[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (19/11/2015, T. Frieberg, K. Soundararajan) et Grande conférence du CRM (A. Granville, K. Soundararajan)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Nov 17 15:37:13 EST 2015


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 19 novembre 2015 / Thursday, November 19, 2015

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

CONFERENCIER(S) / SPEAKER(S) :
Tristan Frieberg (Waterloo)

TITRE / TITLE :
Medium prime gaps.

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
Let $p_n$ denote the $n$th prime and let $d_n = p_{n+1} - p_n$. The prime number theorem states that, on average over $n \le x$, $d_n/\log n \sim 1$ as $x \to \infty$. 
Heuristics based on Cram\'er's model suggest that the proportion of $n \le x$ for which $d_n/\log n \in (a, b]$, for any given numbers $b \ge a > 0$, is asymptotically equal to $\int_a^b e^{-t} dt$ as $x \to \infty$. However, we do not even know any specific limit points of the sequence $(d_n/\log n)$, except for $0$ and $\infty$. In spite of this, we are able to combine the recent breakthroughs of Ford, Green, Konyagin, Maynard and Tao on long gaps between consecutive primes, and Maynard and Tao on bounded gaps between primes, to establish the following. If $f(n)$ is any ``reasonable'' function (such as $\log n$) tending to infinity more slowly than $\log n\log_2 n\log_4 n/\log_3 n$, then at least $25\%$ of positive real numbers are limit points of the sequence $(d_n/f(n))$. We discuss the strategy of proof, as well as some other results it may be used to prove.

This includes joint work with William Banks and James Maynard, joint work with Roger Baker, as well as independent work of 
Pintz.


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DATE :
Le jeudi 19 novembre 2015 / Thursday, November 19, 2015

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

CONFERENCIER(S) / SPEAKER(S) :
Kannan Soundararajan (Stanford)

TITRE / TITLE :
Variance of divisor functions in arithmetic progressions.  

LIEU / PLACE :
Concordia University, Library Building, 9th floor

RESUME / ABSTRACT :
I will discuss recent work with Rodgers and Harper on the variance of divisor functions in progressions, motivated by recent 
conjectures of Keating, Rodgers, Roditty-Gershon and Rudnick.



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

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GRANDE CONFÉRENCE DU CRM

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DATE :
Le jeudi 19 novembre 2015 / Thursday, November 19, 2015

HEURE / TIME :
19 h 30 / 7:30 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Andrew Granville (Université de Montréal)
Kannan Soundararajan (Stanford University)

TITRE / TITLE :
Documentaire: «Counting from Infinity, Yitang Zhang and the Twin Prime Conjecture» / 
Documentary: «Counting from Infinity, Yitang Zhang and the Twin Prime Conjecture»

LIEU / PLACE :
Université de Montréal, Pavillon Jean-Coutu, 2940, chemin de Polytechnique, Salle S1-151

RESUME / ABSTRACT :
En avril 2013, un chargé de cours de l'Université du New Hampshire soumet un article aux prestigieuses Annals of Mathematics. En quelques semaines la communauté mathématique réalise que Yitang Zhang, un chercheur isolé et sans poste permanent, vient de réaliser une avancée spectaculaire.

La Grande Conférence présentera un documentaire réalisé sur le chercheur et sa contribution. La projection sera suivie par une période de questions avec les Profs. Granville (Université de Montréal) et Soundararajan (Stanford University). (Le documentaire est en anglais; la période de questions se déroulera dans les deux langues.) 
In April 2013, a lecturer at the University of New Hampshire submitted a paper to the Annals of mathematics. Within weeks word spread – a little-known mathematician, with no permanent job, working in complete isolation had made an important breakthrough towards solving the Twin Prime Conjecture.

The Grande Conférence will show the documentary "Counting from Infinity" (in English). Profs. Granville (Université de Montréal) and Soundararajan (Stanford University) will then be available to answer questions from the public. 


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http://www.crm.umontreal.ca/ZhangYitang/
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