Fri, 07 May 2021

15:00 - 16:00
Virtual

Investigating Collective Behaviour and Phase Transitions in Active Matter using TDA - Dhananjay Bhaskar

Dhananjay Bhaskar
(Brown University)
Abstract

Active matter systems, ranging from liquid crystals to populations of cells and animals, exhibit complex collective behavior characterized by pattern formation and dynamic phase transitions. However, quantitative analysis of these systems is challenging, especially for heterogeneous populations of varying sizes, and typically requires expertise in formulating problem-specific order parameters. I will describe an alternative approach, using a combination of topological data analysis and machine learning, to investigate emergent behaviors in self-organizing populations of interacting discrete agents.

Thu, 10 Jun 2021

13:00 - 14:00
Virtual

Dynamic Fluid-Solid Interactions at the Capillary Scale

Daniel Harris
(Brown University)
Abstract

Understanding the motion of small bodies at a fluid interface has relevance to a range of natural systems and technological applications. In this talk, we discuss two systems where capillarity and fluid inertia govern the dynamics of millimetric particles at a fluid interface.

In the first part, we present a study of superhydrophobic spheres impacting a quiescent water bath.  Under certain conditions particles may rebound completely from the interface - an outcome we characterize in detail through a synthesis of experiments, modeling, and direct numerical simulation.  In the second half, we introduce a system wherein millimetric disks trapped at a fluid interface are vertically oscillated and spontaneously self-propel.  Such "capillary surfers" interact with each other via their collective wavefield and self-assemble into a myriad of cooperative dynamic states.  Our experimental observations are well captured by a first theoretical model for their dynamics, laying the foundation for future investigations of this highly tunable active system.

Mon, 08 Feb 2021
14:15
Virtual

Punctured invariants and gluing

Dan Abramovich
(Brown University)
Abstract
Associativity in quantum cohomology is proven using a gluing formula for Gromov-Witten invariants. The gluing formula underlying orbifold quantum cohomology has additional interesting features. The Gross-Siebert program requires an analogue of quantum cohomology in logarithmic geometry, with underlying gluing formula for punctured logarithmic invariants. I'll attempt to explain how this works and what new subtle features arise. This is based on joint work with Q. Chen, M. Gross and B. Siebert (https://arxiv.org/pdf/2009.07720.pdf).
Thu, 09 May 2019

11:00 - 12:00
L4

Finite element exterior calculus with smoother finite element spaces

Johnny Guzmán
(Brown University)
Abstract

The finite element exterior calculus is a powerful approach to study many problems under the same lens. The canonical finite element spaces (see Arnold, Falk and Winther) are tied together with an exact sequence and have the required smoothness to define the exterior derivatives weakly. However, some applications require spaces that are more smooth (e.g. plate bending problems, incompressible flows). In this talk we will discuss some recent results in developing finite element spaceson simplicial triangulations with more smoothness, that also fit in an exact sequence. This is joint work with Guosheng Fu, Anna Lischke and Michael Neilan.

Thu, 26 Nov 2015

13:30 - 14:30
L4

Recent advances in symplectic duality (COW SEMINAR)

Alexander Braverman
(Brown University)
Abstract

It has been observed long time ago (by many people) that singular affine symplectic varieties come in pairs; that is often to an affine singular symplectic variety $X$ one can associate a dual variety $X^!$; the geometries of $X$ and $X^!$ (and their quantizations) are related in a non-trivial way. The purpose of the talk will be 3-fold:

1) Explain a set of conjectures of Braden, Licata, Proudfoot and Webster which provide an exact formulation of the relationship between $X$ and $X^!$

2) Present a list of examples of symplectically dual pairs (some of them are very recent); in particular, we shall explain how the symplectic duals to Nakajima quiver varieties look like.

3) Give a new approach to the construction of $X^!$ and a proof of the conjectures from part 1).

The talk is based on a work in progress with Finkelberg and Nakajima.

Tue, 24 Nov 2015

15:45 - 16:45
L4

The Tamagawa number formula for affine Kac-Moody groups

Alexander Braverman
(Brown University)
Abstract

Let F be a global field and let A denote its adele ring. The usual Tamagawa number formula computes the (suitably normalized) volume of the quotient G(A)/G(F) in terms of values of the zeta-function of F at the exponents of G; here G is simply connected semi-simple group. When F is functional field, this computation is closely related to the Atiyah-Bott computation of the cohomology of the moduli space of G-bundles on a smooth projective curve.

I am going to present a (somewhat indirect) generalization of the Tamagawa formula to the case when G is an affine Kac-Moody group and F is a functional fiend. Surprisingly, the proof heavily uses the so called Macdonald constant term identity. We are going to discuss possible (conjectural) geometric interpretations of this formula (related to moduli spaces of bundles on surfaces).

This is joint work with D.Kazhdan.

Mon, 03 Dec 2012
00:00
SR2

Cutting sequences and Bouw-Möller surfaces

Diana Davis
(Brown University)
Abstract

We will start with the square torus, move on to all regular polygons, and then look at a large family of flat surfaces called Bouw-Möller surfaces, made by gluing together many polygons. On each surface, we will consider the action of a certain shearing action on geodesic paths on the surface, and a certain corresponding sequence.

Thu, 15 Nov 2012

14:00 - 15:00
Gibson Grd floor SR

Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and Non-Standard Reduced Integration

Professor Mark Ainsworth
(Brown University)
Abstract
We study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent (finite element) mass matrix and lumped (spectral element) mass matrix for the small wave number limit. We find and prove that for the optimum blending the resulting scheme

(a) provides $2p+4$ order accuracy for $p$th order method (two orders more accurate compared with finite and spectral element schemes);

(b) has an absolute accuracy which is $\mathcal{O}(p^{-3})$ and $\mathcal{O}(p^{-2})$ times better than that of the pure finite and spectral element schemes, respectively;

(c) tends to exhibit phase lag.

Moreover, we show that the optimally blended scheme can be efficiently implemented merely by replacing the usual Gaussian quadrature rule used to assemble the mass and stiffness matrices by novel nonstandard quadrature rules which are also derived.

Mon, 17 Jan 2011

17:00 - 18:00
Gibson 1st Floor SR

Linear instability of the Relativistic Vlasov-Maxwell system

Jonathan Ben-Artzi
(Brown University)
Abstract
We consider the Relativistic Vlasov-Maxwell system of equations which

describes the evolution of a collisionless plasma. We show that under

rather general conditions, one can test for linear instability by

checking the spectral properties of Schrodinger-type operators that

act only on the spatial variable, not the full phase space. This

extends previous results that show linear and nonlinear stability and

instability in more restrictive settings.

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