## Spring 2011

Friday, January 21 at 2:00 pm in the conference room |

Patricia Hersh, NC State University |

Regular CW complexes, total positivity and Bruhat order |

“For regular CW complexes, one may deduce topological structure from the combinatorics of the poset of closure relations on cells. However, two different stratified spaces with the same closure poset may have very different topological structure. I will discuss this interplay of combinatorics with topology, including the positive resolution of a conjecture regarding the topology of stratified spaces having the intervals of Bruhat order as their closure posets. A key ingredient is a new criterion for deciding if a finite CW complex is regular with respect to a choice of characteristic maps. I will review background and history of this area along the way.” |

Friday, March 25 at 1:00 pm in the conference room |

Sam Hsiao, Bard College |

Enumerating chains in partially ordered sets |

“The flag f-vector of a finite partially ordered set, or poset, is a vector of positive integers whose entries enumerate chains (i.e., linearly ordered subsets) that pass through various sets of ranks. What does the set of all flag f-vectors of fixed length n look like as a subset Euclidean n-space? I will describe progress on this question that resulted from joint work with colleague Lauren Rose and two undergraduate students–Rachel Stahl and Ezra Winston–at Bard College. The main result is a simple characterization of the closed convex cone spanned by the flag f-vectors of length n. A key ingredient is to construct certain “limit posets” whose flag f-vectors are in some sense extremal, an idea that originated in the work of Louis Billera and Gabor Hetyei.” |

Friday, April 15 at 10:00 am in the conference room |

Guojin Chen, Xiamen University (China) |

Do Imports Crowd Out Domestic Consumption?- A Comparative Study of China, Japan and Korea |

“A decline in the relative price of imported goods compared to that of domestically produced goods may have different effects on domestic consumption. Such effects may not be accurately detected and measured in a classical permanent-income model without considering consumption habit formation as pointed out by Nishiyama (2005). To resolve this problem, this paper employs an extended permanent-income model which encompasses consumption habit formation. Both cointegration analysis and GMM are used to estimate the (modified) intertemporal elasticities of substitution (IES) between imports and domestic consumption and the parameters of habit formation as well as the (modified) intratemporal elasticities of substitution (AES). We find that import and domestic consumptions are complements in China, but substitutes in Japan and Korea. Different per capita incomes and consumer behaviors between China and the other two countries are two possible reasons for different relationships between import and domestic consumptions. The research findings have important implications on policies such as exchange rate adjustments in China.” |

Friday, April 29 at 2:00 pm in the conference room |

Nathan Reading, NC State University |

Coxeter groups and cluster algebras |

” Coxeter groups and cluster algebras are two classes of mathematical objects that tend to pop up in other seemingly unrelated mathematical and physical systems. Coxeter groups (or the related root systems) have been studied in generality for more than 100 years, while primordial examples date back to ancient Greece. Cluster algebras were defined in general only about 11 years ago, with their most “ancient” predecessors probably dating back about 200 years. I’ll mention some of the many places where Coxeter groups/root systems and cluster algebras pop up. (As the most recent example, I was surprised to hear about cluster algebras playing a role in solving the inverse problem for certain KP solitons.)Superficially, Coxeter groups are quite different objects from cluster algebras, but, true to form, Coxeter groups and root systems turn out to be useful tools for understanding the structure of cluster algebras. I’ll give two examples of this usefulness: first, the classification of cluster algebras of finite type in terms of finite root systems; and second, my recent work with David Speyer which builds combinatorial models for cluster algebras in terms of the combinatorics of Coxeter groups.I will assume no prior knowledge of Coxeter groups, root systems or cluster algebras.” |

## Fall 2011

Thursday, October 20 at 2:00pm in the conference room |

Mette Olufsen, NC State University |

Modeling cardiovascular dynamics and its control |

“The main role of the cardiovascular system is to maintain adequate oxygenation of all tissues. This is accomplished by maintaining blood flow and pressure at a fairly constant level. To accomplish the transport, a number of control mechanisms are imposed regulating vascular resistance, compliance, pumping efficiency and frequency. In cardiovascular diseases, both the transport system and its regulation may be compromised, and it is either not known or difficult to study what mechanism that lead to the breakdown of homeostasis. Typically, some general observations can be made, but these vary significant between individuals. Furthermore, for most patients only a few quantities can be measured, making it difficult to assess essential quantities such as cerebral vascular resistance, cardiac contractility, or the gain and time constants associated with the regulation. This presentation will discuss development of patient specific models obtained by combining models predicting control of blood flow, pressure, and heart rate with parameter estimation techniques. Models analyzed are composed of systems of nonlinear equations each specified via a set of model parameters. Nominal parameter values are obtained from analysis of populations and data available. Subsequently, sensitivity analysis, correlation analysis, and subset selection, are combined with parameter estimation techniques to obtain a subset of patient specific parameters.” |

Friday, October 21 at 11:00am in the conference room |

Yuri Kabanov, from University of Franche-Comté, Besanéon, France. |

An introduction to the arbitrage theory for markets with transaction costs |

“A geometric approach to the theory of financial markets with transaction will be explained. A criteria of absence of arbitrage and hedging theorems will be discussed in comparison with the classical theory.”Professor Yuri Kabanov is one of the world-known specialists in the area of financial mathematics and stochastic processes. He is an author of two monographs in the field and is a Member of Editorial Board of Statistical Inference for Stochastic Processes, a Member of Advisory Board of Finance and Stochastic, and in the past was a Member of Editorial Board of Annals of Applied Probability (2000-2005).After the talk and discussion we are planning to take our guest to Thai House University restaurant near the intersection of Harris Bld and N. Tryon. All are welcome to join. |

Monday, October 24 at 3:30pm in the conference room |

De Witt Sumners, Florida State University |

Writhe, Reconnection and Helicity Conservation |

“The directional writhe of a spatial closed curve is the sum of the signed crossings in the projection of the curve in the given direction. The writhe of a simple closed curve in 3-space is the average over all directions of directional writhe. We extend [1] this definition to apply to edge-oriented (each edge has an arrow on it) finite spatial graphs. This definition of writhe covers spatial polygonal arcs and non-connected graphs, and does not require the ad hoc closing of arcs to eliminate the problems posed by endpoints. This talk will discuss the properties of writhe of graphs, and the proof of writhe additivity for connected sums. The proof of additivity of writhe will then be extended to prove conservation of helicity for vortex tubes in fluid dynamics and magnetic fields. If a vortex reconnection event does not insert twist locally at the reconnection site (that is, the twist of the reconnected tube is the sum of the individual twists of each tube), then helicity is conserved. Otherwise, any deviation from helicity conservation is entirely due to twist inserted locally at the reconnection site (the writhe component of helicity is always conserved). It turns out that in some cases, site specific DNA recombination (the analogue of vortex reconnection in the DNA world) inserts local twist; in other cases, DNA recombination does not insert local twist-it depends on the enzyme that is doing the recombination.” |

Friday, November 4 at 2:00pm in the conference room |

Bruce Kellogg, University of South Carolina |

Boundary layers, corner singularities, and mesh refinements |

“We review recent and ongoing work on boundary value problems for a singularly perturbed convection diffusion equation in a domain with corners. The small singular perturbation parameter makes it necessary to use a stretched mesh along the boundary, refined in the direction normal to the boundary. (This is the “Shishkin” mesh.) The corner singularity makes it necessary to use a geometric refinement near the boundary. In each case, the error analysis of a finite element calculation requires good information on derivative bounds for the solution. This talk concerns the case when both a small singular parameter and corners are present in the same problem. Some recent work will be reviewed, our ongoing work will be discussed, and some open problems will be presented. Some ingredients in the error analysis of finite elements for these problems will be given.” |

Wednesday, November 30 at 5:00pm in the conference room |

Serguei Denissov, University of Wisconsin-Madison |

On the instability in two-dimensional fluids |

“The two-dimensional incompressible fluid is governed by the classical 2D Euler equation. Although globally well-posed, this equation poses many interesting mathematical questions including the possible mechanism for the singularity formation. I will explain some results for 2D Euler and for similar models. “ |