Automorphic Forms Seminar |
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The Automorphic Forms Seminar is a web-based mathematics seminar. It is broadcast on the netera network and currently connects mathematicians at the University of Alberta, the University of British Columbia and the University of Calgary. Anyone interested in joining the Automorphic Forms Seminar, either from these locations or elsewhere, should contact Clifton Cunningham (cunning[at]math[dot]ucalgary[dot]ca).
| TIME | SPEAKER | TITLE | LOCATIONS |
| 2008.05.28, 10:00-11:15 MST 09:00-10:15 PST |
Jorge Jimenez Urroz, UPC-Barcelona and CRM-Montreal; |
On the Frobenius fields of Elliptic curves Abstract: Let $E$ be an elliptic curve over $\Q$ without complex multiplication and $a_p^2-4p$, the discriminant of the characteristic polynomial of the Frobenius element modulo the prime $p$. Very little is known about the endomorphism rings, or even the quadratic fields that might appear as algebra of endomorphisms varying the prime. The ring of endomorphisms is obviously related with the arithmetic of $a_p^2-4p$, the discriminant of the characteristic polynomial of the Frobenius element. In this talk we give the precise asymptotic for $\pi_{E,r,h}^{sf}(x)$ counting the number of primes $p$ up to $x$ such that $a_p^2-4p$ is square-free and in the congruence class $r$ modulo $h$ when averaging over elliptic curves defined over the rationals, and we discuss the relation of this result with the Lang-Trotter conjecture, and with some other problems related to the curve modulo $p$. |
2-59A in Edmonton; BioSci 540B in Calgary; Room 110, West Mall Annex in Vancouver |
| 2008.05.28, 10:00-11:15 MST 09:00-10:15 PST |
Lassina Demebele, Institut fŸr Experimentelle Mathematik, Universitat Duisburg Essen |
Computing the Image of the Base Change Map Abstract: For a totally real number field $F$ that is Galois over $\Q$, we discuss an algorithm for computing the Hilbert modular forms over $F$ that are base changes. As an application, we explain how this is used for the computations of the congruences between base change and non-base change Hilbert modular forms. |
CS 2-59A at the University of Alberta, Biosciences 540B at the University of Calgary. |
| 2008.05.14, 11:00-12:15 MST 10:00-11:15 PST |
Jonathan Hanke, Max-Planck-Institut fŸr Mathematik |
Representing integers by ternary quadratic forms Abstract: This talk will give an introduction to the current state of knowledge of "What integers are represented by a quadratic form in 3 or more variables?". Along the way we will explore the close connections with Gauss sums, special values of zeta functions, the Riemann hypothesis, modular forms (of integral and half-integral weight), and even Galois representations. We will conclude by characterizing the set of numbers represented by a ternary quadratic form, and explore several interesting subtleties that exist only in the case of 3 variables. |
CS 2-59A at the University of Alberta, Biosciences 540B at the University of Calgary. |
| 2008.03.12, 15:00-16:30 MST 14:00-15:30 PST |
Matt Greenberg, University of Calgary |
On the p-adic Stark-Heegner conjecture slides (well, blackboard images, really) |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary. |
| 2008.02.13, 15:00-16:30 MST 14:00-15:30 PST |
Gerald Cliff, University of Alberta |
Weil Representation Notes |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary. |
| 2008.01.30, 15:00-17:00 MST 14:00-16:00 PST |
Matthew Greenberg, University of Calgary |
Automorphic forms, Stark units, and Heegner points Slides are available here. A streaming video of this talk is available at rtsp://streaming.netera.ca/automorphicforms/2008-01-30-01-58-presentation-hinted.mov (Open quicktime, open URL, then insert the rtsp url above. The camera image switches to the speaker (Matt Greenberg) after 2 minutes. To get the video file, go to http://video-archive.netera.ca/automorphicforms/2008-01-30-01-58-presentation-hinted.mov.) |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary. |
| 2008.01.23, 15:00-17:00 MST 14:00-16:00 PST |
Hadi Salmasian, University of Alberta |
Weil Representations and Perverse Sheaves Slides |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary. |
| 2007.11.14, 15:00-16:30 MST 14:00-15:30 PST |
William Casselman, University of British Columbia |
Satake Isomorphism, continued |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary, B716 at the University of Lethbridge. |
| 2007.10.31, 15:00-16:30 MST 14:00-15:30 PST |
Julia Gordon, University of British Columbia |
On some work by Thomas Hales Abstract: I'll talk about the work of C. Cunningham and T.C. Hales that uses the philosophy of motivic integration to transfer the Fundamental Lemma from finite characteristic to characteristic zero in some special cases. |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary, B716 at the University of Lethbridge. |
| 2007.10.17, 15:00-16:30 MST 14:00-15:30 PST |
Clifton Cunningham, University of Calgary |
An introduction to endoscopy and orbital integrals |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary, B716 at the University of Lethbridge. |
| 2007.09.19, 15:15-16:30 MST 14:15-15:30 PST |
William Casselman, University of British Columbia |
Satake Isomorphism. Some relevant material : A companion to Macdonald's book on p-adic spherical functions and The Fundamental Lemma (slides) . |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary, L1108 at the University of Lethbridge. |
| 2007.04.11, 11:00-12:00 MST (10:00-11:00 PST) |
Jason Nicholson, University of Calgary |
Artin L-series, part II | GSB 315 at the University of Alberta, Biosciences 540B at the University of Calgary |
| 2007.04.04, 11:00-12:00 MST (10:00-11:00 PST) |
Gerald Cliff, University of Alberta |
Artin L-series, part I slides |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2007.03.28, 11:00-12:00 MST (10:00-11:00 PST) |
Lassina Dembele, University of Calgary |
Hilbert-Siegel modular forms and the Jacquet-Langlands Correspondence preprint |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2007.03.21, 11:00-12:00 MST (10:00-11:00 PST) |
Lassina Dembele, University of Calgary |
Galois representations, modularity and applications to arithmetic, continued | CS 2-59A at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2007.03.07, 11:00-12:00 MST (10:00-11:00 PST) |
Lassina Dembele, University of Calgary |
Galois representations, modularity and applications to arithmetic, continued Slides |
CS 2-59A at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2007.02.28, 11:00-12:00 MST (10:00-11:00 PST) |
Lassina Dembele, University of Calgary |
Galois representations, modularity and applications to arithmetic, continued | GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2007.02.14, 11:00-12:00 MST (10:00-11:00 PST) |
Clifton Cunningham, University of Calgary |
An introduction to Hilbert-Siegel modular forms and automorphic representations, concluded Slides and whiteboard notes |
GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2007.02.07, 11:00-12:00 MST (10:00-11:00 PST) |
Clifton Cunningham, University of Calgary |
An introduction to Hilbert-Siegel modular forms and automorphic representations, continued | GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2007.01.31, 11:00-12:00 MST (10:00-11:00 PST) |
Clifton Cunningham, University of Calgary |
An introduction to Hilbert-Siegel modular forms and automorphic representations | GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2006.12.07, 15:30-16:30 MST (14:30-15:30 PST) |
Lassina Dembele, University of Calgary |
Galois representations, modularity and applications to arithmetic | GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2006.11.30, 15:30-16:30 MST (14:30-15:30 PST) |
David McNeilly, University of Alberta |
Elliptic curves over Q and associated Galois representations | GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2006.11.23, 15:30-16:30 MST (14:30-15:30 PST) |
Terry Gannon, University of Alberta |
An introduction to automorphic representations, part II | GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2006.11.16, 15:30-16:30 MST (14:30-15:30 PST) |
Terry Gannon, University of Alberta |
An introduction to automorphic representations, part I | GSB 315 at the University of Alberta, ICICS/CS Building Room x521 at the University of British Columbia, Biosciences 540B at the University of Calgary |
| 2006.11.09, 15:30-16:30 MST (14:30-15:30 PST) |
Jason Nicholson, University of Calgary |
On the full L-function attached to a Grossencharacter | GSB 315 at the University of Alberta, Biosciences 540B at the University of Calgary |
| 2006.11.02, 15:30-16:30 MST (14:30-15:30 PST) |
Jason Nicholson, University of Calgary |
Hecke Theory for GL(1), part II | Biosciences 540B at the University of Calgary |
| 2006.10.19, 15:30-16:30 MST (14:30-15:30 PST) |
Jason Nicholson, University of Calgary |
Hecke Theory for GL(1), part I | Biosciences 540B at the University of Calgary |
The goal of the Automorphic Forms Seminar is to create an informal inter-university collaborative research group involving faculty and graduate students and drawing on strengths from all participating universities in order to deepen our understanding of the Langlands Programme and related mathematics. To that end, seminar topics for the 2006-2007 academic year were fairly broad and, for the most part, were meant to survey basic notions. During the 2007-2008 and 2008-2009 academic years we intend to survey major problems in the field, such as the (local and global) Langlands Correspondence, endoscopy and the fundamental lemma, and the Jacquet-Langlands Correspondence. However, the focus of the seminar is not so narrow as to preclude lectures on topics less obviously connected with automorphic forms.