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| == Cohen-Lenstra heuristics == | == Informal Reading Groups == |
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| * chair: Bjorn Poonen * The first meeting of the reading group will be Tuesday, January 25, 11-12. It will be in the 2nd floor seminar room if that room is available. * Informal reading group on the Cohen-Lenstra heuristics * Reading list (in increasing order of sophistication): * MR0750661 Cohen, H. ; Lenstra, H. W., Jr. Heuristics on class groups. Number theory (New York, 1982), 26--36, Lecture Notes in Math., 1052, Springer, Berlin, 1984. * MR0756082 (85j:11144) Cohen, H. ; Lenstra, H. W., Jr. Heuristics on class groups of number fields. Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), 33--62, Lecture Notes in Math., 1068, Springer, Berlin, 1984. * MR1837670 (2003a:11065) Delaunay, Christophe. Heuristics on Tate-Shafarevitch groups of elliptic curves defined over Q. Experiment. Math. 10 (2001), no. 2, 191--196. * Delaunay, Christophe. Formes modulaire et invariants de courbes elliptiques définies sur Q. Thèse, Université Bordeaux I, 2002. * PDFs of these have been placed in Poonen's public directory at MSRI. Type `cd ~bpoonen/Public` at a terminal prompt. == Iwaniec-Luo-Sarnak == * chair: Kaneenika Sinha * times: Wednesdays 11-12. Please note: The first meeting on 19 Jan will be from 2-3 pm in the Baker boardroom. * Wed. 19 Jan in the Common Room: Henryk Iwaniec, ''Introduction to low lying zeros of L-functions'' Abstract: The content of the paper "Low lying zeros of families of L-functions" by Iwaniec, Luo and Sarnak will be described in general terms. * H. Iwaniec, W. Luo, and, P. Sarnak, Low lying zeros of families of L-functions, Publ. IHES, 2000. [[attachment:Iwaniec-Luo-Sarnak.pdf]] * there is also a study guide and reading list by Steven Miller, at Williams: http://www.williams.edu/go/math/sjmiller/public_html/ntandrmt/ == Bhargava-Shankar == * chair: Barry Mazur * times: Thursdays 11-12 * next meeting will be 2-3pm (Simons auditorium), Tuesday 25 January - Melanie Wood, who recommends reading http://arxiv.org/abs/1005.0672 (only for the proofs of the main terms). "Section 1-5,8 of that paper I think are a very good introduction to the ideas in a case small enough to actually picture." * pp. 2-9 (i.e., the Introduction) of Binary quadratic forms having bounded invariants, and the boundedness of average ranks of elliptic curves * Manjul's collected works: http://wstein.org/home/wstein/travel/2011/msri/bhargava/ == Quadratic twists of elliptic curves: 2-Selmer ranks == * chair: Jamie Weigandt * times: Fridays 11-12 * Reading list: * MR1292115 (95h:11064) Heath-Brown, D. R. The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Invent. Math. 118 (1994), no. 2, 331–370. * MR2464773 (2010d:11059) Swinnerton-Dyer, Peter. The effect of twisting on the 2-Selmer group. Math. Proc. Cambridge Philos. Soc. 145 (2008), no. 3, 513–526. * Kane, Daniel. On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve. Preprint. http://arxiv.org/pdf/1009.1365v1 * PDFs of these papers have been placed in my public directory at MSRI, which can be accessed by typing `cd ~weigandt/Public` at a terminal prompt. |
* [[/CohenLenstra|Cohen-Lenstra heuristics]] * [[/ILS|Iwaniec-Luo-Sarnak]] * [[/BhargavaShankar|Bhargava-Shankar]] * [[/QuadraticTwists|Quadratic twists of elliptic curves: 2-Selmer rank]] |
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== Calendar of program events == |
Temporary wiki for organizing the informal reading groups at the Arithmetic Statistics program at MSRI.
This is an example of how to make a separate subpage correctly.
Informal Reading Groups
General question group
- (e.g., average ap ’s, Sato-Tate (the statement), etc.) Not yet scheduled.