ICTP Mathematics Seminar - Wednesday 23 January, at 16:00 (John CREMONA)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2019


Wednesday 23 January, at 16:00 hrs.


John Cremona (University of Warwick)


Title: The L-functions and modular forms database project


Abstract:  The simplest and most famous L-function is the Riemann Zeta 
function. L-functions are ubiquitous in number theory, and have 
applications to mathematical physics and cryptography.  Two of the seven 
Clay Mathematics Million Dollar Millennium Problems deal with their 
properties: the Riemann Hypothesis and the Birch and Swinnerton-Dyer 
Conjecture.  They arise from and encode information about a number of 
mathematical objects, and also provide links between them: for example, 
Wiles' celebrated proof of Fermat's Last Theorem centred on proving that 
L-functions associated with certain elliptic curves were also associated 
with other objects called modular forms.

At least a dozen different mathematical objects are connected in various 
ways to L-functions.  The study of those objects is highly specialized, 
and most mathematicians have only a vague idea of the objects outside 
their specialty and how everything is related. Helping mathematicians to 
understand these connections was the motivation for the L-functions and 
Modular Forms Database (LMFDB) project, which started at AIM in 2007 and 
has been supported by major grants from the NSF, the UK EPSRC and the 
Simons Foundation.  Its mission is to chart the landscape of L-functions 
and modular forms in a systematic and concrete fashion.  This involves 
developing their theory, creating and improving algorithms for computing 
and classifying them, and hence discovering new properties of these 
functions, and testing fundamental conjectures.

In the lecture I will explain and demonstrate how we organise our large 
collection of data and display it, together with the interrelations 
between linked objects, through our website [www.lmfdb.org]. I will also 
show how this has been built via a world-wide collaborative open source 
project which we hope to be a model for others.

VENUE: Stasi Seminar Room (ICTP Leonardo da Vinci Building, first floor)

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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