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The University of Tennessee

Mathematics Department

Frequently Used Tools:

Seminars and Colloquiums
for 2010-2011

Week of February 7, 2011

Mr. Matt Turner, Monday
Mr. Evan Lancaster, Tuesday
Ms. Anastaiia Tsvietkova, Tuesday
Professor Ohannes Karakashiann, Wednesday
Professor Mike Frazier, Wednesday
Mr. Hai Nguyen (UT Math Honors Graduate), Thursday
Dr. Lev Kapitanski, Friday

If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.

If you have questions, or a date you would like to confirm, please contact Dr. Fernando Schwartz.

Monday, February 7

TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 114
SPEAKER: Mr. Matt Turner
TITLE: "Ito isomorphisms for stochastic integrals driven by Levy processes with applications. Part II continued."
ABSTRACT: "In this talk we will use results presented last semester on moments of infinitely divisible random variables to develop Ito isomorphisms for stochastic integrals driven by Levy processes."

Tuesday, February 8

TIME: 9:45 – 10:35 a.m.
ROOM: NIMBioS Classroom
SPEAKER: Mr. Evan Lancaster
TITLE: "Branching Processes"

TIME:   3:40 – 4:30 p.m.
ROOM:  Ayres Hall 406
SPEAKER:  Ms. Anastasiia Tsvietkova
TITLE: "Investigating hyperbolic link complements 2"

Wednesday, February 9

TIME: 3:35 - 4:30 p.m.
ROOM: Ayres 111
SPEAKER: Professor Ohannes Karakashian
TITLE: "Adaptive Methods for Elliptic PDEs", Part I

TIME: 3:35 pm
ROOM: Ayres 114
SPEAKER: Professor Michael Frazier
TITLE: "Estimates for Green's functions of Schrodinger operators via Neumann series" Part III

Thursday, February 10

TIME: 3:35 pm
ROOM: Ayres 405
SPEAKER: Mr. Hai Nguyen (UT Math Honors Graduate)
TITLE: "Analysis of the Expected Industry Price"
ABSTRACT: We explore an intuitive microeconomic question of the behavior of the expected industry price, and see how we can apply basic concepts of Calculus to arrive at the answer. The question here is: given firms in a certain industry that are constrained by some production capacity K, what will happen to the overall price when we exogenously raise K?

To answer this question, we consider a simplified market in which demand is represented by a simple linear function, and supply is made available by only two identical firms. Furthermore, capacities of the firms are bounded by K. We then introduce some game theoretic notions to derive firms' strategies in setting prices, given K. With appropriate assumptions, the prices that firms set will be identical, and given in the form of a probability distribution over a set of prices. This probability distribution, as expected, is a function of K. We use this information, together with the expected market share of each firm, to arrive at a formula for the overall expected industry price. From there, we examine the derivative of a double integral to obtain our primary result.

Intuitively, when firms are able to produce more, the competition in the market becomes more intense, and thus the expected overall price will drop. We will see that, indeed, this is the result that we get from our calculations.

Join us for pizza in Ayres 401 prior to the talk.

Friday, February 11

TIME: 3:35 pm
ROOM: Ayres 405
SPEAKER: Dr. Lev Kapitanski
TITLE: "Dynamics with choice"
ABSTRACT: Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. Many real life processes studied in chemical physics, engineering, biology and medicine, from autocatalytic reaction systems to switched systems to cellular biochemical processes to malaria transmission in urban environments, exhibit the properties described by dynamics with choice. We study the long-term behavior in dynamics with choice. We prove very general results on the existence and properties of global compact attractors in dynamics with choice. In addition, we study the dynamics with restricted choice when the allowed sequences of operators correspond to subshifts of the full shift. One of practical consequences of our results is that when the parameters of a discrete-time system are not known exactly and/or are subject to change due to internal instability, or a strategy, or Nature's intervention, the long term behavior of the system may not be correctly described by a system with ``averaged" values of the parameters. There may be a Gestalt effect.

The talk is based on my joint work with Sanja Zivanovic.

Refreshments available in Ayres 401 at 3:15 p.m.

Past notices:




winter break















Seminars from 2009-2010 academic year

Seminars from 2008-2009 academic year

Seminars from 2007-2008 academic year

Seminars from 2006-2007 academic year

Seminars from 2005-2006 academic year