Special Seminars

2021-11-08 09:00 - 10:00

During the 2021–22 academic year, the CMSA will be hosting a few special seminars which will be listed below.

The Economics Seminar Series, organized by Jörn Boehnke, will take place virtually on Zoom. To learn how to attend, please contact boehnke@cmsa.fas.harvard.edu. The schedule below will be updated as talks are confirmed.

1:30 –2:30 PM ET
Minh-Binh TRAN (SMU & MIT) Random Matrix & Probability Theory Seminar

Location: CMSA, Room G02**

**** Note:  Non-Harvard affiliates must complete the CMSA Covid Form prior to arrival: https://forms.gle/xKykcNcXq7ciZuvJ8

Title: On the wave turbulence theory for a stochastic KdV type equation

Abstract: We report recent progress, in collaboration with Gigliola Staffilani (MIT), on the problem of deriving kinetic equations from dispersive equations. To be more precise, starting from the stochastic  Zakharov-Kuznetsov equation, a multidimensional KdV type equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave  kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is  $d\ge 2$, the smallness of the nonlinearity $\lambda$ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation.  Unlike the cubic nonlinear Schrodinger equation, for which such a general result is commonly expected without the noise, the kinetic description of the deterministic lattice ZK equation is unlikely to happen. One of the key reasons is that the dispersion relation of the lattice ZK equation leads to a singular manifold, on which not only 3-wave interactions but also all m-wave interactions are allowed to happen. This phenomenon has been first observed by Lukkarinen as a counterexample for which one of the main tools to derive kinetic equations from wave equations (the suppression of crossings) fails to hold true.

9:00 am – 10:00 am ET
 Alberto Bracci
(City, University of London)
Title:  Macroscopic properties of buyer-seller networks in online marketplaces

Abstract:  Online marketplaces are the main engines of legal and illegal e-commerce, yet the aggregate properties of buyer-seller networks behind them are poorly understood. We analyse two datasets containing 245M transactions (16B USD)  between 2010 and 2021 involving online marketplaces: 28 dark web marketplaces (DWM), unregulated markets whose main currency is Bitcoin, and 144 product markets of one regulated e-commerce platform. We show how transactions in online marketplaces exhibit strikingly similar patterns of aggregate behavior despite significant differences in language, products, time, regulation, oversight, and technology. We find remarkable regularities in the distributions of (i) transaction amounts, (ii) number of transactions, (iii) inter-event times, (iv) time between first and last transactions. We then show how buyer behavior is affected by the memory of past interactions, and draw on these observations to propose a model of network formation able to reproduce the main stylised facts of the data. Our findings have important implications for understanding market power on online marketplaces as well as inter-marketplace competition.