Forthcoming Seminars

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series
26 February 2018

We present a support theorem for subcritical parabolic stochastic partial differential equations (SPDEs) driven by Gaussian noises. In the spirit of the classical theorem by Stroock and Varadhan for ordinary stochastic differential equations, we identify the support of the solution to singular SPDEs with the closure of the union of the support of solutions to approximate and renormalized equations. We implement our approach in the setting of regularity structures and obtain a general result covering a range of singular SPDEs (including $\Phi^4_3$, $\Phi^d_2$, KPZ, PAM (2D+3D), SHE, ...). As a Corollary to our result we obtain the uniqueness of invariant measures for various interesting SPDEs. This is a joint work with Martin Hairer.

  • Stochastic Analysis Seminar
27 February 2018
Jared Tanner

Topological data analysis (TDA) is a method by which the topology one seeks to uncover the topology consistent with a data set.  Persistent homology considers the process of small balls growing around data points until they (sufficiently) interest at which point the associated points are connected and a simplicial complex formed.   The duration by which a topology is determined is then computed by forming and reducing a boundary matrix that denotes when a faces of a simplex are formed.  Reduction of the boundary matrix is qualitatively similar to gaussian elimination 
over a finite field, and historically is implemented in a very sequential manner.As the boundary matrix size grows polynomially on the dimension, a sequential method isn’t ideal for large data sets.  In this talk I will sketch the above process and a new algorithm with Rodrigo Mendoza-Smith by which the boundary matrix can be reduced in a massively parallel fashion.

  • Numerical Analysis Group Internal Seminar
27 February 2018
Alexander Stasinski

Let $F$ be a non-Archimedean local field with ring of integers $\mathcal O$ and maximal ideal $\mathfrak p$. T. Shintani and G. Hill independently introduced a large class of smooth representations of $GL_N(\mathcal O)$, called regular representations. Roughly speaking they correspond to elements in the Lie algebra $M_N(\mathcal O)$ which are regular mod $\mathfrak p$ (i.e, having centraliser of dimension $N$). The study of regular representations of $GL_N(\mathcal O)$ goes back to Shintani in the 1960s, and independently and later, Hill, who both constructed the regular representations with even conductor, but left the much harder case of odd conductor open. In recent simultaneous and independent work, Krakovski, Onn and Singla gave a construction of the regular representations of $GL_N(\mathcal O)$ when the residue characteristic of $\mathcal O$ is not $2$.

In this talk I will present a complete construction of all the regular representations of $GL_N(\mathcal O)$. The approach is analogous to, and motivated by, the construction of supercuspidal representations of $GL_N(F)$ due to Bushnell and Kutzko. This is joint work with Shaun Stevens.


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