[Liste-CICMA] SÉMINAIRE QVSS (06/11/2014, Ghathe, Radziwill) + Sém. Analytic Number Theory (07/11, Harper)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Nov 4 12:09:52 EST 2014


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 6 novembre 2014 / Thursday, November 6, 2014

HEURE / TIME :
10 h 30 - 12 h / 10:30 a.m. - 12:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Eknath Ghathe (Tata Institute)

TITRE / TITLE :
Local reductions of Galois representations via the mod p LLC

LIEU / PLACE :
CRM, Université de Montréal, Pav. André Aisenstadt, 2920 chemin de la Tour, salle 6214

RESUME / ABSTRACT :
The mod p Local Langlands Correspondence (LLC) for GL(2) over Q_p was originally used by Breuil and most recently by Buzzard-Gee to understand the reductions of local Galois representations attached to modular forms away from the level. The problem has been solved completely for small weights (at most 2 p + 1) and for small slopes (in the range 0 < v < 1). The complexity of the problem increases with the weight and with the slope. It involves understanding how the Hecke operator acts on certain sections of local systems on the underlying building (tree). We shall discuss the case when the slopes are in the range 1 < v < 2. This is joint work with A. Ganguli, for weights roughly less than p^2, and work in progress with S. Bhattacharya for _all_ weights.

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DATE :
Le jeudi 6 novembre 2014 / Thursday, November 6, 2014

HEURE / TIME :
14 h - 15 h 30 / 2:00 p.m. - 3:30 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Maksym Radziwill (Rutgers/CRM)

TITRE / TITLE :
Multiplicative functions in short intervals and applications

LIEU / PLACE :
CRM, Université de Montréal, Pav. André Aisenstadt, 2920 chemin de la Tour, salle 6214

RESUME / ABSTRACT :
I will discuss recent work with Kaisa Matomaki on multiplicative functions in short intervals (we'll focus on multiplicative functions taking values in [-1,1]). Our main result shows that the behavior of a multiplicative function over "short intervals" of bounded length is often close to the behavior on a "long interval" (which is easier to understand). This result has many consequences. I'll describe in more detail the following three: consequences towards Chowla's conjecture on correlations of Liouville's function, the existence of smooth numbers in short intervals of "square root length", and the distribution of zeros of Hecke cusp forms on the vertical geodesic.


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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Andrew Granville (andrew at dms.umontreal.ca)
Dimitris Koukoulopoulos (koukoulo at CRM.UMontreal.CA)
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http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html

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SÉMINAIRE ANALYTIC NUMBER THEORY

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DATE :
Le vendredi 7 novembre 2014 / Friday, November 7, 2014

HEURE / TIME :
14 h 30 - 16 h / 2:30 p.m. - 4:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Adam Harper (Université de Montréal)

TITRE / TITLE :
Halász theorem in short intervals

LIEU / PLACE :
Université de Montréal, Pavillon André Aisenstadt, salle 4336

RESUME / ABSTRACT :
I will try to describe how Halász's theorem on mean values of multiplicative functions can and cannot be extended to short intervals. Parts of the talk will be based on my work, and also on my joint work with Granville and Soundararajan. (Hopefully this talk will complement Maksym's talk in QVNTS on Thursday.)


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Responsable(s) :
Sary Drappeau (sary.drappeau at gmail.com)
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http://www.dms.umontreal.ca/~qvnts/index.html
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