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Series: CDSNS Colloquium

Several modern footbridges around the world have experienced large lateral vibrations during crowd loading events. The onset of large-amplitude bridge wobbling has generally been attributed to crowd synchrony; although, its role in the initiation of wobbling has been challenged. In this talk, we will discuss (i) the contribution of a single pedestrian into overall, possibly unsynchronized, crowd dynamics, and (ii) detailed, yet analytically tractable, models of crowd phase-locking. The pedestrian models can be used as "crash test dummies" when numerically probing a specific bridge design. This is particularly important because the U.S. code for designing pedestrian bridges does not contain explicit guidelines that account for the collective pedestrian behavior. This talk is based on two recent papers: Belykh et al., Science Advances, 3, e1701512 (2017) and Belykh et al., Chaos, 26, 116314 (2016).

Monday, November 20, 2017 - 14:00 ,
Location: Skiles 005 ,
Yat Tin Chow ,
Mathematics, UCLA ,
ytchow@math.ucla.edu ,
Organizer: Prasad Tetali

In this talk, we will introduce a family of stochastic processes on the
Wasserstein space, together with their infinitesimal generators. One of
these processes is modeled after Brownian motion and plays a central
role in our work. Its infinitesimal generator defines a partial
Laplacian on the space of Borel probability measures, taken as a
partial trace of a Hessian. We study the eigenfunction of this partial
Laplacian and develop a theory of Fourier analysis. We also consider
the heat flow generated by this partial Laplacian on the Wasserstein
space, and discuss smoothing effect of this flow for a particular class
of initial conditions. Integration by parts formula, Ito formula and an
analogous Feynman-Kac formula will be discussed.
We note the use of the infinitesimal generators in the theory of Mean
Field Games, and we expect they will play an important role in future
studies of viscosity solutions of PDEs in the Wasserstein space.

Series: Geometry Topology Seminar

It is generally a difficult problem to compute the Betti numbers of a
given finite-index subgroup of an infinite group, even if the Betti
numbers of the ambient group are known. In this talk, I will describe a
procedure for obtaining new lower
bounds on the first Betti numbers of certain finite-index subgroups of
the braid group. The focus will be on the level 4 braid group, which is
the kernel of the mod 4 reduction of the integral Burau representation.
This is joint work with Dan Margalit.

Series: Algebra Seminar

Real-valued smooth differential forms on Berkovich analytic spaces were introduced by Chambert-Loir and Ducros. They show many fundamental properties analogous to smooth real differential forms on complex manifolds, which are used for example in Arakelov geometry. In particular, these forms define a real valued bigraded cohomology theory for Berkovich analytic space, called tropical Dolbeault cohomology. I will explain the definition and properties of these forms and their link to tropical geometry. I will then talk about results regarding the tropical Dolbeault cohomology of varietes and in particular curves. In particular, I will look at finite dimensionality and Poincar\'e duality.

Series: PDE Seminar

The aim of talk is threefold. First, we solve the cubic nonlinear Schr\"odinger equation on the real line with initial data a sum of Dirac deltas. Secondly, we show a Talbot effect for the same equation. Finally, we prove an intermittency phenomena for a class of singular solutions of the binormal flow, that is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. If time permits some questions concerning the transfer of energy and momentum will be also considered.

Series: Combinatorics Seminar

Official School Holiday: Thanksgiving Break