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Program of the Sessions – Salt Lake City, UT, Saturday, October 26 (Cont’D.)

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Program of the Sessions Salt Lake City, Utah, October 26–27, 2002 Special Session on Representation Theory of Saturday, October 26 Semisimple Lie Groups, I 8:00 AM –10:40AM Room 121, Leroy Cowles Building Meeting Registration Organizers: Dragan Milicic, University of Utah 7:30 AM –4:30PM Math Office, Room 233, Peter Trapa, University of Utah John Widtsoe Building 8:00AM Annihilators and associated varieties of (7) Harish-Chandra modules over classical Lie algebras. Preliminary report. Special Session on Analytic Number Theory, I William M. McGovern, University of Washington (981-22-06) 8:00 AM –10:50AM Room 219, Leroy Cowles Building 9:00AM On the Howe correspondence for (8) symplectic-orthogonal dual pairs. Organizers: Roger Baker, Brigham Young Annegret Paul, Western Michigan University University (981-22-28) Xian-Jin Li, Brigham Young University 9:30AM Unipotent supports for character sheaves. Andrew D. Pollington, Brigham Young (9) Preliminary report. University Pramod N. Achar*, University of Chicago, and 8:00AM Estimates for the number of algebraic numbers of Anne-Marie Aubert,E´cole Normale Supe´rieur (1) fixed degree and bounded height. Preliminary (981-20-91) report. 10:00AM Holomorphic continuation of generalized Jacquet Jeffrey D. Vaaler, University of Texas at Austin (10) integrals for degenerate principal series. (981-11-29) Preliminary report. 8:30AM Evidence for a Spectral Interpretation of the Zeros Nolan R. Wallach, University of California, San (2) of L-functions from One-Parameter Families of Diego (981-22-56) Elliptic Curves. Steven J Miller, Princeton University (981-11-23) 9:00AM The pair coerrelation function of n2α modulo one AMS Exhibit and Book Sale (3) and an equidistribution problem in hyperbolic geometry. 8:00 AM –4:30PM Faculty Lounge, Room Andreas Strombergsson, Princeton University 228, John Widtsoe Building (981-11-89) 9:30AM The Integer Chebyshev Problem. (4) Peter B Borwein, Mathematics Department, Simon Special Session on Geometry and Topology, I Fraser University, Vancouver, Canada (981-11-31) 10:00AM Counting automorphic forms associated to Galois 8:30 AM –10:50AM Room 215, Leroy Cowles Building (5) representations. Akshay Venkatesh, MIT (981-11-70) Organizers: Mladen Bestvina, University of Utah 10:30AM On Ternary Quadratic Forms. Michael Kapovich, University of Utah (6) WDuke, UCLA (981-11-35) Grigory Mikhalkin, University of Utah The time limit for each contributed paper in the sessions is ten minutes. found in Volume 23, Issue 4of Abstracts of papers presented to the In the Special Sessions the time limit varies from session to session and American Mathematical Society, ordered according to the numbers in within sessions. To maintain the schedule, time limits will be strictly parentheses following the listings. The middle two digits, e.g., 897-20- enforced. 1136, refer to the Mathematical Reviews subject classification assigned For papers with more than one author, an asterisk follows the name of by the individual author. Groups of papers for each subject are listed the author who plans to present the paper at the meeting. chronologically in the Abstracts. The last one to four digits, e.g., 897-20- Papers flagged with a solid triangle () have been designated by the 1136, refer to the receipt number of the abstract; abstracts are further author as being of possible interest to undergraduate students. sorted by the receipt number within each classification. Abstractsofpaperspresentedin the sessions at this meeting will be Appendix–32 NOTICES OF THE AMS VOLUME 49, NUMBER 9 SaltLakeCity,UT,Saturday,October26– Program of the Sessions 8:30AM Surface subgroups of Coxeter groups. 9:00AM Group-Cohomological field theories. (11) Cameron McA Gordon*, University of Texas at (21) Tyler Jarvis, Brigham Young University (981-14-53) Austin, Darren D Long, UC Santa Barbara, and Alan 10:00AM A geometric Littlewood-Richardson rule. WReid, University of Texas at Austin (981-20-83) (22) Ravi Vakil, Stanford University (981-14-37) 9:30AM Bounded cochains on 3-manifolds. (12) D Calegari, California Institute of Technology Special Session on Time Series, Heavy Tails, and (981-57-62) Applications, I 10:30AM Compactifications of leaves and foliations. (13) Alberto Candel, CSUN (981-58-69) 9:00 AM –10:50AM Room 308, John Widtsoe Building Special Session on Area-Minimization and Minimal Organizers: Davar Khoshnevisan, University of Utah Surfaces, I Piotr Kokozska, Utah State University 9:00 AM –10:50AM Room 222, Leroy Cowles Building 9:00AM Limits of On/Off Hierarchical Product Models for (23) Data Transmission. Organizers: Michael Dorff, Brigham Young Sidney Resnick*andGennady Samorodnitsky, University Cornell University (981-60-15) Denise Halverson, Brigham Young 9:30AM Subsampling heavy-tailed models. University (24) Piotr S Kokoszka, Utah State University (981-62-09) Gary R. Lowler , Brigham Young 10:00AM River flow time series with heavy tails. University (25) Mark M Meerschaert*, University of Nevada, and 9:00AM Shortest networks for regular n-gons on a 480 Paul L Anderson, Albion College (981-62-16) (14) degree cone. Preliminary report. 10:30AM Long Memory Models in Atomic Timekeeping. Gary R Lawlor*, Brigham Young University, Joseph (26) Lara S Schmidt*, U.S.Naval Observatory, David Rabinoff, Harvard University, Mark Burkhardt, Neil Crosby and I-Lok Chang, American University Hoffman and Aaron Magid, Williams College (981-62-19) (981-49-103) 10:00AM Area-minimizing minimal graphs over nonconvex (15) domains. Invited Address Denise M Halverson*, Michael Dorff and Gary 11:00 AM – 11:50 AM Room 335, John Widtsoe Building Lawlor, Brigham Young University (981-49-58) 10:30AM A least-area division of Gauss space into three (27) Comparing Symplectic and Contact Topologies (16) equal pieces. Preliminary report. Joseph A Corneli, University of Texas–Austin Yakov Eliashberg, Stanford University (981-51-80) Invited Address Special Session on Nonlinear Elliptic Partial Differential Equations, I 2:00 PM –2:50PM Room 335, John Widtsoe Building 9:00 AM –10:50AM Room 225, Leroy Cowles Building (28) Partially hyperbolic dynamics on 3-manifolds Amie Wilkinson, Northwestern University Organizers: David A. Hartenstine, University of Utah Special Session on Area-Minimization and Minimal Jon T. Jacobsen, Harvey Mudd College Surfaces, II 9:00AM The Monge-Ampere Equation in Domains that are (17) not Strictly Convex. Preliminary report. 3:00 PM –4:40PM Room 222, Leroy Cowles Building David A Hartenstine, University of Utah (981-35-88) Organizers: Michael Dorff, Brigham Young University 9:30AM A priori estimates for a parabolic Monge-Amp`ere (18) equation from evolution of surfaces. Preliminary Denise Halverson, Brigham Young report. University Qingbo Huang*, Wright State University, and Gary R. Lowler, Brigham Young Guozhen Lu, Wayne State University (981-35-50) University 10:00AM W (2,p) estimates for the Linearized Monge Ampere 3:00PM Delaunay’s rolling curves and rotating drops. (19) equation. Preliminary report. (29) Preliminary report. Federico Tournier*, Purdue University, and J. Elm, R. Hynd*, R. Lopez and J. McCuan,Georgia Cristian Gutierrez, Temple University (981-35-73) Tech (981-53-92) 10:30AM Numerical Investigations of Monge-Ampere Type 4:00PM Instabilities in Bubble Clusters. (20) Equations. Preliminary report. (30) Kenneth Brakke, Susquehanna University, and John M. Neuberger, Northern Arizona University Frank Morgan*, Williams College (981-49-57) (981-35-94) Special Session on Analytic Number Theory, II Special Session on Recent Trends in Algebraic Geometry, I 3:00 PM –6:20PM Room 219, Leroy Cowles Building Organizers: Roger Baker, Brigham Young 9:00 AM –10:40AM Room 323, Leroy Cowles Building University Organizers: Aaron J. Bertram, University of Utah Xian-Jin Li, Brigham Young University Christopher Derek Hacon, University Andrew D. Pollington, Brigham Young of California Riverside University OCTOBER 2002 NOTICES OF THE AMS Appendix–33 Program of the Sessions – Salt Lake City, UT, Saturday, October 26 (cont’d.) 3:00PM Elements of class groups of imaginary quadratic 5:00PM A Reduction Program for Semisimple Groups. (31) fields and Shafarevich-Tate groups of elliptic (45) Arthur Lim, University of Minnesota (981-22-21) curves. 5:30PM A Localization Argument for Characters of Antal Balog, Math.Institute of Hungarian Acad. (46) Reductive Lie Groups: An Introduction and Sci., and Ken Ono*, University of Wisconsin at Examples. Madison (981-11-25) Matvei Libine, University of Massachusetts 3:30PM Weierstrasspointsonmodularcurves. (981-22-20) (32) Scott Ahlgren, University of Illinois, Urbana-Champaign (981-11-49) 4:00PM A generalization of Vinogradov’s mean value (33) theorem. Preliminary report. Special Session on Recent Trends in Algebraic Scott T Parsell, Penn State University (981-11-97) Geometry, II 4:30PM Second order modular forms and GL(2) converse (34) theorems. Preliminary report. 3:00 PM –5:40PM Room 323, Leroy Cowles Building David W Farmer, American Institute of Organizers: Aaron J. Bertram, University of Utah Mathematics (981-11-51) Christopher Derek Hacon, University 5:00PM Nearly multiplicative powers of η. of California Riverside (35) Adrian D Stanger, Brigham Young University (981-11-38) 3:00PM Local Gromov-Witten theory of curves in Calabi-Yau (47) 3-folds and Topological Quantum Field Theory. 5:30PM The frequency of vanishings of quadratic twists of Jim Bryan, University of British Columbia (36) modular form L-functions. (981-14-40) Michael Rubinstein*, Brian Conrey,American Institute of Mathematics, Jonathan Keating and 4:00PM Semisimple Frobenius manifolds and Witten’s Nina Snaith, University of Bristol (981-11-54) (48) conjecture on spin curves and Gelfand-Dickey hierarchies. 6:00PM Correlations of Short Divisor Sums and Small Gaps YP Lee (37) Between Primes. Preliminary report. , University of Utah (981-14-60) Daniel A Goldston, San Jose State University 5:00PM Quantum Chow rings of Deligne-Mumford stacks. (981-11-84) (49) Tom Graber, UC Berkeley (981-14-82) Special Session on Nonlinear Elliptic Partial Differential Equations, II Special Session on Geometry and Topology, II 3:00 PM –5:20PM Room 225, Leroy Cowles Building 3:00 PM –5:20PM Room 215, Leroy Cowles Building Organizers: David A.
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  • On a Theorem of Friedlander and Iwaniec

    On a Theorem of Friedlander and Iwaniec

    ON A THEOREM OF FRIEDLANDER AND IWANIEC JEAN BOURGAIN AND ALEX KONTOROVICH Abstract. In [FI09], Friedlander and Iwaniec studied the so- called Hyperbolic Prime Number Theorem, which asks for an in- a b finitude of elements γ = c d ∈ SL(2, Z) such that the norm squared 2 2 2 2 2 kγk = a + b + c + d = p, a prime. Under the Elliott-Halberstam conjecture, they proved the existence of such, as well as a formula for their count, off by a constant from the conjectured asymptotic. In this note, we study the analogous question replacing the integers with the Gaussian integers. We prove unconditionally that for every odd n ≥ 3, there is a γ ∈ SL(2, Z[i]) such that kγk2 = n. In particular, every prime is represented. The proof is an application of Siegel’s mass formula. 1. Introduction The Affine Linear Sieve, introduced by Bourgain, Gamburd and Sar- nak [BGS06], aims to produce prime points for functions on orbits of groups of morphisms of affine space. Friedlander and Iwaniec [FI09] considered the case of the full modular group Γ = SL(2, Z), with the function being the norm-square. Let S be the set of norm-squares in Γ, that is, S := n ∈ Z : n = kγk2 for some γ ∈ SL(2, Z) . + arXiv:1008.0825v1 [math.NT] 4 Aug 2010 They proved, assuming an approximation to the Elliott-Halberstam conjecture, that S contains infinitely many primes.1 Unconditionally, one can easily show the existence of 2-almost primes in S. Indeed, for any x ∈ Z, the parabolic elements 1 x n := x 0 1 Date: September 18, 2018.