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Upcoming Talks

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Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

A proof of the prime number theorem IV

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Speaker: 
Efthymios Sofos
Affiliation: 
University of Leiden/MPIM
Date: 
Thu, 2018-09-20 11:15 - 12:15
Location: 
MPIM Lecture Hall

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

A proof of the prime number theorem III

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Speaker: 
Efthymios Sofos
Affiliation: 
University of Leiden/MPIM
Date: 
Mon, 2018-09-17 11:15 - 12:15
Location: 
MPIM Lecture Hall

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

A proof of the prime number theorem II

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Speaker: 
Efthymios Sofos
Affiliation: 
University of Leiden/MPIM
Date: 
Thu, 2018-09-13 11:15 - 12:15
Location: 
MPIM Lecture Hall

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

tba

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Speaker: 
Simon Myerson
Affiliation: 
University College London/MPIM
Date: 
Wed, 2018-09-12 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

A proof of the prime number theorem I

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Speaker: 
Efthymios Sofos
Affiliation: 
University of Leiden/MPIM
Date: 
Mon, 2018-09-10 11:15 - 12:15
Location: 
MPIM Lecture Hall

 

The prime number theorem asserts that the $n$-th largest prime has approximate size $n \log n$.
We shall give the proof of Iwaniec in his recent AMS book on the Riemann zeta function.
These lectures are at the level of beginning graduate students.

 

tba

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Speaker: 
Maryna Viazovska
Affiliation: 
EPFL Lausanne
Date: 
Fri, 2018-09-07 11:35 - 12:20
Location: 
MPIM Lecture Hall

Summing $\mu(n)$: a better elementary algorithm

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Speaker: 
Harald Helfgott
Affiliation: 
Universität Göttingen
Date: 
Fri, 2018-09-07 10:15 - 11:00
Location: 
MPIM Lecture Hall

Joint with Lola Thompson.

Consider either of two related problems: determining the precise
number $\pi(x)$ of prime numbers $p\leq x$, and computing the Mertens
function $M(x) = \sum_{n\leq x} \mu(n)$, where $\mu$ is the Möbius function.

The two best algorithms known are the following:

Locally harmonic Maass forms and central $L$-values

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Speaker: 
Larry Rolen
Affiliation: 
Trinity College Dublin
Date: 
Fri, 2018-09-07 09:25 - 10:10
Location: 
MPIM Lecture Hall

In this talk, we will discuss a relatively new modular-type object known as
a locally harmonic Maass form.
We will discuss recent joint work with Ehlen, Guerzhoy, and Kane with
applications to the theory of $L$-functions. In particular, we find
finite formulas for certain twisted central $L$-values of a family of
elliptic curves in terms of finite sums over canonical binary quadratic
forms. Applications to the congruent number problem will be given.

Speed Talks

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On Maeda's Conjecture

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Speaker: 
Paloma Bengoechea
Affiliation: 
ETH Zürich
Date: 
Thu, 2018-09-06 14:05 - 14:50
Location: 
MPIM Lecture Hall

In 1997 Maeda established a conjecture in his work with Hida
that has been popularized in the following form:
the characteristic polynomials of the Hecke operators  acting on the
space of cusp forms of fixed weight for SL(2,Z) are all irreducible and
have full Galois group. Beyond Maeda-Hida's work, this conjecture, if
true, would have different consequences; for example for the
non-vanishing of L-functions or the inverse Galois problem. We will
explain the significance of the conjecture and discuss some recent
progress.

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