# Colloquia

## Mr. Dong Ye 7/5/2012

An algebraic proof of

Erdos-Ko-Rado Theorem

Date: 7/5/2012

Time: 2:00 PM

Place: 315 Armstrong Hall

A family of subsets F of some sets is intersecting if any two members of

F have at least one point in common. Erdos-Ko-Rado Theorem says a

intersecting family of $k$-subsets of an $n$-set where $n\ge 2k$ has size

at most ${n-1} \choose {k-1}$. In this talk, I will present an algebraic

proof of Erdos-Ko-Rado Theorem.

## Dr. Jennifer Bruce 5/22/2012

Date: 5/22/2012

Time: 3:00PM

Place: 315 Armstrong Hall

The talk will be on two topics, first about her experiences working with

high school and middle school teachers on the East Tennessee Math and

Science Partnership, and then on a Quantitative Literacy Research Study,

which was a first year seminar course project that will be used for

future development of Maryville's core curriculum.

## Mr. Amsaad Mohamed 5/7/2012

Well-posedness Theory of the Transport Equation

Date: 5/7/2012

Time: 11:30AM-12:30 PM

Place: 315 Armstrong Hall

In this talk, first we

will try to introduce the connection between the ordinary differential

equation(ODE) and the transport equation under some regularity assumptions

on the vector field. We will start by recalling the classical results of

the Cauchy-Lipschitz theory (in which Lipschitz regularity of the vector

field is assumed) and then will present some ideas of the theory of

characteristics and the connection between the ODE and the transport and

the continuity equations in the smooth case. Next, we will begin to

investigate the well-posedness of the transport equation out of the smooth

setting and then we will illustrate the importance of the notion of

renormalization property and how this property implies well-posedness of

the transport equation.

## Professor Matt Pascal 4/20/2012

Homeschooling and Mathematics Education: Results, Trends, and Trajectories

Date: 4/20/2012

Time: 2:30-3:30 PM

Place: 422 Armstrong Hall

Beginning the 1970s, homeschooling gainedmomentum as an option for parents who want more control over the education oftheir children than public or private schools can offer and it is legally confirmedto be an acceptable format for education in all 50 states. Research on homeschoolingis unfortunately difficult and, thus, uncommon, primarily because of broad diversityin the regulatory control that states have over home schools. Using a top-down (orobjective-oriented) approach, this project investigated several groups of collegestudents who had been homeschooled prior to college admissions to compare theirperformance in mathematics and their academic trajectories in comparison totheir traditionally educated peers.

## Professor Elizabeth A. Burroughs 4/5/2012

Research in Professional Development for Grades K-8 Mathematics Classroom

Coaches

Date: 4/5/2012

Time: 2:30-3:30 PM

Place: 422 Armstrong Hall

This talk will provide a description of the design, implementation, and evaluation of a professional development course for grades K-8 mathematics classroom coaches in seven states across the western United States. The course is one component of a larger research project studying the knowledge held by effective mathematics coaches. The professional development is centered upon standards-based mathematics practice and eight themes aboutknowledge held by coaches. The course is a 45-hour summer residential course attended by approximately 60 coaches across two summers. The coaches are randomly assigned to attend one of two summers to allow for an experimental design with a treatment and a control group. The results document a significant change in coaching knowledge held by participants. The results from this project provide a research-based model for a professional development course for mathematics classroom coaches.

## Dr. Minchul Kang 3/19/2012

Mathematical modeling of fluorescence microscopy and its applications to

cancer systems biology

Date: 3/19/2012

Time: 4:30-5:30 PM

Place: 422 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

All living cells sense, integrate and respond to their environment by a complex system of communication known as cell signaling, which is mostly mediated by protein-protein interactions. Therefore, to determine proteins’ binding partners and binding rate constants are crucial steps to understand cell signaling. While high-throughput methods to screen binary protein binding pairs are now well-established, still no genomic scale kinetic rate calibration tools are available. To this end, simple, accessible yet accurate methods to measure kinetic constants under physiological condition were sought by a combination of mathematical modeling and fluorescence microscopy techniques such as Fluorescence Recovery After Photobleaching (FRAP) and Förster resonance energy transfer (FRET). In addition, a further application of this research to cancer systems biology will be discussed.

## Professor Mikhail Feldman 3/16/2012

University of Wisconsin Madison Professor, Mikhail Feldman, will host a

colloquium on Lagrangian Solutions of Semigeostrophic

System and all are invited to attend.

Date: 3/16/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

Semigeostrophic system is a model of large-scale

atmospheric/ocean flows. I will discuss some

results on existence and properties of weak Lagrangian solutions in

physical space. The approach is based

on Monge-Kantorovich mass transport theory, and on theory of transport

equations for BV vector fields.

Open problems will be also discussed.

## Dr. Yan Hao 3/8/2012

A tale of two stochastic models

Date: 3/8/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

Modeling and analysis of biological phenomena require techniques and tools from various disciplines. Though deterministic models have been broadly used and proved to be a powerful tool in the study of mathematical biology, stochastic models often compliment them on capturing individual behavior and effects of noise, molecular fluctuations and random environmental changes for example. In this talk, I will present two examples to show when and how stochastic models can be applied to study biological problems. In the first example, an agent based model is used to study resource sharing rules among human populations under realistic ecological conditions and revealed that simple sharing is an effective risk reducing strategy that plays an important role in maintaining human populations. In the second example, Markov chains and stochastic differential equations are applied to model the cardiac calcium dynamics which is crucial for cardiac rhythm regulation and is known to be the key to understanding many cardiac diseases.

## Dr. Leobardo Rosales 2/24/2012

The single and two-valued minimal surface equation.

Date: 2/24/2012

Time: 3:30-4:30 PM

Place: 315 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

The two-valued minimal surface equation is a degenerate PDE

used to produce examples of stable minimal immersions with branch

points. In this talk, drawing analogies from the minimal surface

equation, we investigate questions of existence, regularity, and

rigidity of solutions.

## Dr. Kevin Milans 2/22/2012

Sparse Ramsey Hosts

Date: 2/22/2012

Time: 3:30-4:30 PM

Place: 422 Armstrong Hall

*Refreshments will be served at 3:00PM in 310 Armstrong Hall.

In Ramsey Theory, we study conditions under which every partition of a large structure yields a part with additional structure. For example, Van der Waerden's theorem states that every s-coloring of the integers contains arbitrarily long monochromatic arithmetic progressions, and the Hales--Jewett Theorem guarantees that every game of tic-tac-toe in high dimensions has a winner. Ramsey's Theorem implies that for any target graph G, every s-coloring of the edges of some sufficiently large host graph contains a monochromatic copy of G. In Ramsey's Theorem, the host graph is dense (in fact complete). We explore conditions under which the host graph can be sparse and still force a monochromatic copy of G.

We write H→sG if every s-edge-coloring of H contains a monochromatic copy of G. The s-color Ramsey number of G is the minimum k such that some k-vertex graph H satisfies H→sG. The degree Ramsey number of G is the minimum k such that some graph H with maximum degree k satisfies H→sG. Chvátal, Rödl, Szemerédi, and Trotter proved that the Ramsey number of bounded-degree graphs grows only linearly, sharply contrasting the exponential growth that generally occurs when the bounded-degree assumption is dropped. We are interested in the analogous degree Ramsey question: is the s-color degree Ramsey number of G bounded by some function of s and the maximum degree of G? We resolve this question in the affirmative when G is restricted to a family of graphs that have a global tree structure; this family includes all outerplanar graphs. We also investigate the behavior of the s-color degree Ramsey number as s grows. This talk includes results from three separate projects that are joint with P. Horn, T. Jiang, B. Kinnersley, V. Rödl, and D. West.

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