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Is a random polynomial irreducible?
Abstract
Given a "random" polynomial over the integers, it is expected that, with high probability, it is irreducible and has a big Galois group over the rationals. Such results have been long known when the degree is bounded and the coefficients are chosen uniformly at random from some interval, but the case of bounded coefficients and unbounded degree remained open. Very recently, Emmanuel Breuillard and Peter Varju settled the case of bounded coefficients conditionally on the Riemann Hypothesis for certain Dedekind zeta functions. In this talk, I will present unconditional progress towards this problem, joint with Lior Bary-Soroker and Gady Kozma.
19th Oxford Cambridge Applied Maths Meeting (aka The Woolly Owl)
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OCIAM @ 30 years - PROGRAM RELEASED
Please register here
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OCIAM was created in 1989, when Alan Tayler, the first director, moved with a group of applied mathematicians into the annex of the Mathematical Institute in Dartington House.
To celebrate our 30th anniversary we have invited twenty speakers, all of whom have spent time in OCIAM, to talk on some of the many aspects of work generated by the group.
This programe will build on the success of ‘Mathematics in the Spirit of Joe Keller’, hosted by the Isaac Newton Institute, Cambridge in 2017.
Programme
The scientific talks commence on Monday 24th June and finish early afternoon on Tuesday 25th June, with lunch served on both days.
There will be a conference dinner on Monday evening at Somerville College, and on Tuesday afternoon the Mathematical Institute cricket match and BBQ at Merton College Pavilion, to which everyone is invited.
Mathematrix - Meet Vicky Neale
Sharing her academic path and experience with teaching and outreach
Mathematrix - Friendly food with Mirzakhani Society
This session is open to all women and non-binary students, and joined with Mirzakhani society, the undergraduate mathematics society for women and non-binary students. The topic will be related to women and confidence.
12:45
String theory compactifications with sources
In recent years, more and more compactifications have emerged whose existence depends crucially on the presence of internal sources to the supergravity fields, such as D-branes and orientifold planes. I will review some solutions of this type in various dimensions, and illustrate their applications to holography and potentially to the problem of finding de Sitter solutions.
12:45
Large-N Non-Supersymmetric 6D CFTs: Hologram or Mirage?
Abstract
In this talk I will present a large class of non-supersymmetric AdS7 solutions of IIA supergravity, and their (in)stabilities. I will start by reviewing supersymmetric AdS7 solutions of 10D supergravity dual to 6D (1,0) SCFTs. I will then focus on their non-supersymmetric counterpart, discussing how they are related. The connection between supersymmetric and non-supersymmetric solutions leads to a hint for the SUSY breaking mechanism, which potentially allows to evade some of the assumptions of the Ooguri-Vafa Conjecture about the AdS landscape. A big subset of these solutions shows a curious pattern of perturbative instabilities whenever many open-string modes are considered. On the other hand an infinite class remains apparently stable.
We are the largest research group within the Mathematical Institute; between students, faculty, researchers, and visitors, the Centre has around 80 active members and many friends and collaborators around the world. Because of the collaborative nature of all of our research it is difficult to divide OCIAM into neat groups and even harder to fit any of its members into a single group, but dividing by application area we can list the following:
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