- September 2:
**Organization meeting**

- September 19:
**Sylvia Carlisle**

**Title:**Model theory of $\R$-trees, again.

**Abstract:**An $\R$-tree is a metric space such that between any two points there is a unique arc, and that arc is a geodesic segment. Continuous logic is an extension of classical first-order logic which is set up to deal with metric structures. The continuous theory of $\R$-trees has a model companion. I will give a very quick introduction to continuous logic and model theory for metric structures. Then I will very generally explain what it means to have a model companion and how to characterize the one for the theory of $\R$-trees. I hope to make liberal use of pictures, hand waiving and analogies.

- September 26:
**Valerie Peterson**

**Title:**Robots and cube complexes: a geo-group-ological perspective

**Abstract:**A variety of settings in manufacturing, robotics, biology, chemistry and other areas suggest a need to coordinate moving agents in some optimal fashion. In this talk, I'll introduce a cube complex that records independent moves in many 'reconfigurable systems' and helps determine optimal paths for motion (or at least helps us keep our robots from colliding). I will also present some interesting geometric, topological and group theoretic properties of these complexes. This talk has been designed with undergraduates in mind but I hope it will be entertaining for those from a wide variety of backgrounds.

- October 10:
**Lale Ozkahya**

**Title:**Cycles in Hypercube

**Abstract:**$Q_n$ denotes the n-dimensional hypercube, which is the graph on vertex-set $\{0,1\}^n$ and edge-set assigned between pairs differing in exactly one coordinate. Given graphs P and Q, the generalized Turan number ex(Q,P) denotes the maximum number of edges of a P-free subgraph of Q.

Erd\"os (1984) conjectured that $ex(Q_n,C_4) = (1/2+o(1))e(Q_n)$, where $e(Q_n)$ is the number of edges in $Q_n$. We consider the case when P is a cycle of length 4k+2 for positive integer k and Q is $Q_n$. This is joint work with Zolt\'an F\"uredi.

- October 24:
**Supawadee Prugsapitak**

**Title:**The Tarry-Escott problem over Gaussian integers

**Abstract:**The Tarry-Escott problem asks to find two different sets of integers $A = \{a_1,\dots,a_n\}$ and $B = \{b_1,\dots,b_n\}$ so that $\sum a_i^j = \sum b_i^j$ for $1 \le j \le k$. We call $k$ the degree of a solution. In any solution $n \ge k+1$; if $n=k+1$, the solution is called ideal. In this talk, we discuss the Tarry-Escott problem over the Gaussian integers and characterize ideal solutions of degree 2. If we have time, we will discuss about how to obtain the higher degree solutions over Gaussian integers.

- November 7:
**Jeehyeon Seo**

**Title:**Bi-Lipschitz embedding on doubling space

**Abstract:**I will talk about doubling space that can be embedded Bi-Lipschitzly in some Euclidean space.

- November 21:
**Veena Paliwal**

**Title:**Moving boundary value problem with noise

**Abstract:**We will consider effect of noise on moving boundary value problem. In particular, we will look at heat equation with 2 parameter noise.

- December 5:
**Mercredi Chasman**

**Title:**Vibrations of a beam under variable tension

**Abstract:**We'll look at the vibrational modes and frequencies of an unconstrained beam and see how they change as functions of a tension parameter. When this parameter is positive, the beam is under tension; when it is negative, the beam is under compression and has both vibrating and buckling modes.