**Seminars and Colloquiums
for 2010-2011
Week of February 7, 2011**

**Speaker:
**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,

### 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**

PROBABILITY SEMINAR

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**

MATH BIOLOGY SEMINAR

TIME: 9:45 – 10:35 a.m.

ROOM: NIMBioS Classroom

SPEAKER: Mr. Evan Lancaster

TITLE: "Branching Processes"

TOPOLOGY SEMINAR

TIME: 3:40 – 4:30 p.m.

ROOM: Ayres Hall 406

SPEAKER: Ms. Anastasiia Tsvietkova

TITLE: "Investigating hyperbolic link complements 2"

**Wednesday, February 9**

APPLIED/COMPUTATIONAL MATH SEMINAR

TIME: 3:35 - 4:30 p.m.

ROOM: Ayres 111

SPEAKER: Professor Ohannes Karakashian

TITLE: "Adaptive Methods for Elliptic PDEs", Part I

ANALYSIS SEMINAR

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**

JUNIOR COLLOQUIUM

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**

COLLOQUIUM

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