire en calcul mathematique algebrique); jointly, Adjunct Assistant Professor, Mathematics Department, Concordia University.
- July 1993-June 1998: Benjamin Peirce Assistant Professor, Mathematics Department, Harvard University (on leave 1994-1995).
- Academic year 1994-1995: Member, School of Mathematics, Institute for Advanced Study (IAS), Princeton, New Jersey.
- 1987 (summer): Engineering Assistant, Computer-Aided Design group, Lawrence Livermore National Laboratory. Worked on algorithms for VLSI circuit design.

### Publications and Preprints:

My profile on Google Scholar

All my Arxiv preprints

- “An analog of the Edwards model for Jacobians of genus 2 curves,” joint with E. V. Flynn, Research in Number Theory 10 (2024), no. 2, Paper No. 32.
- published version: https://doi.org/10.1007/s40993-024-00518-5
- preprint: https://arxiv.org/abs/2211.01450

- “Values of L-Series of Hecke Eigenforms,” joint with W. Kohnen and W. Raji, Journal of Number Theory 211 (2020), 28-42.
- published version: https://doi.org/10.1016/j.jnt.2019.10.014
- preprint: http://arxiv.org/abs/1904.04219

- “Fake proofs for identities involving products of Eisenstein series,” in Automorphic Forms and Related Topics, Contemporary Mathematics vol. 732, 133-138 (AMS, 2019), eds. S. Anni, J. Jorgenson, L. Smajlovic, and L. Walling.
- AMS Bookstore listing for CONM-732: https://bookstore.ams.org/conm-732
- preprint: http://arxiv.org/abs/1612.08434

- “Modular forms constructed from moduli of elliptic curves, with applications to explicit models of modular curves” (expository), in Automorphic Forms and Related Topics, Contemporary Mathematics vol. 732, 139-154 (AMS, 2019), eds. S. Anni, J. Jorgenson, L. Smajlovic, and L. Walling.
- AMS Bookstore listing for CONM-732: https://bookstore.ams.org/conm-732
- preprint: http://arxiv.org/abs/1612.08432

- “Upper bounds for some Brill-Noether loci over a finite field,” International Journal of Number Theory 14 (2018), no. 3, 739-749.
- published version: http://www.worldscientific.com/doi/abs/10.1142/S1793042118500471
- preprint: http://arxiv.org/abs/1609.03349

- “On Jacobian group arithmetic for typical divisors on curves,” Research in Number Theory 4 (2018), no. 1, article 3, 29 pp.
- published version: https://link.springer.com/article/10.1007/s40993-018-0101-6
- preprint: http://arxiv.org/abs/1310.6324

- “Periods of modular forms and identities between Eisenstein series,” joint with W. Raji, Mathematische Annalen 367 (2017), no. 1, 165-183.
- published version: https://link.springer.com/article/10.1007/s00208-016-1380-7
- preprint: http://arxiv.org/abs/1402.1854

- “Moduli interpretation of Eisenstein series,” International Journal of Number Theory 8 (2012), no. 3, 715-748.
- published version: http://www.worldscinet.com/ijnt/08/0803/S1793042112500418.html
- preprint: http://arxiv.org/abs/0903.1439

- “On the maps from X(4p) to X(4),” joint with S. Jaafar, International Journal of Number Theory 5 (2009), no. 5, 831-844.
- published version: http://www.worldscinet.com/ijnt/05/0505/S1793042109002390.html
- preprint: http://arxiv.org/abs/math.NT/0702545

- “Generating functions for Hecke operators,” joint with H. Al Hajj Shehadeh and S. Jaafar, International Journal of Number Theory 5 (2009), no. 1, 125-140.
- published version: http://www.worldscinet.com/ijnt/05/0501/S1793042109001979.html
- preprint: http://arxiv.org/abs/math.NT/0610962

- “On inverting the Koszul complex,” Communications in Algebra 36 (2008), 1830-1837.
- published version: https://doi.org/10.1080/00927870801941044
- preprint: http://arxiv.org/abs/math.RT/0702876

- “Fast Jacobian group operations for C_{3,4} curves over a large finite field,” joint with F. Abu Salem, LMS Journal of Computation and Mathematics 10 (2007), 307-328.
- published version, with Magma code: http://dx.doi.org/10.1112/S146115700000142X
- preprint: http://arxiv.org/abs/math.NT/0610121

- “Asymptotically fast group operations on Jacobians of general curves,” Mathematics of Computation 76 (2007), 2213-2239.
- published version: http://www.ams.org/mcom/2007-76-260/S0025-5718-07-01989-8/home.html
- preprint: http://arxiv.org/abs/math.NT/0409209

- “Linear algebra algorithms for divisors on an algebraic curve,” Mathematics of Computation 73 (2004), 333-357.
- published version: http://www.ams.org/mcom/2004-73-245/S0025-5718-03-01567-9/home.html
- preprint: http://arxiv.org/abs/math.NT/0105182

- “An exact sequence in the representation theory of SL(2),” Communications in Algebra 31 (2003), 4153-4160.
- published version: https://doi.org/10.1081/AGB-120022783
- preprint: https://sites.aub.edu.lb/kmakdisi/cv/sympowers/

- “On the curves associated to certain rings of automorphic forms,” Canadian Journal of Mathematics 53 (2001), 98-121.
- published version: https://doi.org/10.4153/CJM-2001-005-5
- preprint: https://sites.aub.edu.lb/kmakdisi/cv/quaternion/

- “Representations of SL(2) x G,” in Automorphic Forms, Automorphic Representations, and Arithmetic, Proceedings of Symposia in Pure Mathematics, vol. 66, no. 2, 251-276 (American Mathematical Society, 1999), eds. R. Doran, Z.-L. Dou, and G. Gilbert.
- AMS Bookstore listing for PSPUM-66: https://bookstore.ams.org/pspum-66
- preprint: https://sites.aub.edu.lb/kmakdisi/cv/sl2g/

- “On the Iwahori-Hecke algebra of a p-adic group,” joint with N. Chriss, International Mathematical Research Notices (1998), no. 2, 85-100.
- published version: http://imrn.oxfordjournals.org/cgi/content/citation/1998/2/85
- preprint: https://sites.aub.edu.lb/kmakdisi/cv/papwnc/

- “Relations between Fourier coefficients of nonholomorphic Hilbert modular forms of half-integral weight and special values of Dirichlet series,” Ph.D. thesis, Princeton University, 1993, revised version published as “On the Fourier coefficients of nonholomorphic Hilbert modular forms of half-integral weight,” Duke Mathematical Journal 84 (1996), 399-452.
- published version: https://projecteuclid.org/euclid.dmj/1077243836
- preprint: https://sites.aub.edu.lb/kmakdisi/cv/thes/

### Memorial article:

- “Memories of Goro Shimura,” joint with D. Blasius, T. Bluher, H. Hida, K. Ribet, A. Silverberg, and H. Yoshida, Notices of the American Mathematical Society 67 (2020), no. 5, 677-689.
- published version: https://doi.org/10.1090/noti2076

### Talks since 2003:

- An analog of the Edwards model for Jacobians of genus 2 curves, Explicit methods in automorphic forms and arithmetic geometry, Hamilton Mathematics Institute, Trinity College Dublin, Ireland, June 2023.
- Edwards models for elliptic curves and abelian surfaces, 7th Mini-symposium of the Roman number theory association, Universita Roma Tre, Rome, May 2023.
- An analog of the Edwards model for Jacobians of genus 2 curves, SAGA conference (Symposium on Arithmetic Geometry and its Applications), C.I.R.M., Luminy, February 2023.
- Meromorphic functions and projective embeddings of abelian varieties (survey talk), AUB Mathematics Department seminar, December 2022.
- Searching for “moduli-friendly” automorphic forms, Number Theory Lunch Seminar, Max Planck Institute for Mathematics, Bonn, September 2021 (online talk).
- Moduli of elliptic curves over
**C**, with application to obtaining equations for modular curves, mini-course (6 hours total) at the Harish-Chandra Research Institute Allahabad (HRI), January 2020. - Jacobian group operations for typical divisors on curves, AMS-MAA Joint Mathematics Meetings, Baltimore, January 2019.
- Periods of modular forms and identities between Eisenstein series, Algebraic Geometry and Number Theory conference, Indian Statistical Institute, Bangalore, December 2017.
- Jacobian group operations for typical divisors on curves, Workshop on Algorithms in Number Theory and Arithmetic Geometry, University of Leiden, August 2017.
- Bounding Brill-Noether loci over a finite field, LSMS Annual Conference (Lebanese Society for Mathematical Sciences), University of Balamand, April 2017.
- (i) Explicit equations for modular curves, two lectures given for a mini-course, and (ii) Periods of modular forms and identities between Eisenstein series, conference talk, at the Building Bridges 3 Summer School and Workshop on Automorphic Forms and Related Topics, Sarajevo, July 2016.
- Eisenstein series of weight 1, and Periods of modular forms and identities between Eisenstein series, two talks given at POSTECH, Pohang, South Korea, May 2016.
- The ring of modular forms on Gamma(N), Mathematics Department Seminar, Notre Dame University, Louaize, Lebanon, April 2016.
- Algorithmic representation of a curve and its Jacobian, conference on Arithmetic Geometry: Explicit Methods and Applications, Moscow Center for Continuous Mathematical Education, December 2015.
- Bounding Brill-Noether loci over finite fields, with applications to Jacobian arithmetic, AGCT-15 Conference (Arithmetic, Geometry, Cryptography and Coding Theory),

C.I.R.M., Luminy, May 2015. - Typical divisors on curves and some applications to Jacobian arithmetic (survey talk), AUB Mathematics Department seminar, February 2015, repeated at Lebanese University Mathematics Department seminar, February 2015.
- Ideal generating sets and Las Vegas algorithms for colon ideals on curves, Number Theory in Kaiserslautern 20 conference, November 2014.
- On Jacobian group arithmetic for typical divisors on curves, Moduli interpretation of Eisenstein series, and Periods of modular forms and identities between Eisenstein series, three talks presented at Universite Bordeaux, Mathematics

department and INRIA, July 2014. - Eisenstein series of weight 1, Boston College Number Theory and Algebraic Geometry Seminar, April 2014.
- Eisenstein series of weight 1, Princeton University/IAS Number Theory Seminar, March 2014.
- Eisenstein series of weight 1, Brown University Algebraic Geometry Seminar, March 2014.
- Periods of modular forms and identities between Eisenstein series, Boston University Number Theory Seminar, March 2014.
- Periods of modular forms and identities between Eisenstein series, MIT Number Theory Seminar, February 2014.
- Eisenstein series of weight 1, Harvard University Number Theory Seminar, February 2014.
- Eisenstein series of weight 1, Texas A&M University in Qatar, June 2013.
- On Jacobian group arithmetic for typical divisors on curves, Center for Advanced Mathematical Sciences (CAMS), American University of Beirut (AUB), November 2012.
- Some classical calculations with _2F_1s (survey talk), School and Workshop on Computational Algebra and Number Theory, ICTP, Trieste, June 2012.
- Eisenstein series of weight 1, International Workshop in Mathematics, German University of Technology, Oman, February 2012.
- Using algebraic values of modular forms to obtain models of modular curves, Workshop on Explicit Methods in Number Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany, July 2011.
- Using algebraic values of modular forms to obtain models of modular curves, part of workshop “Algorithms for Curves, Moduli, and Isogenies”, Laboratoire LIX, Ecole Polytechnique, July 2011.
- Two talks: (i) Algorithmic representation of a curve and its Jacobian, and (ii) Using algebraic values of modular forms to obtain models of modular curves, ALGOL conference, University of Lyon, June 2011.
- Projective embeddings of algebraic curves, with applications to modular curves (survey talk), AUB Mathematics Department Colloquium, May 2011.
- Using algebraic values of modular forms to obtain models of modular curves, AGCT-13 Conference (Arithmetic, Geometry, Cryptography and Coding Theory), C.I.R.M., Luminy, March 2011.
- Using algebraic values of modular forms to obtain models of modular curves, Rational Points 3 workshop, University of Bayreuth, July 2010.
- Periods of modular forms and identities between Eisenstein series, University of Bristol seminar, May 2010.
- Equations for modular curves (survey talk), University of Cyprus Mathematics Department Colloquium, December 2009.
- Equations for modular curves (survey talk), Center for Advanced Mathematical Sciences (CAMS), American University of Beirut (AUB), November 2009.
- Fast arithmetic in Picard groups of general curves, MAGMA seminar, University of Sydney, September 2009.
- Moduli interpretation of Eisenstein series, Conference on modular forms and related topics, Center for Advanced Mathematical Sciences (CAMS), American University of Beirut (AUB), July 2009.
- Moduli interpretation and equations for modular curves, four-hour minicourse presented at the Centre de Recherches Mathematiques, Universite de Montreal, as part of the CRM Summer School on Automorphic Forms and L-Functions: Computational Aspects, June-July 2009.
- Generating functions for Hecke operators, AUB Mathematics Department Colloquium, February 2009.
- Moduli interpretation and improved convergence for Eisenstein series, Center for Advanced Mathematical Sciences (CAMS), American University of Beirut, October 2008.
- Representing algebraic curves by interpolation, with applications to modular curves, seminar at T.U. Berlin, June 2008.
- Algorithmic representation of a curve and its Jacobian, Center for Advanced Mathematical Sciences (CAMS), American University of Beirut, October 2007.
- Fast Jacobian arithmetic on C_{3,4} curves, Workshop on Rational Points on Curves and Higher-Dimensional Varieties: Theory and Explicit Methods, International University of Bremen, Germany, July 2007.
- Algorithmic representation of a curve and its Jacobian, Workshop on Explicit Methods in Number Theory, Mathematisches Forschungsinstitut Oberwolfach, Germany, July 2007.
- Algorithmic representation of a curve and its Jacobian, Universite Grenoble Number Theory Seminar, June 2007.
- Fast group operations on Jacobians of C_{3,4} curves, presentation at internal seminar of Ecole Polytechnique Algorithmic Number Theory and Cryptology Group, June 2007.
- Algorithmic representation of a curve and its Jacobian, Computer Algebra Conference in Kaiserslautern, May 2007.
- Algorithmic representation of a curve and its Jacobian, Universites Paris 6 and 7 Number Theory Seminar, May 2007.
- Algorithmic representation of a curve and its Jacobian, Universite Rennes Cryptography Seminar, May 2007.
- Algorithmic representation of a curve and its Jacobian, University of Montpellier Number Theory Seminar, March 2007.
- Algorithmic representation of a curve and its Jacobian, University of Bordeaux Number Theory Seminar, March 2007.
- Fast algorithms for Picard groups of general curves, Magma 2006 conference, Technical University of Berlin, August 2006.
- Fast algorithms for Picard groups of general curves, University of Leipzig Mathematics Department, July 2006.
- On equations for modular curves, Fast group arithmetic on Jacobians I, and Fast group arithmetic on Jacobians II: three talks presented at the University of Duisburg-Essen, as part of a scientific visit to the Institute for Experimental Mathematics in Essen, August 2005.
- Implementing addition on J(k), Workshop on Rational Points on Curves – Explicit Methods, International University of Bremen, July 2005.
- Applications of elliptic curves in cryptography and computational number theory (mini course), 6 hours of lectures delivered as part of CIMPA-UNESCO-LEBANON Summer School, Beirut, July 2004 (see below under “Organizing Conferences”).
- Fourier Coefficients of Maass Forms, AUB Mathematics Department Colloquium, April 2004.
- Asymptotically fast algorithms for Jacobians of general curves, Courant Institute (NYU) Joint Mathematics and Computer Science Seminar, September 2003.
- Asymptotically fast algorithms for Jacobians of general curves, presentation at internal seminar of Ecole Polytechnique Algorithmic Number Theory and Cryptology Group, Paris, July 2003.
- Asymptotically fast algorithms for Jacobians of general curves, Journees Arithmetiques XXIII, Graz, Austria, July 2003.

### Experience in Organizing Conferences:

- Co-organizer, Conference on Modular Forms and Related Topics, Mathematics Department and CAMS, AUB, Beirut, Lebanon, May 2018.
- Program Committee Member, Algorithmic Number Theory Symposium ANTS-XII, University of Kaiserslautern, Germany, August 2016.
- Scientific Committee, Fourth annual meeting of the Lebanese Society for Mathematical Sciences (LSMS), Universite Saint Joseph, Lebanon, May 2013.
- Co-organizer, Workshop on Number Theory, CAMS, AUB, Beirut, Lebanon, April 2013.
- Scientific Committee, Third annual meeting of the Lebanese Society for Mathematical Sciences (LSMS), American University of Beirut, Lebanon, April 2012.
- Co-organizer, Workshop on Modular forms and Related Topics, CAMS, AUB, Beirut, Lebanon, February 2012.
- Scientific Committee Member, Second annual meeting of the Lebanese Society for the Mathematical Sciences (LSMS), Lebanese American University, Beirut, Lebanon, April 2011.
- Program Committee Member, Algorithmic Number Theory Symposium ANTS-IX, LORIA, Nancy, France, July 2010.
- Scientific Committee Member, First annual meeting of the Lebanese Society for the Mathematical Sciences (LSMS), Lebanese University, Fanar, Lebanon, January 2010.
- Organizing Committee Member, Conference on Modular Forms and Related Topics, CAMS, AUB, Beirut, Lebanon, July 2009.
- Scientific Committee Member, CIMPA-UNESCO-LEBANON summer school on algebraic geometry and arithmetic of curves, CAMS, AUB, Beirut, Lebanon, July 2004. The summer school was sponsored by CIMPA (Centre International de Mathematiques Pures et Appliquees, Nice, France). Lecturer for one of the courses of the lecture school. Lecture notes available from https://sites.aub.edu.lb/kmakdisi/cv/makdisi-cimpa-lectures-2004/ . Also involved in significant organizational work for the school.
- Organizing Committee Member, Second International Conference on Trends in Mathematics Education (ICTME-2) at the Lebanese American University, June 2003. As secretary of organizing committee, handled registration information, paper submission and refereeing, and other correspondence (such as enquiries) for 80 participants.
- Organizing Committee Member, First Beit Mery Workshop on Mathematical Sciences: Geometry and Physics, organized by CAMS, January 2000.

### Teaching Experience:

- Awarded two teaching prizes and nominated for a third on seven occasions, described under Honors and Awards below.
- Successful experience in teaching a wide variety of courses, including single and multivariable calculus, discrete mathematics, differential equations, linear algebra (basic and advanced), honors advanced calculus and linear algebra, abstract algebra, Galois theory, number theory (elementary number theory, algebraic number theory, and algorithmic number theory), introductory real analysis, an advanced undergraduate course in Fourier analysis and partial differential equations, courses in graduate abstract algebra including commutative algebra and symbolic computation, and a graduate course on the analytic theory of modular forms.
- Supervision of M.S. theses at the mathematics department at AUB:
- Theta series and its application to the sum of squares, 2019-2020
- Admissible representations of GL(2,
**Q**_p), the Kirillov model, and application to local new vectors, 2018-2019 - Some discrete series representations for noncompact unitary groups, 2012-2013
- Some classical and p-adic L-functions for number fields, 2012-2013
- Reduction theory for GL(n) and O(p,q), 2010-2012
- Iwasawa, Cartan, and Bruhat decompositions for GL(n) and O(p,q), 2010-2012
- Arithmetic of quaternion algebras, 2010-2011
- Theta functions on g-dimensional complex tori, 2008-2009
- Siegel modular forms and theta functions, 2008-2009
- Descent on elliptic curves and the Mordell-Weil theorem, 2006-2007
- Quadratic forms over
**Q**and**Z**, 2005-2007 - Elliptic curves and applications to cryptography, 2002-2003
- The quadratic sieve algorithm for factoring large integers, 2001-2002

- Supervised an undergraduate thesis at Harvard on Artin L-functions, 1997-1998.
- AUB mathematics department ad hoc committee on teaching and learning objectives for the department’s programs, 2008.
- AUB mathematics department committee on mathematics courses for engineering students, 2005-2006.
- AUB faculty of arts and sciences committee for the computational science program, 2004-2010.
- AUB mathematics department ad hoc committee on curriculum revision, Fall 2000.
- Qualifying exams committee, Harvard University, 1995-1997.

### Honors and Awards:

- 2022: Member, Institute for Advanced Study (IAS), Princeton, New Jersey, February 2022-July 2022.
- 2021: Visiting Scientist (12 months), Max-Planck Institute for Mathematics, Bonn, February 2021-January 2022.
- 2020: Scientific visitor (two weeks) at the Harish-Chandra Research Institute, Allahabad, India, January 2020.
- 2017: Scientific visitor (two months), Institut des Hautes Etudes Scientifiques (IHES), Bures-sur-Yvette, France, June-August 2017.
- 2016: Visitor (one week), POSTECH, Pohang, South Korea, May 2016.
- 2015: Visitor (one and a half weeks), ICERM, Brown University, during special semester on computational aspects of the Langlands program, September 2015.
- 2015: Visiting scientist (one month), Max-Planck Institute for Mathematics, Bonn, June 2015.
- 2014: Visitor (one and a half weeks), Institut de Mathematiques de Bordeaux and INRIA, July 2014.
- 2014: Visiting scholar, Harvard University, spring semester 2014.
- 2011: Visiting scholar (two weeks), Ecole Polytechnique, Paris, July 2011.
- 2010: Visitor, Centre de Recherches Mathematiques, Universite de Montreal (one month), March-April 2010.
- 2009: Visiting scholar, University of Sydney Computational Algebra Group (one month), August-September 2009.
- 2008: Faculty development grant, University Research Board, AUB. Partial funding to attend a workshop on rational points at the University of Warwick and for a scientific visit to Technische Universitat Berlin.
- 2007: Visiting Professor, University of Paris (Paris 7 and 8, for one month each).
- 2007: Visiting Professor, University of Bordeaux (one month).
- 2005, 2007, 2008, 2009, 2013, 2016, and 2020: Nominated seven times for AUB Award for Excellence in Teaching.
- 2003-2005: Awarded grants from University Research Board, AUB (2003-05), and from Lebanese National Council for Scientific Research (2003-04), for research project in algorithmic number theory “Equations for Modular and Shimura Curves.”
- 2003: Clay Mathematics Institute Prize Fellow, August 1-September 15, 2003. Visited Princeton University and attended “Unity of Mathematics” conference at Harvard University.
- 2003: TEMPUS Individual Mobility Grant from the European Training Foundation, for the month of July. Visited Universite Paris 13 and participated at the Journees Arithmetiques XXIII conference in Graz, Austria.
- 2003: Short-term faculty development grant, University Research Board, AUB. Attended conferences at the Ohio State University, Columbus, and Indiana University, Bloomington.
- 2002: Hewlett Junior Faculty Research grant, for a semester of research leave in the fall of 2002.
- 2002: Long-term faculty development grant, University Research Board, AUB, for summer 2002. Visited the Park City Mathematics Institute Workshop on Automorphic Forms in Park City, Utah.
- 2000: Clay Mathematics Scholar for the summer of 2000. Visited Centre Emile Borel in Paris, Harvard University in Cambridge, Massachusetts, and Mathematical Sciences Research Institute, Berkeley, California.
- 1998: Received Phi Beta Kappa award for excellence in teaching, Harvard University.
- 1996: Received Levenson award for excellence in undergraduate teaching, Harvard University.
- 1989-1993: Supported by a National Science Foundation Graduate Fellowship and a grant from the U.S. Department of Education.
- 1988: DeForest prize for proficiency in pure and applied mathematics, Yale University.
- 1988: Edward O. Lanphier memorial award in electrical engineering, Yale University.
- 1986-1987: Honorable Mention, 47th and 48th annual Putnam mathematics competition (ranked in the top 30).
- 1986: Elected to Phi Beta Kappa (national arts and sciences honor society) and to Tau Beta Pi (national engineering honor society) during junior year of college.

### Previous academic work in electrical engineering and computer science:

- Basic coursework in electronic circuit analysis and design, control theory, data structures, systems programming, digital electronics, computer architecture, and VLSI design.
- Graduate courses in theoretical computer science (mainly complexity theory) and in algorithms for computer-aided design of integrated circuits (including a project that involved implementing a new algorithm for the placement problem).