Un of Tenn | Math Department

Seminars and Colloquiums
for the week of March 3, 2008

Speakers:

Professor Xiaowen Zhou, Monday
Dr. Renee Fister, Monday
Professor Remus Nicoara, Wednesday
Professor Y. Jiang, Wednesday
Mr. Drew Schmidt, Wednesday
Dr. David Nualart, Thursday

Monday, March 3

PROBABILITY SEMINAR
TIME: 10:10 – 11:00 a.m.
ROOM: Ayres 309A

SPEAKER: Professor Xiaowen Zhou, Concordia University, Canada
TITLE: “The exit problem for a spectrally negative Levy process partially reflected from its maximum (II)”
ABSTRACT: Let $X$ be a L\'evy process with only negative jumps and $S$ be its running maximum process. For any constant $0<\gamma<1$, define \[Y_t=X_t-\gamma S_t.\] For $-a<0<b $ let \[\tau^+_b=\inf\{t: Y_t>b\}\] and \[\tau^-_{-a}=\inf\{t: Y_t<-a\}.\]

In this talk we are going to find an expression for $E\left[e^{-\lambda \tau^+_b}, \tau^+_b<\tau^-_{-a}\right]$. This result is from a recent joint work with Hansjorg Albrecher and Jean-Francois Renaud.

DE/APPLIED AND COMPUTATIONAL MATH SEMINAR
TIME: 3:35 – 4:25
ROOM: Ayres 104

SPEAKER: Dr. Renee Fister, Murray State University
TITLE: “Curing Cancer with Mathematics?”
ABSTRACT: Optimal control techniques are applied to mathematical models describing cancer dynamics. The results include discussion of bang-bang and singular controls. Numerical results are presented.

Wednesday, March 5

ANALYSIS SEMINAR
TIME: 2:30 – 3:30 p.m.
ROOM: TBA

SPEAKER: Professor Remus Nicoara
TITLE: “On von Neumann Algebras Arising from 2-Cocycles of Property (T) Groups” (continued)
ABSTRACT: We consider von Neumann algebras $L(G,\mu)$ associated to Kazhdan property (T) discrete groups $G$ with scalar 2-cocycles $\mu$. We show that, for fixed $G$, there exists no separable finite von Neumann algebra containing $L(G,\mu_i)$ for uncountably many non-equivalent 2-cocycles $\mu_i$ of $G$. In particular, $L(G,\mu_i)$ are non-isomorphic modulo countable sets. This is joint work with S.Popa and R. Sasyk.

In this second talk we give a brief introduction to property (T) and relative property (T) for groups, and connections with projective representations.

COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 214

SPEAKER: Professor Y. Jiang
TITLE: “Multiscale modeling framework for cancer development”
ABSTRACT: Cancer remains one of the leading cause of disease death for middle aged Americans. Moreover the overall effectiveness of therapeutic treatments is only approximately 50%. Therefore the development of prognostic tools could have immediate impact on the lives of millions of cancer patients. We have developed an integrated, cell-based modeling framework that includes a cellular model for cell dynamics (cell growth, division, death, migration and adhesion), an intracellular regulatory network for cell cycle control and a signaling network for cell decision-making, and a partial differential equation system for extracellular chemical dynamics. This model has produced avascular tumor growth dynamics that agree with tumor spheroid experiments; it has generated realistic sprout patterns and dynamics in tumor-induced angiogenesis; it has also shown potential for comparing chemotherapeutic strategies for vascular tumor. In particular, we investigate the mechanisms for tumor growth saturation and the roles of VEGF and ECM in tumor angiogenesis. Given the biological realism and flexibility of the model, we believe that it can facilitate a deeper understanding of the cellular and molecular interactions associated with cancer progression and treatment.

ALGEBRA SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 309A

SPEAKER: Drew Schmidt
Mr. Schmidt will be disccussing some results from set theory to be used in a later algebra talk.

Thursday, March 6

COLLOQUIUM
TIME: 3:40 – 4:30 p.m.
ROOM: Ayres 214

SPEAKER: Dr. David Nualart
TITLE: "Fractional Brownian motion: Stochastic calculus and applications"
ABSTRACT: The fractional Brownian motion is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H in (0,1) called the Hurst index. In this talk we will describe some basic properties of the fractional Brownian motion, and we will present some recent advances in the stochastic calculus with respect to this process. Different approaches have been introduced to construct stochastic integrals with respect to the fractional Brownian motion: pathwise techniques and Malliavin calculus. We will describe these methods and present the corresponding change of variable formulas. Some applications will be discussed.

Interested in giving or arranging a talk? Check out our calendar.

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