# David S. Yuen

### Professor of Mathematics and Computer Science

#### Specialization

Siegel Modular Forms

Geometry of Numbers

Theta Functions

Computer Science

#### Education

PhD Mathematics, Princeton University 1988

MS Mathematics, University of Chicago 1985

BA Mathematics, University of Chicago 1985

#### Courses Taught

Mathematics 110: Calculus 1

Mathematics 111: Calculus 2

Mathematics 210: Multivariable Calculus

Mathematics 231: Linear Algebra

Mathematics 310: Complex Analysis

Mathematics 311: Real Analysis

Mathematics/Computer Science 323: Cryptography

Mathematics 329: Number Theory

Mathematics 330, 331: Modern Algebra I, Modern Algebra 2

Mathematics 340: Geometry

Mathematics/Computer Sciene 375: Combinatorics and Graph Theory

Mathematics 411: Topics in Modern Analysis (Real Analysis 2)

Mathematics 499: Senior Seminar in Mathematics

Computer Science 312: Client-Server Web Applications

Computer Science 489: Advanced Topics in Computer Science

#### Books

WEB APPLICATIONS (co-written with Craig Knuckles), Wiley, 2005.

#### Articles

“*Paramodular forms of level 8 and weights 10 and 12”*, International Journal of Number Theory, **to appear**. (with Cris Poor, Ralf Schmidt)

“*Siegel Paramodular Forms of Weight 2 and Squarefree Level**”*, International Journal of Number Theory, **to appear**. (with Jerry Shurman, Cris Poor)

“*Using Katsurada’s Determination of the Eisenstein Series to Compute Siegel Eigenforms”*, Mathematics of Computations, **to appear** (2017). (with Oliver King, Cris Poor, Jerry Shurman)

“*Computations of Spaces of Paramodular Forms of General Level**”*, Journal of the Korean Mathematical Society, **53** (2016) pp. 645-689. (with Jeffrey Breeding III, Cris Poor)

“*Paramodular Cusp Forms*”, Mathematics of Computation, **84** (2015) pp. 1401-1438. (with Cris Poor).

“*Borcherds Products Everywhere*”, Journal of Number Theory, **148 **(2015) pp. 164-195. (with Valery Gritsenko, Cris Poor).

“*Congruences to Ikeda-Miyawaki Lifts and Triple L-Values of Elliptic Modular Forms*”, Journal of Number Theory, **134** (2014) pp 142-180. (with Tomoyoshi Ibukiyama, Hidenori Katsurada, Cris Poor).

“*Characterizing Fourier-Jacobi Expansions of Paramodular Forms*”, Abhandlungen aus dem Mathematisches Seminar der Universitat Hamburg, **83** (2013) pp 111-128. (with Tomoyoshi Ibukiyama, Cris Poor)

“*The Cusp Structure of the Paramodular Groups of Degree Two*”, Journal of the Korean Mathematical Society, **50** (2013) 445-464. (with Cris Poor)

“*The Chiral Superstring Siegel Form in Degree Two is a Lift*”, Journal of the Korean Mathematical Society, **49** (2012) 293-314. (with Cris Poor)

*“Computing Siegel Modular Forms and Paramodularity”*, Proceedings of the RIMS conference, Automorphic forms, trace formulas and zeta functions, (2011), pages 90-95.

“*Binary Forms and the Hyperelliptic Superstring Ansatz*”, Mathematische Annalen, **352 ** (2011) 1-24. (with Cris Poor)

“*Modular Forms of Weight 8 for Gamma_g(1,2)*, Mathematische Annalen, **346** (2010) 477-498. (with Manabu Oura, Cris Poor, Riccardo Salvati-Manni)

“*Lifting Puzzles in Degree Four*”, Bulletin of the Australian Mathematical Society, **80** (2009) 65-82. (with Cris Poor and Nathan Ryan)

“*Towards the Siegel Ring in Genus Four*”, International Journal of Number Theory, **4** (2008) 563-586. (with Manabu Oura and Cris Poor)

“*Paramodular Cusp Forms*”, Proceedings of the Fourth Spring Conference on Modular Forms and Related Topics (2007) 198-215. (with Cris Poor).

“*Dimensions of Cusp Forms for Gamma_0(p) in Degree Two and Small Weights*”, Abhandlungen aus dem Mathematisches Seminar der Universitat Hamburg, **77** (2007) 59-80. (with Cris Poor)..

“*Computations of Spaces Siegel Modular Cusp Forms*”, Journal of the Mathematics Society of Japan, **59** (2007) 185-222 (with Cris Poor)..

“*The Berge-Martinet Constant and Slopes of Siegel Cusp Forms*”, Bulletin of the London Mathematical Society, **38** (2006) 913-924 (with Cris Poor)..

“*A generalization of the Valence Inequality for Siegel Modular Forms*”, Proceedings of the Third Spring Conference on Modular Forms and Related Topics, (2005) 73-78 (with Cris Poor)..

“*The Extreme Core*”, Abhandlungen aus dem Mathematisches Seminar der Universitat Hamburg, **75** (2005) 51-75.

“*Projectile Motion with Resistance and the Lambert W Function*”, The College Mathematics Journal, **35** (2004) 337-350 (with Ed Packel)..

“*Slopes of Integral Lattices*”, Journal of Number Theory, **100** (2003) 2363-380 (with Cris Poor).

“*Restrictions of Siegel modular forms to modular curves*” , Bulletin of the Australian Mathematical Society, **65** (2002) 239-252 (with Cris Poor).

“*The dyadic trace and odd weight computations for Siegel modular cusp forms* “, Bulletin of the Australian Mathematical Society, **63** (2001) 269-271 (with Cris Poor).

“*Linear dependence among Siegel modular forms* “, Mathematische Annalen, **318** (2000) 205-234 (with Cris Poor).

“*On the volume of a certain polytope*” , Experimental Mathematics, **9** (2000) 91-99 (with C. Chan and D. Robbins).

“*Dimensions of spaces of Siegel cusp forms and theta series with pluri-harmonics*”, The Far East Journal of Mathematics, **1** (1999) 849-863 (with Cris Poor).

“*An elementary proof of the irreducibility of the rank g picard bundle*”, Rocky Mountain Journal of Mathematics, **26** (1996) 1581-1591.

“*Estimates for dimensions of spaces of Siegel modulr cusp forms*”, Abhandlungen aus dem Mathematisches Seminar der Universitat Hamburg, **66** (1996) 337-354 (with Cris Poor).

“*Dimensions of Siegel modular forms of low weight in degree four*”, Bulletin of the Australian Mathematical Society, **54** (1996) 309-315 (with Cris Poor).

“*Relations on the period mapping giving extensions of mixed Hodge structures on compact Riemann surfaces*”, Geometrica Dedicata, **59** (1996) 243-291 (with Cris Poor).

“*Second order theta functions and vector bundles over Jacobi varieties*”, Transactions of the American Mathematical Society, **320** (1990) 457-492.

#### Talks

2016 Number Theory Seminar, University of Hawaii, “Modularity in Degree Two”.

2015 Workshop on Computational Aspects of L-functions, ICERM, “Using Katsurada’s determination of the Eisenstein series to compute Siegel eigenforms in degree three”.

2015 Workshop on Curves and Modular Forms of Low Genus: Computational Aspects, ICERM, “Modularity of the Abelian Surface of Conductor 277”.

2014 E^2: North Central Math Circle Series, North Central College, “The Topology of a World”.

2014 International Conference on Explicit Theory of Automorphic Forms, Tongji University, Shanghai, “Paramodular Forms and Borcherds Products”.

2014 Conference on Curves and Automorphic Forms, University of Arizona, “Modularity in Degree Two”.

2013 Number Theory Seminar, Northwestern University, “Modularity in Genus Two”.

2013 Workshop on Automorphic Forms, University College of Dublin, “Cusp Structure of the Paramodular Group”.

2012 1^{st} EU-US Conference on Automorphic Forms and Related Topics, Aachen University, “The Utility of Computations” and “The Satake Compactification of the Paramodular Group”.

2011 Conference on Modular Forms, Research Institute for Mathematical Sciences, Kyoto University, “Paramodular Cusp Forms”.

2010 Workshop on Siegel Modular Forms, Max Planck Institute fur Mathematiks.

2009 Number Theory Seminar, Bristol University, “Paramodularity”.

2009 Conference on Mock Theta Functions, Max Planck Institute fur Mathematiks, “Binary Invariants and the Hyperelliptic Superstring Ansatz”.

2009 Workshop on Automorphic Forms, Bucknell University.

2009 Elmhurst College Math Colloquium, “Public Key Cryptography”.

2008 Workshop on Automorphic Forms, Texas A&M.

2008 Special Speaker at 25th Mathcounts Regional Competition, Parkside, WI. “Public Key Cryptography”

2007 Bucknell University Math Colloquium, “Extreme Lattices”.

2007 Workshop on Automorphic Forms, Santa Barbara, “Paramodular Forms”

2006 Workshop on Automorphic Forms, Boulder, “Characterization of Fourier Series of Siegel Modular Forms” (with Cris Poor).

2005 Reed College Mathematics Colloquium, “Extreme Lattices”.

2005 Workshop on Automorphic Forms, Denton, “Identities among Second Order Theta Constants” (with Cris Poor).

2004 Workshop on Automorphic Forms, Santa Barbara, “The Extreme Core for Siegel Modular Forms” (with Cris Poor).

2004 Conference on Modular Forms, Hamana Lake, Japan, “The Extreme Core”.

2003 Workshop on Automorphic Forms, Boulder, “Degree 4 Siegel Modular forms” (with Cris Poor).

2002 Conference on Modular Forms, Oberwolfach Institute, Germany, “Dimensions of spaces of Siegel modular forms”.

2002 Workshop on Automorphic Forms, UCLA, “Computation of Siegel Modular Forms” (with Cris Poor).

2001 Workshop on Automorphic Forms, Palo Alto, “Slopes of Integral Lattices” (with Cris Poor).

2000 Lake Forest College Mathematics Colloquium, “Fermat’s Last Theorem via Modular Forms”.

1999 Small College Computing Symposium, LaCrosse, WI, “Introduction to Object Oriented Programming via Robot Gladiators”

#### Awards and Honors

2012 Lake Forest College Trustee Award for Teaching Excellence and Campus Leadership

National Science Foundation graduate fellowship, 1985-1988

Princeton First Year Prize, 1985-1986

Ninth place on the 1983 Putnam Mathematical Examination

Sixth place on the 1984 Putnam Mathematica Examination

Phi Beta Kappa, 1985, University of Chicago.

Member of the 1981 USA team for the International Mathematics Olympiad (the USA team placed 1st that year).