Preliminary version Last update made Tue Mar 10 22:08:40 EDT 2009.

QUADRATIC FORMS, SUMS OF SQUARES, THETA FUNCTIONS AND INTEGRAL LATTICES CONFERENCE

March 11 – 14, 2009

University of Florida, Gainesville, FL 32611

SCHEDULE

\underline{Location}. All lectures are in Little Hall Room 101. Refreshments will be in Little Hall Room 339, which is also known as the Atrium.

⋆ ⋆ ⋆

Wednesday, March 11, 2009

9:00am - 9:50am Noam Elkies, Harvard University Weighted theta functions, and a coding analog

10:00am - 10:20am Ryan Skip Garibaldi, Emory University Vanishing of trace forms on Lie algebras

10:30am - 11:00am BREAK

11:00am - 11:50am Jonathan Hanke, University of Georgia at Athens The 290-Theorem and representing numbers by quadratic forms

12:00pm - 2:00pm LUNCH

2:00pm - 2:20pm Guillermo Mantilla, University of Wisconsin Integral trace forms associated to cubic extensions

2:30pm - 2:50pm John Voight, University of Vermont Characterizing quaternion rings

3:00pm - 3:20pm Gabriele Nebe, RWTH Aachen, Germany Automorphism groups of Type II codes 3:30pm - 4:00pm BREAK

4:00pm - 4:20pm Byungchan Kim, University of Illinois, Urbana Combinatorics of partial theta functions

4:30pm - 4:50pm Jaebum Sohn, Yonsei University, Korea / University of Illinois Character analogues of theorems of Ramanujan, Koshliakov and Guinand

5:10pm - 6:00pm Akshay Venkatesh, Stanford University Geometry of Numbers, Old and New

7:00pm - 9:00pm BANQUET at the Friends of the Music Room

⋆ ⋆ ⋆

Thursday, March 12, 2009

9:00am - 9:50am Raman Parimala, Emory University Isotropy of quadratic forms over function fields of p-adic curves

10:00am - 10:20am Hershel Farkas, Hebrew University, Jerusalem Theta Constant Identities and Number Theory

10:30am - 11:00am BREAK

11:00am - 11:50am George Andrews, Pennsylvania State University Parity in Partition Identities

2:00pm - 2:50pm Robert Griess , University of Michigan Barnes-Wall Lattices and their Cousins

3:00pm - 3:20pm Hideyo Sasaki, Otemae College, Itami, Japan Quaternary universal forms over Q(\sqrt{13})

3:30pm - 4:00pm BREAK

4:00pm - 4:20pm Jeremy Rouse, University of Illinois, Urbana Bounds for the coefficients of powers of the Δ-function 4:30pm - 4:50pm Ae Ja Yee, Pennsylvania State University Parity Problems in Partitions

5:00pm - 5:30pm Kagan Kursungoz, Pennsylvania State University Parity Considerations in Andrews-Gordon Identities

7:30pm - 10:00pm PARTY at the home of Krishna and Mathura Alladi

⋆ ⋆ ⋆

Friday, March 13, 2009

9:00am - 9:50am Rainer Schulze-Pillot, Saarland University, Saarbruecken Representation of quadratic forms

10:00am - 10:20am Roger Baker, Brigham Young University The values of quadratic forms at squarefree points

10:30am - 11:00am BREAK

11:00am - 11:50am Ken Ono, University of Wisconsin Heegner divisors, L-functions and Maass forms

12:00pm - 2:00pm LUNCH

2:00pm - 2:50pm John Thompson , University of Florida and Cambdridge Dirichlet Series and SL(2,Z)

3:00pm - 3:20pm Amanda Folsom, University of Wisconsin q-series and weight 3/2 Maass forms

3:30pm - 4:00pm BREAK

4:00pm - 4:20pm Riad Masri , University of Wisconsin Equidistribution of Heegner points and the partition function

4:30pm - 4:50pm Atul Dixit, University of Illinois at Urbana-Champaign Analogues of a transformation formula of Ramanujan 5:00pm - 5:30pm Heiko Todt, Pennsylvania State University Asymptotic formulas for partitions into (distinct) k-th powers

⋆ ⋆ ⋆

Saturday, March 14, 2009

9:00am - 9:50am Bruce Berndt, University of Illinois, Urbana Ramanujan’s Contributions to Theta Functions

10:00am - 10:20am Karl Mahlburg, MIT Asymptotics for crank and rank moments

10:30am - 11:00am BREAK

11:00am - 11:50am Stephen C. Milne, The Ohio State University Sums of squares, the Leech lattice, and new formulas for Ramanujan’s tau function and other classical cusp forms

12:00pm - 2:00pm LUNCH

2:00pm - 2:20pm Sander Zwegers, University College Dublin Multivariable Appell functions and non-holomorphic modular forms

2:30pm - 2:50pm Richard McIntosh, University of Regina, Canada Divisor sums and theta functions

3:00pm - 3:20pm James Sellers, Pennsylvania State University Elementary proofs of parity results for 5–regular partitions

3:30pm - 4:00pm BREAK

4:00pm - 4:20pm Andrew Sills, Georgia Southern University A new look at some partition identities of Goellnitz

4:30pm - 4:50pm Michael Rowell, Pacific University Obtaining New Indefinite Quadratic Forms