Wen-Ch'ing Winnie Li

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EDUCATION.

   1966-70 National Taiwan University, B.S.,
   1970-71 National Taiwan University, Graduate School in Mathematics;
   1971-74 University of California, Berkeley, Ph.D.
     These Advisor: Andrew P. Ogg


RESEARCH INTERESTS.

   Automorphic Forms, Number Theory, Representation Theory, Coding Theory and Graph Theory


EMPLOYMENT.

   1974-77 Assistant Professor, Benjamin Pierce Lecturer, Harvard University;

   1978 Member, Institute for Advanced Study, Princeton, N. J.;

   1978-79 Assistant Professor, University of Illinois at Chicago;

   1979-84 Associate Professor, Pennsylvania State University;

   1984- Professor, Pennsylvania State University


CONCURRENT.

   Visiting Inst. of Math., Bonn, Germany, summer of 1977 and 1983;

   Visiting Harvard University, fall, 1981;

   Visiting Inst. des Hautes Etudes Scientifiques, France, fall 1982;

   Visiting Inst. for Advanced Study, Princeton, spring 1984, spring 2000 (sabbatical leave);

   Visiting National Tsinhua University, Taiwan, summer 1984;

   Visiting Univ. de Paris-Sud, Centre díŽOrsay, France, 1985-86 (sabbatical leave);

   Visiting Stanford University, summer 1986;

   Visiting Academia Sinica, Taiwan, summer of 1988, 1990, 1994, 1997;

   Visiting Nankai Inst. of Math., Tianjin, China, spring 1990, 1993;

   Visiting Academia Sinica, Beijing, China, 1990, 1992, 1997;

   Visiting University of Pennsylvania, 1991-92 (under NSF VPW award);

   Visiting Sichuan University, China, summer 1992;

   Visiting National Taiwan University, 1992-93 (sabbatical leave);

   Consultant at AT&T Bell Laboratories and AT&T Shannon Laboratories, N. J.

   Visiting Mathematical Sciences Research Institute, Berkeley, CA, spring 1995;

   Visiting the National Center of Theoretical Sciences, Mathematics Division, Taiwan,

     Summer and Dec. 1998, Aug 1999-Jan 2000 (sabbatical leave), Aug 2001, Aug 2002, Aug. 2003, July 2005;

   Visiting Tamkang University, Taipei, Taiwan, summer, 2000;

   Visiting the National Center of Theoretical Sciences at Taipei, National Taiwan University, July 2004

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HONORS.

   Alrfed Sloan Fellow, 1981-83;
   Invited Half-hour Speaker at the XI International Symposium on Mathematical Programming, August, 1982, Bonn, West Germany;
   NSF Visiting Professorship for Women Award, 1991-92; 
   Editor of Transactions of Amer. Math. Soc., 1992-96;
   Editor of Taiwanese Journal of Mathematics, 1998-;
   Editor of Proceedings of Amer. Math. Soc., 2002-; 
   Editor of International Journal of Number Theory, 2005-;

   Distinguished Visiting Professor at National Tsinghua University, Taiwan, Aug 1999-Jan 2000;


PUBLICATIONS.

[1]

Newforms and functional equations, Math. Ann. 212, 285-315 (1975)

[2] 

On modular functions in characteristic p, Trans. Amer. Math. Soc. 246, 231-259 (1978)

[3]

(with A.O.L. Atkin) Twists of newforms and pseudo-eigenvalues of W-operators, Invent, Math. 48, 221-243 (1978)

[4]

Eisenstein series and decomposition theory over function fields, Math. Ann. 240, 115-139 (1979)

[5]

L-series of Rankin type and their functional equations, Math. Ann. 244, 135-166 (1979)

[6]

On the representations of GL(2), Part I: "-factors and n-closeness, J. reine ang. Math. 313, 27-42 (1980)

[7]

On the representations of GL(2), Part II: "-factors of the representations of GL(2) íĐ GL(2), J. reine ang. Math. 314, 3-20(1980)

[8]

(with R.L. Graham and S.-Y. R. Li) On the structure of t-designes, SIAM J. Alg. and Disc. Meth. 1(1), 8-14 (1980)

[9]

Hecke-Weil-Jacquet-Langlands theorem revisited. In: Lectures Notes in Math. 751, 206-220, Springer-Verlag, N. Y. (1979)

[10]

Une caracterisation des representations automorphes de GL1 et GL2, C.R. Acad. Sci. Serie A 29, 681-684 (1980)

[11]

(with G. Harder and J. Weisinger) Dimensions of spaces of cusp forms over function fields, J. reine ang. Math. 319, 73-103 (1980)

[12]

(with S.-Y. R. Li) On generators of ideals associated with unions of linear varieties, Bull. London Math. Soc. 13, 59-65 (1981)

[13]

On a theorem of Hecke-Weil-Jacquet-Langlands. In: Recent Progress in Analytic Number Theory, vol. 2, 119-152, Academic Press (1980)

[14]

(with S.-Y. R. Li) Independence numbers of graphs and generators of ideals, Combinatorica 1, 55-61 (1981)

[15]

(with E. Formanek and P. Halpin) The Poincare series of the ring of 2 íĐ 2 generic matrices, J. Alg. 69, 105-112 (1981)

[16]

On converse theorems for GL(2) and GL(1), Amer. J. Math. 103, no. 5, 851-885 (1981)

[17]

(with R. L. Graham and J. L. Paul) Homogeneous collinear sets in partitions of Zn, J. Combinatorial Theory, Series A, vol. 31, 21-32 (1981)

[18]

Generators for the ideal of polynomial identities satisfied by 2 íĐ 2 matrices, J. Alg. 74, no. 1, 2446-263 (1982)

[19]

(with R.L. Graham and J.L. Paul) Monochromatic lines in partitions of Zn. In: Lecture Notes in Math. 884, 35-48, Springer-Verlag, N. Y. (1981)

[20] 

(with J. Soto-Andrade) Barnes identities and representations of GL2. Part I: Finite field case, J. reine ang. Math. 344, 171-179 (1983)

[21]

Barnes identities and representations of GL2. Part II: Nonarchimedean local field case, J. reine ang. Math. 345, 69-92 (1983)

[22]

Determination of the residue classes of a polynomial at integral arguments, Disc. Math. 47, 83-90 (1983)

[23]

Diagonalizing modular forms, J. Alg. 99, no. 1, 210-231 (1986)

[24]

(with B. Z. Moroz) On ideal classes of number fields containing integral ideals of equal norms, J. Number Theory 21, 185-203 (1985)

[25]

A criterion for automorphic representations of GL(1) and GL(2), SíŽem. de ThíŽeorie des Nombres de Bordeaux, 1982-83, exposíŽe no. 7 (1984)

[26]

(with P. GíŽerardin) Fourier transforms of representations of quaternions, J. reine ang. Math. 359, 121-173 (1985)

[27]

A criterion on automorphic forms for GL1 and GL2 over global fields. In: SíŽem. de ThíŽeorie des Nombres de Paris 1982-83, Progress in Math., vol. 51, 161-172, Birkhauser, Boston (1984)

[28]

(with P. GíŽerardin) A functional equation for degree two local factors, Canad. Math. Soc. Bull., vol. 28(3), 355-371 (1985)

[29]

(with P. GíŽerardin) Establishing correspondences without the trace formula, AMS Contemporary Math. 53, 185-200 (1986)

[30]

Various aspects of BarnesíŽ identity. In: SíŽem. de ThíŽeorie des Nombres de Paris 1984-85, Progress in Math., vol. 63, 187-203, Birkhauser, Boston (1986)

[31]

(with P. GíŽerardin) Identities on degree two local factors. In: Proceedings of the conference on íĘRepresentation Theory and Number Theory in connection with Local Langlands ConjectureíĘ, held at Irsee, West Germany, Dec. 15-20, 1985, in AMS Contemporary Math. 86 (1989), 225-248

[32]

(with P. GíŽerardin) Identities on quadratic Gauss sums, Transactions Amer. Math. Soc., vol. 321, no. 1, 159-182 (1990)

[33]

(with P. GíŽerardin) Degree two monomial representations of local Weil groups, J. fíLur reine und angewandt Math. 394 (1989), 1-30

[34]

On quadratic Gauss sums over local fields. In : SíŽem. de ThíŽeorie des Nombres de Paris 1985-86, Progress in Math., vol. 71, 133-145, Birkhauser, Boston (1987)

[35]

(with P. GíŽerardin) Functional equations and periodic sequences, in: ThíŽeorie des nombres . Number Theory (Proceedings of the International Congress on Number Theory, held in Quebec City, Canada, July 5-18, 1987), J.-M. De Koninck & C. Levesque ed., 267-279, Walter de Gruyter, Berlin, New York (1989)

[36]

(with P. GíŽerardin) Twisted Dirichlet series and distributions, CompositioMathematica 73, 271-293 (1990)

[37]

The role of Fourier transform in correspondences of representations of degree two algebras, in: Algebra, Analysis and Geometry, M.-C. Kang and K.-W. Lih edited, 121-136, World Scientific, Singapore, New Jersey, London, Hong Kong, 1989

[38] 

On local exceptional representations of GL(2), preprint

[39]

On local modular representations of GL(2), preprint

[40]

(with A. Harnchoowong) Sylow subgroups of ideal class groups with moduli, J. Number Theory, vol. 36, no. 3, 354-372 (1990)

[41]

Character sums and abelian Ramanujan graphs, J. Number Theory 41 (1992), 199-214

[42]

(with K. Feng) Eigenvalues of regular directed graphs, Appendix to no. 41, J. Number Theory 41 (1992), 214-217

[43]

(with F. K. Hwang) Hamiltonian circuits for 2-regular interconnection networks, in: Network Optimization Problems, Algorithms, Applications and Complexity, D.-Z. Du and P. M. Pardalos edited, World Scientific, Singapore, New Jersey, London, Hong Kong, 1993

[44]

(with F. K. Hwang) Reliabilities of double loop networks, Prob. Eng. and Info. Sci. 5 (1991), 255-272.

[45]

Ideal class groups and Galois modules. In: SíŽeminaire de ThíŽeorie des Nombres Paris 1989-90, Progress in Math., 163-176, Birkhauser, Boston, Basel, Berlin, 1992.

[46]

(with X.-D. Hu and F. K. Hwang) Most reliable double loop networks in survival reliability, Network, vol. 23 (1993), 451-458.

[47]

(with F. K. Hwang) 2-connectivities of extended double loop networks. In: Combinatorial Network Theory, D.-Z. Du and F. D. Hsu eds, 107-124, Kluwer Academic Publishers, 1995.

[48]

(with A. R. Calderbank, P. Frankl, R. L. Graham, and L. A. Shepp) The Sperner capacity of linear and nonlinear codes for the cyclic triangle, J. of Algebraic Combinatorics 2 (1993), 31-48.

[49]

(with R. W. Chen and F. K. Hwang) Consecutive-2-out-of-n: F systems with node and link failures, IEEE Trans. Rel. vol. 42, No. 3 (1993), 497-502.

[50]

(with R. W. Chen and F. K. Hwang) A reversible model for consecutive-2-out-of-n: F systems with node and link failures, Prob. Eng. and Info. Sci., 8 (1994), 189-200.

[51]

(with F. K. Hwang) Connectivity reliabilities and Hamiltonian reliabilities of linear and circular consecutive-2 link systems, International Journal of Reliability, Quality and Safety Engineering, vol 1, no. 2(1994), 247-256.

[52]

Number-theoretic constructions of Ramanujan graphs. In: Columbia University Number Theory Seminar, New York 1992, AstíŽerisque, vol. 228 (1995), Soc. Math. de France, 101-120.

[53]

(with Keqin Feng) Spectra of hypergraphs and applications, J. Number Theory, vol. 60 (1996), 1-22.

[54]

Number Theory with Applications (book), World Scientific, Singapore-New Jersey -London-Hong Kong, 1996.

[55]

A survey of Ramanujan graphs. In: Arithmetic, Geometry and Coding Theory, Proceedings of International Conference held at Luminy, France, June 28 - July 2, 1993, de Gruyter, Berlin-New York, 127-143, 1996

[56]

(with P. SolíŽe) Spectra of regular graphs and hypergraphs and orthogonal polynomials, European Journal of Combinatorics, vol. 17 (1996). 461-477.

[57]

European Journal of Combinatorics, vol. 17 (1996). 461-477. 57. (with S. Burr, P. ErdíLos and R. L. Graham) Complete sequences of sets of integer powers, Acta Arithmetica 77, vol. 2 (1996), 133-138.

[58]

(with M-K Leu) On the series for L(1,), Nagoya Math. J., vol. 141 (1996), 125-142.

[59]

(with R. Calderbank and B. Poonen) A 2-adic approach to the analysis of cyclic codes, IEEE Information Theory, vol. 43, no. 3 (1997), 977-986.

[60]

Estimates of character sums arising from finite upper half planes. In: Finite Fields and Applications, Proc. of the third international conference, Glasgow, 11-14 July, 1995, S. Cohen and H. Niederreiter eds., Lecture Note Series 233, London Math. Soc., Cambridge Univ. Press, 219-228, 1996.

[61]

Character sums over p-adic fields, Journal of Number Theory, vol. 74, 181-229 (1999).

[62]

Geometry, graph theory and number theory. In: Algebra and Geometry (Taipei 1995), 83-102, Lect. Alg. Geom. 2, Internat. Press, Cambridge, MA. 1998.

[63]

(with B. Gao, F. Hwang and U. Rothblum) Partition-polytopes over 1-dimensional points, Mathematical Programming 85 (1999), no. 2, Ser. A, 335-362.

[64]

In Search of randomness: distributions of eigenvalues. In: Proc. of International Conference on Aspects of Mathematics, June 10-13, 1996, Hong Kong University, Hong Kong, 197-222 (2002).

[65]

Elliptic curves, Kloosterman sums and Ramanujan graphs. In: Computational Perspectives on Number Theory: Proceedings of a Conference in Honor of A. O. L. Atkin, D. A. Buell and J. T. Teitelbaum edited, AMS/IP Studies in Advanced Math., vol. 7, Amer. Math. Soc., Providence (1998), 179-190.

[66]

Eigenvalues of Ramanujan graphs. In: Emerging Applications of Number Theory (Minneapolis, MN, 1996), 387-403, IMA Vol. Math. Appl. 109, Springer, New York, 1999.

[67]

(with Ching-Li Chai) Function fields: arithmetic and applications, Contemporary Math. 245, 189-199 (1999)

[68]

Exponential sum estimates and applications, Proc. of 35th Annual Allerton Conference on Communication, Control and Computing, Sept. 29-Oct 1, 1997, Universityof Illinois at Urbana-Champaign, 14-22, 1998.

[69]

(with Xuning Feng) On Z4 codes with large Lee weight, preprint.

[70]

(with Hiren Maharaj) Coverings of curves with asymptotically many rational points, Journal of Number Theory 96, 232-256 (2002).

[71]

Various constructions of good codes. Contemporary Math., vol. 264, 271-285, (2000).

[72]

Recent developments in automorphic forms and applications, Number Theory for the Millennium II, M. A. Bennett et al. eds., A K Peters, Boston, 2002, 331-354.

[73]

Recent developments in automorphic forms and applications, Surveys in Number Theory: Papers from The Millennial Conference on Number Theory, Bennett et al. editors, A K Peters, Boston, 2002, 125-148.

[74]

(with C.-L. Chai) Character sums, automorphic forms, equidistribution, and Ramanujan graphs, Part I. The Kloosterman sum conjecture over function fields, Forum Math 15, Issue 5 (2003), 679-699.

[75]

(with C.-L. Chai) Character sums, automorphic forms, equidistribution, and Ramanujan graphs, Part II. Eigenvalues of Terras graphs, Forum Math. 16 (2004), 631-661.

[76]

The arithmetic of modular forms, IAS/Park City Mathematics Series Volume 9, Arithmetic Algebraic Geometry, 479-504, 2001.

[77]

On negative eigenvalues of regular graphs, C. R. Acad. Sci. Paris, t. 333, SíŽerie I, 907-912, 2001.

[78]

(with H. Maharaj and H. Stichtenoth, and an appendix by N. Elkies) New optimal tame towers of function fields over small finite fields, Lecture Notes in Computer 4 Science 2369 (Proceedings of the 5th conference on Algorithmic Number Theory Symposium, 2002) C.Fieker and D.R.Kohel, eds., Springer-Verlag, Berlin, 372-389 (2002).

[79]

(with Mats NíLaslund and I. Shparlinski) Hidden number problem with the trace and bit security of XTR and LUC, Lect. Notes in Comp. Sci. 2442, Springer-Verlag, Berlin, 433íV448 (2002).

[80]

Ramanujan hypergraphs, GAFA, Geom. funct. anal., vol. 14 (2004), 380-399.

[81]

Ramanujan graphs and Ramanujan hypergraphs, IAS/Park City MathematicsSeries, to appear.

[82]

Modularity of asymptotically optimal towers of function fields, Progress in Computer Science and Applied Logic, vol. 23, BirkhíLauser Verlag, Basel, 51-65 (2004).

[83]

Character sums over norm groups, Finite Fields Appl. 12 (2006), 1-15.

[84]

(joint with Ling Long and Zifeng Yang) On Atkin-Swinnerton-Dyer congruence relations, Journal of Number Theory, 113 (2005), 117-148.

[85]

(joint with Ralf Koetter, Pascal O. Vontobel, and Judy Walker) Pseudo-Codewords of cycle codes via zeta functions, Proc. IEEE Information TheoryWorkshop, San Antonio, TX, USA, Oct. 24-29, 2004, 7-12.

[86]

(joint with Ling Long and Zifeng Yang) Modular forms for noncongruence subgroups, Quaterly Journal of Pure and Applied Math., vol 1, No. 1, 205-221, 2005.

[87]

(joint with Yotsanan Meemark) Ramanujan graphs on cosets of PGL2(Fq), Finite Fields Appl., 11 (2005), 511-543.

[88]

(joint with Ralf Koetter, Pascal O. Vontobel, and Judy Walker) Characterizations of pseudo-codewords of LDPC codes, preprint, 2005.

[89]

(joint with A. O. L. Atkin and L. Long) On Atkin and Swinnerton-Dyer congruence relations (2), preprint, 2005.

[90]

Upper and lower bounds for A(q). In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear.

[91]

ElkiesíŽ modularity conjecture. In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear.

[92]

Improved algebraic geometry bounds. In: Recent Trends in Coding Theory and Its Applications, AMS/IP monograph, to appear.

                          
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