|Michael Bush||Michael Bush||Zoom||Title:Extension Theory and Finite Rank Perturbations
Abstract: From the moment we are taught the definition of a function, the notion of a function's domain, and its importance is emphasized. This work hinges on the profound way that altering the domain of an operator impacts its behavior. We will examine the minimal and maximal domains of some differential operators as well as self-adjoint extensions of those operators. Ultimately, we will connect varying the boundary conditions associated with an operator to its representation as a self-adjoint extension.
||5/13/2020 5:30:00 PM||5/13/2020 6:30:00 PM||False|
|Himanshu Gupta||Himanshu Gupta||Zoom||<br>
Title: Correlation Functions in the Finite Toom Model
Abstract: The Toom model is a famous mathematical model given by A. Toom in 1980. It is a discrete time dynamical model on Z2 where each site is occupied either by + or − spins. In 2015, A. Ayyer considered a finite version of the one-dimensional Toom model with closed boundaries. In this model, each site is occupied either by a particle of type 0 or of type 1, where the total number of particles of type 0 and type 1 are fixed to be n0 and n1 respectively. We call this an (n0, n1)-Toom model. The dynamics are as follows: the leftmost particle in a block can exchange its position with the leftmost particle of the block to its right. In this talk, we start with some basic definitions like continuous time Markov chain (CTMC), generator matrix, steady state distribution, balance equation and correlation function. After this, we define the model and prove some results regarding the model that we have worked on in my master's thesis in 2018.
||5/6/2020 5:30:00 PM||5/6/2020 6:30:00 PM||False|
|Jerome Troy||Jerome Troy||Zoom||Title: An introduction to the finite element method using FEniCS
Abstract: The finite element method provides a high accuracy framework to solve differential equations in various geometries. However, getting started with finite element software can prove daunting for newbies. The FEniCS software provides an intuitive interface to solve even the most complex problems. We will explore several examples in which FEniCS can be employed to solve a range of problems, from Laplace's equation to nonlinear time dependent problems.||4/29/2020 5:30:00 PM||4/29/2020 6:30:00 PM||False|
|Gautam Aishwarya||Gautam Aishwarya||Zoom||Title:On the behaviour of the unit normal to the hyperplane spanned by randomly chosen vertices of the cube
Abstract: Let A be a 1/2-Bernoulli random matrix. Consider the unit vector v perpendicular to the n-1 columns A e1 , ⋯ , A en-1 of A. We will discuss some evidence towards the claim that || v ||p behaves as if v is uniformly distributed on the unit sphere and connect it to the problem of determining how close is X/ ||X||, where X is uniformly distributed on an isotropic convex body K, to the uniform distribution on the unit sphere.
||4/22/2020 5:30:00 PM||4/22/2020 6:30:00 PM||False|
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