Perturbative sigma models, elliptic cohomology and the Witten genus

We provide a differential cocycle model for elliptic cohomology with complex coefficients and use analytic methods to construct a cocycle representative for the Witten class in this language. Our motivation stems from the conjectural connection between 2-dimensional field theories and elliptic cohomology originally due to G. Segal and E. Witten. The specifics of our constructions are informed by the work of S. Stolz and P. Teichner on super Euclidean field theories and K. Costello's construction of the Witten genus using perturbative quantization. As a warm-up, we prove analogous results for supersymmetric quantum mechanics and K-theory with complex coefficients.Comment: Changes made from referees suggestions: statements of main theorems were sharpened, physical motivations were separated from the main mathematical discussion, and the relation to Witten's original construction was clarifie

News from Academy Bay

Donation Made in Memory of Last Grandchild of Ecuador's First President. Deaths of CDF Board Members. Major Gift by Mrs. Louise Van Straelen-Poirier. Itasca to Galápagos. Station Research Vessel

Birationally rigid complete intersections of codimension two

We prove that in the parameter space of $M$-dimensional Fano complete intersections of index one and codimension two the locus of varieties that are not birationally superrigid has codimension at least $\frac12 (M-9)(M-10)-1$.Comment: 29 pages, 2 figure

Analysis of Policy Issues Relating to Public Investment in Private Freight Infrastructure, MTI Report 99-03

The Norman Y. Mineta International Institute for Surface Transportation Policy Studies (IISTPS) at San José State University conducted this study to review the issues and implications involved in the investment of public funds in private freight infrastructure. After thorough legal research, the project team reached the following conclusions: LEGAL ANALYSIS: The California legislature has the legal power to invest public funds in privately-owned freight infrastructure projects State Highway funds, excepting gas tax revenues, may be used for investment in freight infrastructure projects. Gas tax revenues are restricted to highway use by current interpretations of the California Constitution. A challenge to this interpretation is not recommended. Gas tax revenues may be invested in roadway segments of freight infrastructure projects. RECOMMENDATIONS An analytical system of guidelines should be developed to score and evaluate any proposed freight infrastructure project. Economic development must be included in these scoring guidelines. Public agencies should maintain political contacts in order to control the political short-circuits of the planning process. The California Department of Transportation should develop a Freight Improvement Priority System for the purpose of prioritizing all freight improvement projects

Smooth one-dimensional topological field theories are vector bundles with connection

We prove that smooth 1-dimensional topological field theories over a manifold are the same as vector bundles with connection. The main novelty is our definition of the smooth 1-dimensional bordism category, which encodes cutting laws rather than gluing laws. We make this idea precise through a smooth generalization of Rezk's complete Segal spaces. With such a definition in hand, we analyze the category of field theories using a combination of descent, a smooth version of the 1-dimensional cobordism hypothesis, and standard differential geometric arguments.Comment: 20 pages. Comments and questions are very welcom

Foodi - Automated Ordering System

We worked for BeSprout Technology to create an automated ordering system called Foodi. The Foodi system uses a combination of Java, IBM Watson, and MySQL to gather all the necessary information needed for the conversation, and is dynamic so it can be used in multiple restaurants. Many people still place orders via a phone call, so in an effort to streamline the ordering process, this project was created to enable automatic order placing so employees can focus on other tasks within the restaurant. When a customer calls a restaurant, Foodi will take care of any orders and answer questions the customer may have. The input from the user is sent to Watson, and is filtered through a conversation tree created with IBM’s Bluemix. Bluemix uses the user input to navigate to certain nodes. When a node in the conversation tree is hit, the user input is passed into Java code and parsed appropriately. After the input has been parsed in Java, Watson is told which node in the conversation tree to travel to next and how to respond to the user. This process is repeated until the user is finished ordering and the final order is repeated back to the customer. The restaurant receives the final order and begins preparing the food.https://scholarscompass.vcu.edu/capstone/1181/thumbnail.jp