Title: Interval hypergraphic lattices

Abstract: For a hypergraph~$\mathbb{H}$ on~$[n]$, the hypergraphic poset~$P_{\mathbb{H}}$ is the transitive closure of the oriented skeleton of the hypergraphic polytope~$\triangle_{\mathbb{H}}$ (the Minkowski sum of the standard simplices~$\triangle_H$ for all~$H \in \mathbb{H}$).Hypergraphic posets include the weak order for the permutahedron (when~$\mathbb{H}$ is the complete graph on~$[n]$) and the Tamari lattice for the associahedron (when~$\mathbb{H}$ is the set of all intervals of~$[n]$), and it is natural to study lattice properties of hypergraphic posets.

In this talk, we focus on interval hypergraphs, where all hyperedges are intervals of~$[n]$.

We characterize the interval hypergraphs~$\mathbb{I}$ for which~$P_{\mathbb{I}}$ is a lattice, and if times allows, a distributive lattice, a semidistributive lattice, and a lattice quotient of the weak order. Joint work with Vincent Pilaud.

In-person or Zoom

Title: Rational Expectations Equilibrium with Optimal Information Acquisition

Abstract: In this talk, we establish equilibrium in the presence of heterogenous information. In particular, there is an insider who receives a private signal, as well as uninformed agents with no private signal, and noise traders with price-inelastic demand. The novelty of the current work is that we allow the insider to decide (optimally) when to acquire the private signal. This endogenizes the entry time and stands in contrast to the existing literature which assumes the signal is received at the beginning of the period. Allowing for optimal entry also enables us to study what happens before the insider enters with private information, and how the possibility for future information acquisition both affects current asset prices and creates demand for information related derivatives. Results are valid in continuous time, when the private signal is a noisy version of the assets’ terminal payoff (the terminal value of an Ornstein Uhlenbeck diffusion), and when the quality of the signal depends on the entry time. This is joint work with Jerome Detemple and Nikos Vingos, both of Boston University.

Join Zoom Meeting: https://usc.zoom.us/j/94973619069?pwd=VnU5bVlMc1pzVTlEYUVaZUYyNSt6UT09

Meeting ID: 949 7361 9069

Passcode: 925028

Title: TBA

Abstract: TBA

]]>Title: Hecke and Artin monoids and their homomorphisms

Abstract: In the present talk we discuss relations between various types of homomorphisms between Hecke and Artin monoids. Our original motivation was based on a striking observation that parabolic projections of Hecke monoids preserve parabolic elements which appeared naturally in the framework of actions of cacti on geometric crystals. We will present several new infinite families of homomorphisms which in some cases provide a complete classification.

]]>Title: Stationary and slowly traveling solutions to the free boundary Navier-Stokes equations

Abstract: The stationary problem for the free boundary incompressible Navier-Stokes equations lies at the confluence of two distinct lines of inquiry in fluid mechanics. The first views the dynamic problem as an initial value problem. In this context, the stationary problem arises naturally as a special type of global-in-time solution with stationary sources of force and stress. One then expects solutions to the stationary problem to play an essential role in the study of long-time asymptotics or attractors for the dynamic problem. The second line of inquiry, which dates back essentially to the beginning of mathematical fluid mechanics, concerns the search for traveling wave solutions. In this context, a huge literature exists for the corresponding inviscid problem, but progress on the viscous problem was initiated much more recently in the work of the speaker and co-authors. For technical reasons, these results were only able to produce traveling solutions with nontrivial wave speed. In this talk we will discuss the well-posedness theory for the stationary problem and show that the solutions thus obtained lie along a one-parameter family of slowly traveling wave solutions. This is joint work with Noah Stevenson.

]]>In person or Zoom

Title: Active Learning Activities in our Calculus I Classes Part II

Abstract: We are participating in the STEM Faculty Teaching Learning Program and are exploring different ways to add active learning to our lectures. We will do some activities and talk about what we’ve done in our classes, and how we made easy changes to make our lectures more active.

Join Zoom Meeting: https://usc.zoom.us/j/97762180859

]]>Title: The mean field Schrödinger problem: a mean field control perspective

Abstract: The mean field Schrödinger problem (MFSP) is the problem of finding the most likely path of a McKean-Vlasov type particle with constrained initial and final configurations. It was first introduced by Backhoff et al. (2020), who studied its existence and long-time behavior. This talk aims to show how ideas from mean field control theory allow us to derive new interesting results on the MFSP. In particular, we study its existence, characterization, and the so-called convergence problem. The method rests upon studying suitably penalized problems and stochastic control techniques. This talk is based on a joint work with Ludovic Tangpi (Princeton).

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