# Past Forthcoming Seminars

Plumes are a characteristic feature of convective flow through porous media. Their dynamics are an important part of numerous geological processes, ranging from mixing in magma chambers to the convective dissolution of sequestered carbon dioxide. In this talk, I will discuss models for the spread of convective plumes in a heterogeneous porous environment. I will focus particularly on the effect of thin, roughly horizontal, low-permeability barriers to flow, which provide a generic form of heterogeneity in geological settings, and are a particularly widespread feature of sedimentary formations. With the aid of high-resolution numerical simulations, I will explore how a plume spreads and flows in the presence of one or more of these layers, and will briefly consider the implications of these findings in physical settings.

In this interactive workshop, we'll discuss what mathematicians are looking for in written solutions. How can you set out your ideas clearly, and what are the standard mathematical conventions? Please bring a pen or pencil!

This session is likely to be most relevant for first-year undergraduates, but all are welcome.

Transdifferentiation, the process of converting from one cell type to another without going through a pluripotent state, has great promise for regenerative medicine. The identification of key transcription factors for reprogramming is limited by the cost of exhaustive experimental testing of plausible sets of factors, an approach that is inefficient and unscalable. We developed a predictive system (Mogrify) that combines gene expression data with regulatory network information to predict the reprogramming factors necessary to induce cell conversion. We have applied Mogrify to 173 human cell types and 134 tissues, defining an atlas of cellular reprogramming. Mogrify correctly predicts the transcription factors used in known transdifferentiations. Furthermore, we validated several new transdifferentiations predicted by Mogrify, including both into and out of the same cell type (keratinocytes). We provide a practical and efficient mechanism for systematically implementing novel cell conversions, facilitating the generalization of reprogramming of human cells. Predictions are made available via http://mogrify.net to help rapidly further the field of cell conversion.

At first glance the Interdistrict shipping problem resembles a transportation problem. N sources with M destinations with k Stock keeping units (SKU’s); however, we want to solve for the optimal shipping frequency between each node while determining the flow of each SKU across the network. As the replenishment quantity goes up, the shipping frequency goes down and the inventory holding cost goes up (AWI = Replenishment Qty/2 + SS). Safety stock also increases as frequency decreases. The relationship between replenishment quantity and shipping frequency is non-linear (frequency = annual demand/replenishment qty). The trucks which are used to transfer the product have finite capacity and the cost to drive the truck between 2 locations is constant regardless of how many containers are actually on the truck up to the max capacity. Each product can have a different footprint of truck capacity. Cross docking is allowed. (i.e. a truck may travel from Loc A to loc B carrying products X and Y. At loc B, the truck unloads product X, picks up product Z, and continues to location C. The key here is that product Y does not incur any handling costs at Loc B while products X and Z do.)

The objective function seeks to minimize the total costs ( distribution + handling + inventory holding costs) for all locations, for all SKU’s, while determining how much of each product should flow across each arc such that all demand is satisfied.

Many types of patterns emerging spontaneously can be observed in systems involving thin elastic plates and subjected to external or internal stresses (compression, differential growth, shearing, tearing, etc.). These mechanical systems can sometime be seen as model systems for more complex natural systems and allow to study in detail elementary emerging patterns. One of the simplest among such systems is a bilayer composed of a thin plate resting on a thick deformable substrate. Upon slight compression, periodic undulations (wrinkles) with a well-defined wavelength emerge at the level of the thin layer. We will show that, as the compression increases, this periodic state is unstable and that a second order transition to a localized state (fold) occurs when the substrate is a dense fluid.

We will see some results and conjectures on the zeta and multizeta values in the function field context, and see how they relate to homological-homotopical objects, such as t-motives, iterated extensions, and to Hopf algebras, big Galois representations.

Conical symplectic resolutions are one of the main objects in the contemporary mix of algebraic geometry and representation theory,

known as geometric representation theory. They cover many interesting families of objects such as quiver varieties and hypertoric

varieties, and some simpler such as Springer resolutions. The last findings [Braverman, Finkelberg, Nakajima] say that they arise

as Higgs/Coulomb moduli spaces, coming from physics. Most of the gadgets attached to conical symplectic resolutions are rather

algebraic, such as their quatizations and $\mathcal{O}$-categories. We are rather interested in the symplectic topology of them, in particular

finding smooth exact Lagrangians that appear in the central fiber of the (defining) resolution, as they are objects of the Fukaya category.

In this talk, I will present an incomplete equilibrium model to determine the price of an annuity. A finite number of agents receive stochastic income streams and choose between consumption and investment in the traded annuity. The novelty of this model is its ability to handle running consumption and general income streams. In particular, the model incorporates mean reverting income, which is empirically relevant but historically too intractable in equilibrium. The model is set in a Brownian framework, and equilibrium is characterized and proven to exist using a system of fully coupled quadratic BSDEs. This work is joint with Gordan Zitkovic.

Since the legendary 1972 encounter of H. Montgomery and F. Dyson at tea time in Princeton, a statistical correspondence of the non-trivial zeros of the Riemann Zeta function with eigenvalues of high-dimensional random matrices has emerged. Surrounded by many deep conjectures, there is a striking analogyto the energy levels of a quantum billiard system with chaotic dynamics. Thanks

to extensive calculation of Riemann zeros by A. Odlyzko, overwhelming numerical evidence has been found for the quantum analogy. The statistical accuracy provided by an enormous dataset of more than one billion zeros reveals distinctive finite size effects. Using the physical analogy, a precise prediction of these effects was recently accomplished through the numerical evaluation of operator determinants and their perturbation series (joint work with P. Forrester and A. Mays, Melbourne).