

FRIDAYMAY 12TH 
SATURDAYMAY 13TH 
SUNDAY MAY 14TH 
1:45 PM  2:00 PM
Opening remarks and announcements:
John Meakin, Chair, Department of Mathematics, University of Nebraska Lincoln 
Twenty minute talks will be presented in parallel sessions 
Twenty Minute Talks will be presented in parallel sessions 
Ambar Sengupta, Louisiana State University
Title: Functional Integrals in Lowdimensional Gauge Theories
Abstract: Twodimensional YangMills gauge theory and three dimensional ChernSimons theory have produced mathematical problems ranging from probability theory to topology of the moduli space of flat connections. This talk will present an overview of some of these mathematical problems and results. 
Dong Hyun Cho, Kyonggi University
Title: A Change of Scale Formula for Conditional Wiener Integrals over Paths in Abstract Wiener Space
Abstract: Click here for the PDF file. 
Bong Jin Kim, Daejin University
Title: Integration by Parts Formulas Involving FourierFeynman Transforms
Abstract: In this talk we investigate the FourierFeynman transform, the convolution product and the first variation of a functional on abstract Wiener space. We also study integration by parts formulas for the analytic Feynman integral involving FourierFeynman transform of those functionals. 
Sarada Rajeev, University of Rochester
Title: Quantization of Contact Geometry and Quantum Thermodynamics
Abstract: In classical thermodynamics, like in classical mechanics, there is a notion of canonically conjugate observables; pressure is conjugate to
volume, temperature to entropy, magnetic field to magnetization etc. I will argue that if quantum effects are included in thermodynamics, the observables do not commute and even satisfy a kind of thermodynamic uncertainty principle. This algebra of thermodynamic observables can be determined in most cases of physical interest by analogy to the passage from classical mechanics to quantum mechanics. I will also review the geometric formulation of classical mechanics in terms of contact geometry ( the work of J. W. Gibbs). This is then generalized to the quantum theory to get a
noncommutative contact geometry. A reformulation in terms of path integrals will be discussed briefly as well. 
Tepper Gill, Howard University
Title: Elementary Introduction to the Feynman Operator Calculus, and Unification of Hyperbolic and Parabolic Evolution Equations
Abstract: In this talk, we present an elementary introduction to the Feynman operator calculus by directly extending the notion of strong continuity to the timeordered setting. We then provide generalizations of a few generation theorems (including the Hille Yosida theorem) and use these results to unify the two distinct approaches to existence and uniqueness theorems for general hyperbolic and parabolic (timedependent) evolution equations. We impose no domain restrictions and only assume strong continuity for the given family of operatorvalued functions. 
Jun Tanaka, University of California Riverside
Title: The Feynman Integral
Abstract: First, I will give an expository introduction of the Wiener Integral. From there, I will derive the heat equation from the Schrodinger equation by sending t to i*t. This will serve as a natural
transition to the Semi Heat Equation, for which I will also give an expository outline. Finally, all of these results and the Trotter
Product Formula will be used to show how the FeynmanKac formula is
derived. 
Anna Amirdjanova, University of Michigan
Title: Physically inspired stochastic partial differential
equations.
Abstract: The talk is devoted to advances in the study of three fundamental equations of mathematical physics (heat, Burgers' and NavierStokes) when the classical models are perturbed by random forces. Questions of existence, uniqueness and regularity
of solutions will be discussed and some open problems presented. 
Gopinath Kallianpur, University of North Carolina
Title: A Stochastic Feynman Integral
. 
Brian Jefferies, University of New South Wales
Title: Feynman's Operational Calculus with Brownian TimeOrdering
Abstract: The idea of replacing a timeordering measure in Feynman's operational calculus by Brownian motion is quite natural and has been considered by G.W. Johnson and G. Kallianpur, who use the term "stochastic Dyson series". Solutions to the Schroedinger equation with a stochastic perturbation are represented as a stochastic Dyson series. A similar representation of the solutions of linear stochastic partial differential equations seems to be closely related to problems in harmonic analysis concerning maximal regularity of operators acting in a Banach space. 
Brian DeFacio, University of Missouri
Title: Feynman Functionals for old problems: Understanding some complex systems in modern warfare
Abstract: Wars have been a common activity among our species for longer than written records ; and even beyond oral traditions.While consulting for the LMI Corp. in McLean , VA for the US Navy it became clear to me that the Feynman Functional gave a formulation of the matters our panel was discussing. Some of these issues will be presented to this workshop. 
Seung Jun Chang, Dankook University
Title: Translation Theorems of Generalized Feynman Integrals with Applications
Abstract: TBA

Jean Claude Zambrini, University of Lisbon
Title: Path Integrals and Deformation of Contact Geometry
Abstract: We shall describe a deformation of contact geometry relevant to Feynman Integral strategy,and some applications 
G. W. Johnson, University of Nebraska Lincoln
Title: Remarks on Feynman's Operational Calculi for Noncommuting Operators
Abstract: The heuristic ideas. Some aspects of a rigorous approach to Feynman's operational calculi. Two 'new' resultsenlarging Feynman's operational calculi and decomposing disentanglings. 
Bruce Driver, University of California, San Diego
Title: Geometric Path Integrals
Abstract: Click Here (PDF file) 
Lance Nielsen, Creighton University
Title: An Integral Equation for Feynman's Operational Calculus
Abstract: An integral equation for the operational calculus is presented and one or two applications will be discussed. 
Brett Barwick, University of Nebraska Lincoln
Title: Using Feynman Path Integrals to Model Electron Diffraction
Abstract: This talk will relate how Feynman integrals can be used to model electron diffraction experiments and how they are used to model things in matter optics and interferometry. Theoretical along with experimental data will be presented. 
David Skoug, University of Nebraska Lincoln
Title: Some Favorite Theorems
Abstract: We will briefly discuss two theorems.
1. A simple formula for conditional Wiener integrals.
2. A necessary and sufficient condition that a functional F on Wiener space has an integral transform. 
LUNCH BREAK 
6:30 PM  8:00 PM
Opening reception in the Arbor Room of the Cornhusker Hotel, 333 S. 13th Street, Lincoln, NE 
William Boos, Iowa
Title: A Stochastic Representation of Feynman Integration
Abstract: Click Here
SATURDAYMAY 13TH 
Twenty minute talks will be presented in parallel sessions 
Kun Sik Ryu, Han Nam University
Title: The Dobrakov Integral Over Paths
Abstract: In 2002 the author introduced the definition and its properties of an analogue of Wiener measure over paths. In this article, using these concepts, we will derive an operatorvalued measure over paths and will investigate the properties for integral with respect to the measure, Specifically, we will prove the Wiener integration formula for our integral and give some examples. 
Mark Burgin, UCLA
Title: Feynman Integral in the Context of Hyperintegration
Abstract: Click Here for a PDF of the abstract 
Naoto Kumanogo, Kogakuin University
and Daisuke Fujiwara, Gakushuin University
Title: Smooth Functional Derivatives in Feynman Path Integrals by Time Slicing Approximation
Abstract:We give a fairly general class of functionals on a path space so that Feynman path integral has a mathematically rigorous meaning. More precisely, for any functional belonging to our class, the time slicing approximation of Feynman path integral converges uniformly on compact subsets of the configuration space. Our class of functionals is closed under addition, multiplication, translation, real linear transformation and functional differentiation. The invariance under translation and orthogonal transformation, the integration by parts with respect to functional differentiation, the interchange of the order with RiemannStieltjes integrals, the interchange of the order with a limit, the semiclassical approximation and the fundamental theorem of calculus hold in Feynman path integral. 
Troy Riggs, Union University
Title: Feynman’s operational calculus and the path space integral for the Dirac Equation.
Abstract: The Dirac equation in one (space) dimension has a solution in the form of a path integral. Beginning with a formulation for this path integral given by T. Zastawniak, and using a technique of operator timereordering, we see that this integral can be interpreted as a perturbation series. This development provides a rigorous means of carrying out the “disentangling” process in Feynman’s timeordered operational calculus for noncommuting operators.

Michel Lapidus, University of California, Riverside
Title: From the Feynman Integral to Feynman’s Operational Calculus, and Back
Abstract: In this talk, we will discuss some of the analogies and differences between the Feynman integral approach to quantum physics and the Feynman operational calculus approach. In particular, by using perturbation expansions, one can see that the Feynman integral approach naturally leads to the basic heuristic rules of the operational calculus. After having briefly recalled the heuristic underlying the two approaches, we will show how, in turn, the latter can lead to a precise definition (under suitable hypotheses) of the former. In fact, under suitable assumptions, a mathematical realization of the operational calculus can also be viewed as an appropriate extension of and substitute for the Feynman integral in situations when the ‘integral’ itself is difficult to define directly. Conversely, the latter is a global object whose definition, in principle, does not depend on the existence of any particular perturbation expansion. Much of the usefulness of the heuristic Feynman integral in contemporary mathematics and physics relies on the tension and crossfertilization between these two apparently very different settings and approaches.
Much of the rigorous part of the work presented in this talk is joint work with Gerald Johnson and is discussed in Chapters 16 and 18 of our joint book on the “Feynman Integral and Feynman’s Operational Calculus (Oxford Univ. Press, 2000), as well as in a joint paper in preparation. 
BREAK 
Louis Kauffman, University of Illinois Chicago
Title: Feynman Integrals and the Theory of Knots
Abstract: Witten showed how to formulate the Jones polynomial and its generalizations in terms of functional integrals and quantum field theory. This talk will review the heuristics of these constructions and how they are related to fully rigorous combinatorial models for the topological invariants. We then raise the question of new and as yet undiscovered physical interpretations for the categorifications of these invariants, particularly for Khovanov homology that generalizes the bracket polynomial state summation for the Jones polynomial.

SATURDAYMAY 13TH 
Twenty minute talks will be presented in parallel sessions 
Byoung Soo Kim, Seoul National University of Technology
Title: Extracting a Linear Factor in Feynman's Operational Calculi; Blend of Continuous and Discrete Measures
Abstract: Formulas which simplify the disentangling process under various conditions are important in Feynman's Operational Calculi. Extraction of a linear factor make it possible to carry out the disentangling in an iterative manner. We extend the extraction of a linear factor in the setting where the measures are allowed to have both continuous and discrete parts.

Jan Van Casteren, University of Antwerp
Title: Backward Stochastic Differential Equations and Markov Processes
Abstract: In this lecture we endeavor to explain the notion of stochastic backward differential equations and its relationship with classical (backward) parabolic differential equations of second order. We will employ stochastic processes like Markov processes and martingale theory to treat semilinear partial differential equations of parabolic type. FeynmanKac formulae and heat equations fit in this setup, and so do certain versions of the HamiltonJacobiBellmann equation.

Adrian Lim, University of California San Diego
Title: TBA
Abstract: I will present an extension of a result by B. Driver. By defining a sequence of finite dimensional spaces of piecewise geodesics on a manifold equipped with a measure, one can write a sequence of integrals which converge to an integral over Wiener space. 
Katherine Kime, University of Nebraska Kearney
Title: Finite Difference Approximation of QuantumMechanical Wave Packets
Abstract: If a wave packet is moving along and it reaches a place where things are a little bit different, some of it will continue onward and some of it will bounce back. It’s quite difficult to analyze such a situation using a wave packet because everything varies in time. It is much easier to work with steadystate solutions". The Feynman Lectures on Physics, Volume III
One way that the above difficulty has been approached is through numerical approximation. We will discuss the equations for N coupled harmonic oscillators and finite difference approximations of the wave and Schrodinger equations. We will compare the approximation of the impingement of a quantummechanical wave packet on a potential barrier with the approximation of the wave equation at an interface. 
Banquet in honor of Jerry Johnson and Dave Skoug at the Cornhusker Hotel. For information about the banquet, go to the banquet page. 

