We study a simple one-dimensional coupled heat wave system, obtaining a sharp estimate for the rate of energy decay of classical solutions. Our approach is based on the asymptotic theory of $C_0$-semigroups and in particular on a result due to Borichev and Tomilov (2010), which reduces the problem of estimating the rate of energy decay to finding a growth bound for the resolvent of the semigroup generator. This technique not only leads to an optimal result, it is also simpler than the methods used by other authors in similar situations and moreover extends to problems on higher-dimensional domains. Joint work with C.J.K. Batty (Oxford) and L. Paunonen (Tampere).

TBA

We provide a simple convergence analysis unified for TR and a new ARC algorithms, which we name ARCq and which is very close in spirit to trust region methods, closer than the original ARC is. We prove global convergence to second order points. We also obtain as a corollary the convergence of the original ARC method. Since one of our aims is to achieve a simple presentation, we sacrifice some generality which we discuss at the end of our developments. In this simplified setting, we prove the optimal complexity property for the ARCq and identify the key elements which allow it. We then propose efficient implementations using a Cholesky like factorization as well as a scalable version based on conjugate gradients.

This is an exciting time to study quantum algorithms. As the technological challenges of building a quantum computer continue to be met there is still much to learn about the power of quantum computing. Understanding which problems a quantum computer could solve faster than a classical device and which problems remain hard is particularly relevant to cryptography. We would like to design schemes that are secure against an adversary with a quantum computer. I'll give an overview of the quantum computing that is accessible to a general audience and use a recently declassified project called "soliloquy" as a case study for the development (and breaking) of post-quantum cryptography.

Abstract: (Joint work with Sylvy Anscombe) We consider four properties 
of a field K related to the existence of (definable) henselian 
valuations on K and on elementarily equivalent fields and study the 
implications between them. Surprisingly, the full pictures look very 
different in equicharacteristic and mixed characteristic.

In the real, p-adic and motivic settings, we will present recent results on oscillatory integrals. In the reals, they are related to subanalytic functions and their Fourier transforms. In the p-adic and motivic case, there are furthermore transfer principles and applications in the Langlands program. This is joint work with Comte, Gordon, Halupczok, Loeser, Miller, Rolin, and Servi, in various combinations. 
 

Let M be an algebraic curve over an algebraically closed field and let
$(M, ...)$ be a strongly minimal non-locally modular structure with
basic relations definable in the full Zariski language on $M$. In this
talk I will present the proof of the fact that $(M, ...)$ interprets
an algebraically closed field.

We consider the decision problem of determining whether an exponential
polynomial has a real zero.  This is motivated by reachability questions
for continuous-time linear dynamical systems, where exponential
polynomials naturally arise as solutions of linear differential equations.

The decidability of the Zero Problem is open in general and our results
concern restricted versions.  We show decidability of a bounded
variant---asking for a zero in a given bounded interval---subject to
Schanuel's conjecture.  In the unbounded case, we obtain partial
decidability results, using Baker's Theorem on linear forms in logarithms
as a key tool.  We show also that decidability of the Zero Problem in full
generality would entail powerful new effectiveness results concerning
Diophantine approximation of algebraic numbers.

This is joint work with Ventsislav Chonev and Joel Ouaknine.