InFoMM CDT Group Meeting
InFoMM CDT Group Meeting
InFoMM CDT Group Meeting
InFoMM CDT Group Meeting
Vicky Neale - Closing the Gap: the quest to understand prime numbers
Abstract
Prime numbers have intrigued, inspired and infuriated mathematicians for millennia and yet mathematicians' difficulty with answering simple questions about them reveals their depth and subtlety.
Join Vicky to learn about recent progress towards proving the famous Twin Primes Conjecture and to hear the very different ways in which these breakthroughs have been made - a solo mathematician working in isolation, a young mathematician displaying creativity at the start of a career, a large collaboration that reveals much about how mathematicians go about their work.
Vicky Neale is Whitehead Lecturer at the Mathematical Institute, University of Oxford and Supernumerary Fellow at Balliol College.
Please email @email to register.
11:00
Does decidability go up in finite field extensions?
Abstract
We will follow a suggestion by Udi to construct a decidable field which has an undecidable finite extension.
Governments around the world are seeking to address the economic and humanitarian consequences of climate change. One of the most graphic indications of warming temperatures is the melting of the large ice caps in Greenland and Antarctica. This is a litmus test for climate change, since ice loss may contribute more than a metre to sea-level rise over the next century, and the fresh water that is dumped into the ocean will most likely affect the ocean circulation that regulates our temperature.
15:00
Hierarchical Identity-based Encryption from Ideal Lattices
Abstract
Identity-based cryptography can be useful in situations where a full-scale public-key infrastructure is impractical. Original identity-based proposals relied on elliptic curve pairings and so are vulnerable to quantum computers. I will describe some on-going work to design a post-quantum identity-based encryption scheme using ideas from Ring Learning with Errors. Our scheme has the advantage that it can be extended to the hierarchical setting for more flexible key management.
11:00
Modular Andre-Oort with Derivatives - Recent Developments
Abstract
I will discuss my ongoing project towards a version of the Modular Andre-Oort Conjecture incorporating the derivatives of the j function. The work originates with Jonathan Pila, who formulated the first "Modular Andre-Oort with Derivatives" conjecture. The problem can be approached via o-minimality; I will discuss two categories of result. The first is a weakened version of Jonathan's conjecture. Under an algebraic independence conjecture (of my own, though it follows from standard conjectures), the result is equivalent to the statement that Jonathan's conjecture holds.
The second result is conditional on the same algebraic independence conjecture - it specifies more precisely how the special points in varieties can occur in this context.
If time permits, I will discuss my most recent work towards making the two results uniform in algebraic families.